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   <<< This course is not offered in 2025-2026. Course details are subject to change. >>>

MATH3001 Development of mathematical ideas (6 credits)		Academic Year	2025
Offering Department	Mathematics	Quota	---
Course Co-ordinator	TBC, Mathematics
Teachers Involved
Course Objectives	To acquaint the students with the origin and growth of basic mathematical concepts. To assist the students to gain a deeper insight and broader view of mathematics as a discipline and human endeavour. To provide the students with an opportunity to write on and talk about mathematics, and to engage in independent study.
Course Contents & Topics	- Selected topics in the development of mathematics from ancient to modern times depending on interest of the students and the lecturer, with attention paid to the evolvement of mathematical ideas and the process of mathematical thinking and problem solving.
Course Learning Outcomes	On successful completion of this course, students should be able to: CLO 1 understand and describe the origin and development of basic mathematical concepts CLO 2 recognize and demonstrate the intellectual and the socio-cultural aspects of mathematics, and appreciate mathematics as both an academic discipline and a human endeavour CLO 3 discuss, argue, and write about the development of various mathematical concepts and ideas CLO 4 engage in independent study on a topic about the history or development of mathematics
Pre-requisites (and Co-requisites and Impermissible combinations)	Pass in MATH2101, MATH2102, MATH2211 and MATH2241
Course Status with Related Major/Minor /Professional Core	2025 Major in Mathematics ( Disciplinary Elective ) 2025 Minor in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics ( Disciplinary Elective ) 2024 Minor in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics ( Disciplinary Elective ) 2023 Minor in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics ( Disciplinary Elective ) 2022 Minor in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics ( Disciplinary Elective ) 2021 Minor in Mathematics ( Disciplinary Elective )
Course to PLO Mapping	2025 Major in Mathematics < PLO 1,2,3 > 2024 Major in Mathematics < PLO 1,2,3 > 2023 Major in Mathematics < PLO 1,2,3 > 2022 Major in Mathematics < PLO 1,2,3 > 2021 Major in Mathematics < PLO 1,2,3 >
Offer in 2025 - 2026	N	Examination
Offer in 2026 - 2027	N
Course Grade	A+ to F
Grade Descriptors	A Demonstrate thorough grasp of the subject. Show strong analytical and critical abilities and logical thinking, with evidence of original thought. Critical use of information from sources to draw appropriate and insightful conclusions. Actively engage in and contribute substantially and fruitfully to class discussions. Apply highly effective organizational and presentational skills. B Demonstrate substantial grasp of the subject. Evidence of analytical and critical abilities and logical thinking. Correct use of information from sources to draw appropriate conclusions. Good participation in class discussions with generally good contributions. Apply effective organizational and presentational skills. C Demonstrate general but incomplete grasp of the subject. Evidence of some analytical and critical abilities and logical thinking. Mostly correct but some erroneous use of information from sources to draw appropriate conclusions. Make some but not substantial fruitful contributions to class discussions. Apply moderately effective organizational and presentational skills. D Demonstrate partial but limited grasp, with retention of some relevant information, of the subject. Evidence of some coherent and logical thinking, but with limited analytical and critical abilities. Limited ability to use information from sources to draw appropriate conclusions. Contribute only in a limited way to fruitful and meaningful class discussions. Apply limited or barely effective organizational and presentational skills. Fail Demonstrate evidence of little or no grasp of the knowledge and understanding of the subject. Evidence of little or lack of analytical and critical abilities, logical and coherent thinking. Misuse of information from sources and/or unable to draw appropriate conclusions. Make little or no meaningful contributions to class discussions. Organization and presentational skills are minimally effective or ineffective.
Communication-intensive Course	N
Course Type	Lecture-based course
Course Teaching & Learning Activities	Activities Details No. of Hours Lectures 36.0 Tutorials 12.0 Reading / Self study 100.0
Assessment Methods and Weighting	Methods Details Weighting in final course grade (%) Assessment Methods to CLO Mapping Examination 50.0 Test 50.0
Required/recommended reading and online materials	To be decided by the course instructor. H. Eves and C.V. Newsom: An Introduction to the Foundations and Fundamental Concepts of Mathematics (Holt, Reinhart and Winston, 1958; 1990, 3rd edition) G. Polya: How to Solve It (Princeton University Press, 1971, 2nd edition) R. Laubenbacher and D. Pengelley: Mathematical Expeditions (Springer-Verlag, 1999) R. Calinger (ed.): Classic of Mathematics (Prentice Hall, preprinted 1995) C. Boyer: A History of Mathematics (Wiley, 1968; 1989, 2nd edition (with V.C. Merzbach)) V. Katz: A History of Mathematics (Harper Collins, 1993)
Course Website	NIL
Additional Course Information	NIL

MATH3002 Mathematics seminar (6 credits)		Academic Year	2025
Offering Department	Mathematics	Quota	12
Course Co-ordinator	Dr K H Law, Mathematics < lawkaho@connect.hku.hk >
Teachers Involved	(Dr P Li,Mathematics) (Dr Z Geng,Mathematics) (IMR PDF 1,Mathematics) (IMR PDF 2,Mathematics)
Course Objectives	This is a seminar style course intended for those who have very strong interests and good ability in mathematics.  Students will be given book chapters and elementary research articles for private study and then make presentations in front of the whole class. Individual meetings with the instructors will be arranged prior to their presentations. Active participation in all the discussions is expected.  The aim of the course is to let students learn how to initiate self/independent study in mathematics.
Course Contents & Topics	Topics chosen by the instructors, including chapters from books and elementary research articles.
Course Learning Outcomes	On successful completion of this course, students should be able to: CLO 1 Initiate private independent study on some interesting mathematical topics
Pre-requisites (and Co-requisites and Impermissible combinations)	Pass in MATH2012, MATH2101, MATH2211 and MATH2241 Subject to approval by the Department.
Course Status with Related Major/Minor /Professional Core	2025 Major in Mathematics ( Disciplinary Elective ) 2025 Major in Mathematics (Intensive) ( Core/Compulsory ) 2025 Minor in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics (Intensive) ( Core/Compulsory ) 2024 Minor in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics (Intensive) ( Core/Compulsory ) 2023 Minor in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics (Intensive) ( Core/Compulsory ) 2022 Minor in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics (Intensive) ( Core/Compulsory ) 2021 Minor in Mathematics ( Disciplinary Elective )
Course to PLO Mapping	2025 Major in Mathematics < PLO 3,4,5 > 2025 Major in Mathematics (Intensive) < PLO 2,3,4,5 > 2024 Major in Mathematics < PLO 3,4,5 > 2024 Major in Mathematics (Intensive) < PLO 2,3,4,5 > 2023 Major in Mathematics < PLO 3,4,5 > 2023 Major in Mathematics (Intensive) < PLO 2,3,4,5 > 2022 Major in Mathematics < PLO 3,4,5 > 2022 Major in Mathematics (Intensive) < PLO 2,3,4,5 > 2021 Major in Mathematics < PLO 3,4,5 > 2021 Major in Mathematics (Intensive) < PLO 2,3,4,5 >
Offer in 2025 - 2026	Y        2nd sem	Examination	No Exam
Offer in 2026 - 2027	Y
Course Grade	A+ to F
Grade Descriptors	A Demonstrate thorough grasp of the subject. Show strong analytical and critical abilities and logical thinking, with evidence of original thought. Actively engage in and contribute substantially and fruitfully to class discussions. Apply highly effective organizational and presentational skills. B Demonstrate substantial grasp of the subject. Evidence of analytical and critical abilities and logical thinking. Good participation in class discussions with generally good contributions. Apply effective organizational and presentational skills. C Demonstrate general but incomplete grasp of the subject. Evidence of some analytical and critical abilities and logical thinking. Make some but not substantial fruitful contributions to class discussions. Apply moderately effective organizational and presentational skills. D Demonstrate partial but limited grasp, with retention of some relevant information, of the subject. Evidence of some coherent and logical thinking, but with limited analytical and critical abilities. Contribute only in a limited way to fruitful and meaningful class discussions. Apply limited or barely effective organizational and presentational skills. Fail Demonstrate evidence of little or no grasp of the knowledge and understanding of the subject. Evidence of little or lack of analytical and critical abilities, logical and coherent thinking. Make little or no meaningful contributions to class discussions. Organization and presentational skills are minimally effective or ineffective.
Communication-intensive Course	Y
Course Type	Project-based course
Course Teaching & Learning Activities	Activities Details No. of Hours Meeting with supervisor meeting of the whole class for up to three hours each teaching week 36.0 Reading / Self study individual meetings with the instructors 72.0
Assessment Methods and Weighting	Methods Details Weighting in final course grade (%) Assessment Methods to CLO Mapping Oral presentation 50.0 1 Research report 50.0 1
Required/recommended reading and online materials	NIL
Course Website	http://moodle.hku.hk/
Additional Course Information	(i) Senior students who are interested in taking a seminar course are recommended to take MATH4910.   (ii) This course is not a capstone course.

MATH3301 Algebra I (6 credits)		Academic Year	2025
Offering Department	Mathematics	Quota	---
Course Co-ordinator	Prof Y K Lau, Mathematics < yklau@maths.hku.hk >
Teachers Involved	(Prof Y K Lau,Mathematics)
Course Objectives	This course aims to present those fundamental topics and techniques of algebra that are finding wide applications in mathematics and the applied sciences.  It is complete in itself, and may also be followed by MATH4302 Algebra II and MATH7502 Topics in Applied Discrete Mathematics.
Course Contents & Topics	- Groups: examples of groups, subgroups, cosets, Lagrange theorem, quotient groups, normal subgroups, group homomorphisms, direct product of groups, group actions. - Rings: examples of rings, integral domains, ideals, fields of fractions, principal ideal domains, unique factorization domains. - Fields: definition and examples of fields. - Polynomials: polynomial rings in one variable over fields and over the integers.
Course Learning Outcomes	On successful completion of this course, students should be able to: CLO 1 write down the precise definitions of the basic concepts in the "Course Contents" CLO 2 give examples for each of the concepts in the "Course Contents" CLO 3 understand basic properties of groups, rings, and fields
Pre-requisites (and Co-requisites and Impermissible combinations)	Pass in MATH2101 and MATH2102.
Course Status with Related Major/Minor /Professional Core	2025 Major in Mathematics ( Disciplinary Elective ) 2025 Major in Mathematics (Intensive) ( Core/Compulsory ) 2025 Minor in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics (Intensive) ( Core/Compulsory ) 2024 Minor in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics (Intensive) ( Core/Compulsory ) 2023 Minor in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics (Intensive) ( Core/Compulsory ) 2022 Minor in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics (Intensive) ( Core/Compulsory ) 2021 Minor in Mathematics ( Disciplinary Elective )
Course to PLO Mapping	2025 Major in Mathematics < PLO 1,2,3 > 2025 Major in Mathematics (Intensive) < PLO 1,2,3 > 2024 Major in Mathematics < PLO 1,2,3 > 2024 Major in Mathematics (Intensive) < PLO 1,2,3 > 2023 Major in Mathematics < PLO 1,2,3 > 2023 Major in Mathematics (Intensive) < PLO 1,2,3 > 2022 Major in Mathematics < PLO 1,2,3 > 2022 Major in Mathematics (Intensive) < PLO 1,2,3 > 2021 Major in Mathematics < PLO 1,2,3 > 2021 Major in Mathematics (Intensive) < PLO 1,2,3 >
Offer in 2025 - 2026	Y        1st sem	Examination	Dec
Offer in 2026 - 2027	Y
Course Grade	A+ to F
Grade Descriptors	A Demonstrate an excellent understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and argumentation and being able to carry out computations carefully and correctly, and with some innovative approaches to solving problems. B Demonstrate a good understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, but with some minor inadequacies in arguments, identifying the appropriate theorems or their applications and presentation or with some minor computational errors. C Demonstrate an acceptable understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with some inadequacies in applying the theorems through incorrectly analysing problems with poor argument and presentation or a number of minor computational errors. D Demonstrate some understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with substantial inadequacies in applying the theorems through incorrectly analysing problems with poor argument or presentation or with substantial computational errors. Fail Demonstrate poor and inadequate understanding by not being able to identify appropriate theorems or their applications, or not being able to complete the solution.
Communication-intensive Course	N
Course Type	Lecture-based course
Course Teaching & Learning Activities	Activities Details No. of Hours Lectures 36.0 Tutorials 12.0 Reading / Self study 100.0
Assessment Methods and Weighting	Methods Details Weighting in final course grade (%) Assessment Methods to CLO Mapping Assignments Take-home and/or in tutorials 10.0 1,2,3 Examination 50.0 1,2,3 Test 40.0 1,2,3
Required/recommended reading and online materials	To be decided by the course instructor. S. Lang: Undergraduate Algebra (Springer, 2004) J.B. Fraleigh: A First Course in Abstract Algebra (Addison-Wesley, 1989, 4th edition) I.N. Herstein: Abstract Algebra (Prentice-Hall, 1996) T.W. Hungerford: Abstract Algebra: An Introduction (Saunders College Publishing, 1990, 2nd edition)
Course Website	http://moodle.hku.hk/
Additional Course Information

   <<< This course is not offered in 2025-2026. Course details are subject to change. >>>

MATH3303 Matrix theory and its applications (6 credits)		Academic Year	2025
Offering Department	Mathematics	Quota	---
Course Co-ordinator	Prof T K Wong, Mathematics < takkwong@maths.hku.hk >
Teachers Involved	(Prof T K Wong,Mathematics)
Course Objectives	Matrix theory has a close connection with other mathematical subjects such as linear algebra, functional analysis, and combinatorics.  It also plays an important role in the development of many subjects in science, engineering, and social sciences.  In this course, students will be taught the fundamentals of matrix analysis and its application to various kinds of practical problems.  Mathematical software may be used in the course, so that students can learn how to use the computer to solve matrix problems.
Course Contents & Topics	- Eigenvalues and eigenvectors: similarities, applications on difference equations and differential equations. - Orthogonality: inner products and the induced norms, orthogonality of null spaces and column spaces, applications to over- or under-determined systems, least squares fit. Unitary, normal, and hermitian matrices: Schur's triangularization theorem. Variational description of eigenvalues: applications in optimization and in eigenvalue estimation. - Singular value decomposition: polar decomposition, pseudo inverse, spectral norm of matrices, interlacing inequalities for singular values. Jordan form and applications.
Course Learning Outcomes	On successful completion of this course, students should be able to: CLO 1 have a good understanding on matrices, determinants, linear transformations, eigenvalues and eigenvectors CLO 2 understand the concept of similar matrices and the eigenvalue decomposition CLO 3 understand the concept of orthogonality CLO 4 understand the concept of unitary, normal, and Hermitian matrices CLO 5 find the singular value decomposition of a matrix and apply the theory of singular values to study polar decomposition, pseudo inverse and spectral norm of matrices CLO 6 understand the concept of the Jordan blocks, Jordan matrices and the Jordan canonical form of a matrix
Pre-requisites (and Co-requisites and Impermissible combinations)	Pass in MATH2101 and MATH2102
Course Status with Related Major/Minor /Professional Core	2025 Major in Mathematics ( Disciplinary Elective ) 2025 Minor in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics ( Disciplinary Elective ) 2024 Minor in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics ( Disciplinary Elective ) 2023 Minor in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics ( Disciplinary Elective ) 2022 Minor in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics ( Disciplinary Elective ) 2021 Minor in Mathematics ( Disciplinary Elective )
Course to PLO Mapping	2025 Major in Mathematics < PLO 1,2,3 > 2024 Major in Mathematics < PLO 1,2,3 > 2023 Major in Mathematics < PLO 1,2,3 > 2022 Major in Mathematics < PLO 1,2,3 > 2021 Major in Mathematics < PLO 1,2,3 >
Offer in 2025 - 2026	N	Examination
Offer in 2026 - 2027	N
Course Grade	A+ to F
Grade Descriptors	A Demonstrate an excellent understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and argumentation and being able to carry out computations carefully and correctly, and with some innovative approaches to solving problems. B Demonstrate a good understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, but with some minor inadequacies in arguments, identifying the appropriate theorems or their applications and presentation or with some minor computational errors. C Demonstrate an acceptable understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with some inadequacies in applying the theorems through incorrectly analysing problems with poor argument and presentation or a number of minor computational errors. D Demonstrate some understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with substantial inadequacies in applying the theorems through incorrectly analysing problems with poor argument or presentation or with substantial computational errors. Fail Demonstrate poor and inadequate understanding by not being able to identify appropriate theorems or their applications, or not being able to complete the solution.
Communication-intensive Course	N
Course Type	Lecture-based course
Course Teaching & Learning Activities	Activities Details No. of Hours Lectures 36.0 Tutorials 12.0 Reading / Self study 100.0
Assessment Methods and Weighting	Methods Details Weighting in final course grade (%) Assessment Methods to CLO Mapping Examination 50.0 1,2,3,4,5,6 Test 50.0 1,2,3,4,5,6
Required/recommended reading and online materials	Jack L. Goldberg: Matrix Theory with Applications (McGraw-Hill, 1991) Steven J. Leon: Linear Algebra with Applications (Macmillan, 1994, 4th edition) Chris Rorres & Howard Anton: Applications of Linear Algebra (Wiley, 1984, 3rd edition) Roger A. Horn & Charles R. Johnson: Matrix Analysis (Cambridge University Press, 1987) The Mathworks, Inc.: The Student Edition of Matlab (Version 4 for Microsoft Windows) (Prentice - Hall, 1995)
Course Website	http://moodle.hku.hk/
Additional Course Information

MATH3304 Introduction to number theory (6 credits)		Academic Year	2025
Offering Department	Mathematics	Quota	---
Course Co-ordinator	Prof B Kane, Mathematics < bkane@maths.hku.hk >
Teachers Involved	(Prof B Kane,Mathematics) (Prof Y K Lau,Mathematics)
Course Objectives	To provide students with basic concepts about numbers, their properties and basic knowledge on the arithmetic of congruences. The prime numbers are the building blocks of all the natural numbers under multiplication. The interplay between the multiplicative and additive properties of prime numbers is particularly interesting. The course will study further properties and the distribution of the prime numbers, and some of the longstanding open problems concerning them. Important applications of number theory to modern cryptography will also be introduced.
Course Contents & Topics	-The course will begin with some basic notions in number theory, including divisibility, greatest common divisor, Euclidean algorithm, congruences, etc. It will then be followed by several fundamental theorems, such as Chinese remainder theorem, solutions of linear and polynomial congruences, Fermat's Little theorem, and the quadratic reciprocity law. - Many well-known open problems will be introduced. Application of number theory to public key cryptography will be explained. Some current research on the prime numbers will be discussed. - Depending on the time available, the course will cover a selection of further topics, such as the prime number theorem, sum of squares, Dirichlet's theorem on diophantine approximations, continued fractions, etc.
Course Learning Outcomes	On successful completion of this course, students should be able to: CLO 1 solve a system of linear congruences CLO 2 solve polynomial congruences CLO 3 determine the solubility of quadratic congruences by computation of the Legendre symbol CLO 4 determine the existence of primitive roots and use them in solving some exponential congruences CLO 5 understand the prime number theorem CLO 6 understanding some longstanding problems in number theory
Pre-requisites (and Co-requisites and Impermissible combinations)	Pass in MATH2101 and MATH2211. MATH3301 recommended but not required.
Course Status with Related Major/Minor /Professional Core	2025 Major in Mathematics ( Disciplinary Elective ) 2025 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2025 Minor in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2024 Minor in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2023 Minor in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2022 Minor in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2021 Minor in Mathematics ( Disciplinary Elective )
Course to PLO Mapping	2025 Major in Mathematics < PLO 1,2,3 > 2025 Major in Mathematics (Intensive) < PLO 1,2,3 > 2024 Major in Mathematics < PLO 1,2,3 > 2024 Major in Mathematics (Intensive) < PLO 1,2,3 > 2023 Major in Mathematics < PLO 1,2,3 > 2023 Major in Mathematics (Intensive) < PLO 1,2,3 > 2022 Major in Mathematics < PLO 1,2,3 > 2022 Major in Mathematics (Intensive) < PLO 1,2,3 > 2021 Major in Mathematics < PLO 1,2,3 > 2021 Major in Mathematics (Intensive) < PLO 1,2,3 >
Offer in 2025 - 2026	Y        2nd sem	Examination	May
Offer in 2026 - 2027	Y
Course Grade	A+ to F
Grade Descriptors	A Demonstrate a thorough and coherent understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing number theoretic problems, clearly presenting correct logical reasoning and argumentation and being able to carry out computations carefully and correctly. B Demonstrate a good understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing number theoretic problems, but with some minor errors/inadequacies in arguments and being able to present coherent logical reasoning and carry out computations carefully without major errors. C Demonstrate an acceptable understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with some inadequacies in applying the theorems through incorrectly analysing problems with weak and fragmentary argument and presentation, or with moderate computational errors. D Demonstrate some superficial understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with substantial inadequacies in applying the theorems through incorrectly analysing problems with poor argument or presentation, or with substantial computational errors. Fail Demonstrate poor and inadequate understanding of the key concepts and ideas by not being able to identify appropriate theorems or their applications, or not being able to complete the solution.
Communication-intensive Course	N
Course Type	Lecture-based course
Course Teaching & Learning Activities	Activities Details No. of Hours Lectures 36.0 Tutorials 12.0 Reading / Self study 100.0
Assessment Methods and Weighting	Methods Details Weighting in final course grade (%) Assessment Methods to CLO Mapping Assignments Tutorials and Assignments 10.0 1,2,3,4,5,6 Examination 50.0 1,2,3,4,5,6 Test 40.0 1,2,3,4,5,6
Required/recommended reading and online materials	Kenneth H. Rosen: Elementary number theory (6th edition, Pearson, 2010) David M. Burton: Elementary Number Theory (McGraw-Hill Higher Education, International Edition) J. H. Silverman: A friendly introduction to number theory (Prentice Hall, 2001)
Course Website	http://moodle.hku.hk/
Additional Course Information

MATH3401 Analysis I (6 credits)		Academic Year	2025
Offering Department	Mathematics	Quota	---
Course Co-ordinator	Prof X Zhang, Mathematics < xzhang@maths.hku.hk >
Teachers Involved	(Prof X Zhang,Mathematics)
Course Objectives	This course extends to more general situations some basic results covered in the Mathematics courses in junior level, and introduces some fundamental concepts which are essential for advanced studies in Analysis, Geometry, and Topology.
Course Contents & Topics	Basic properties of metric spaces; openness; closedness; interior; closure; derived set; boundary; compactness; completeness; continuity; connectedness; pathwise connectedness; uniform continuity; uniform convergence; Banach's fixed point theorem.
Course Learning Outcomes	On successful completion of this course, students should be able to: CLO 1 demonstrate knowledge and understanding of the basic features of mathematical analysis and point set topology (e.g., able to identify objects that are topological equivalent) CLO 2 apply knowledge and skills acquired in mathematical analysis to analyze and handle novel situations in a critical way (e.g., able to determine whether a specific function is uniformly continuous) CLO 3 think creatively and laterally to generate innovative examples and solutions to non-standard problems (e.g., able to provide counterexamples to inaccurate mathematical statements)
Pre-requisites (and Co-requisites and Impermissible combinations)	Pass in MATH2211
Course Status with Related Major/Minor /Professional Core	2025 Major in Mathematics ( Core/Compulsory ) 2025 Major in Mathematics (Intensive) ( Core/Compulsory ) 2025 Minor in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics ( Core/Compulsory ) 2024 Major in Mathematics (Intensive) ( Core/Compulsory ) 2024 Minor in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics ( Core/Compulsory ) 2023 Major in Mathematics (Intensive) ( Core/Compulsory ) 2023 Minor in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics ( Core/Compulsory ) 2022 Major in Mathematics (Intensive) ( Core/Compulsory ) 2022 Minor in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics ( Core/Compulsory ) 2021 Major in Mathematics (Intensive) ( Core/Compulsory ) 2021 Minor in Mathematics ( Disciplinary Elective )
Course to PLO Mapping	2025 Major in Mathematics < PLO 1,2,3 > 2025 Major in Mathematics (Intensive) < PLO 1,2,3 > 2024 Major in Mathematics < PLO 1,2,3 > 2024 Major in Mathematics (Intensive) < PLO 1,2,3 > 2023 Major in Mathematics < PLO 1,2,3 > 2023 Major in Mathematics (Intensive) < PLO 1,2,3 > 2022 Major in Mathematics < PLO 1,2,3 > 2022 Major in Mathematics (Intensive) < PLO 1,2,3 > 2021 Major in Mathematics < PLO 1,2,3 > 2021 Major in Mathematics (Intensive) < PLO 1,2,3 >
Offer in 2025 - 2026	Y        1st sem	Examination	Dec
Offer in 2026 - 2027	Y
Course Grade	A+ to F
Grade Descriptors	A Demonstrate a thorough understanding of all concepts and ideas by being able to draw complex connections among various concepts and apply the theorems through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and argumentation, and with some innovative approaches to solving problems. B Demonstrate a good understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, but with some minor inadequacies in arguments, reasoning, identifying the appropriate theorems, applications, or presentation. C Demonstrate an acceptable understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with some inadequacies in applying the theorems through incorrectly analysing problems with acceptable argument and presentation. D Demonstrate some understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with substantial inadequacies in applying the theorems through incorrectly analysing problems with poor argument or presentation. Fail Demonstrate poor and inadequate understanding by not being able to identify appropriate theorems or their applications, or not being able to complete the solution.
Communication-intensive Course	N
Course Type	Lecture-based course
Course Teaching & Learning Activities	Activities Details No. of Hours Lectures 36.0 Tutorials 12.0 Reading / Self study 100.0
Assessment Methods and Weighting	Methods Details Weighting in final course grade (%) Assessment Methods to CLO Mapping Assignments 10.0 1,2,3 Examination 50.0 1,2,3 Test 40.0 1,2,3
Required/recommended reading and online materials	Apostol: Mathematical Analysis Rudin: Principles of Mathematical Analysis
Course Website	http://moodle.hku.hk/
Additional Course Information

MATH3403 Functions of a complex variable (6 credits)		Academic Year	2025
Offering Department	Mathematics	Quota	---
Course Co-ordinator	Prof X Zhang, Mathematics < xzhang@maths.hku.hk >
Teachers Involved	(Prof X Zhang,Mathematics)
Course Objectives	This course is indispensable for studies in higher mathematical analysis and the more theoretical aspects of physics. In this course, the students are introduced to the fundamental concepts and properties of analytic functions and are shown how to look at analyticity from different points of view. At the same time, the techniques of solving problems without losing sight of the geometric picture are emphasized.
Course Contents & Topics	- Complex number system. - Analytic functions and elementary functions. - The Cauchy-Riemann equations. - Cauchy's theorem and its applications. - Taylor's series. - Laurent's series. - Zeros, singularities and poles. - The Residue Theorem and its applications.
Course Learning Outcomes	On successful completion of this course, students should be able to: CLO 1 recognize the theory of functions of a complex variable as a rigorous and foundational subject in mathematics CLO 2 grasp the techniques from Cauchy-Riemann equations, power series expansion and Cauchy integral formulas to study analytic functions from different perspectives CLO 3 compute contour integrals by calculating residues CLO 4 apply such techniques to determine improper integrals such as those for certain rational functions on the real line
Pre-requisites (and Co-requisites and Impermissible combinations)	Pass in MATH2211 and MATH2241
Course Status with Related Major/Minor /Professional Core	2025 Major in Mathematics ( Disciplinary Elective ) 2025 Major in Mathematics (Intensive) ( Core/Compulsory ) 2025 Minor in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics (Intensive) ( Core/Compulsory ) 2024 Minor in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics (Intensive) ( Core/Compulsory ) 2023 Minor in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics (Intensive) ( Core/Compulsory ) 2022 Minor in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics (Intensive) ( Core/Compulsory ) 2021 Minor in Mathematics ( Disciplinary Elective )
Course to PLO Mapping	2025 Major in Mathematics < PLO 1,2,3 > 2025 Major in Mathematics (Intensive) < PLO 1,2,3 > 2024 Major in Mathematics < PLO 1,2,3 > 2024 Major in Mathematics (Intensive) < PLO 1,2,3 > 2023 Major in Mathematics < PLO 1,2,3 > 2023 Major in Mathematics (Intensive) < PLO 1,2,3 > 2022 Major in Mathematics < PLO 1,2,3 > 2022 Major in Mathematics (Intensive) < PLO 1,2,3 > 2021 Major in Mathematics < PLO 1,2,3 > 2021 Major in Mathematics (Intensive) < PLO 1,2,3 >
Offer in 2025 - 2026	Y        2nd sem	Examination	May
Offer in 2026 - 2027	Y
Course Grade	A+ to F
Grade Descriptors	A Demonstrate an excellent understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and argumentation and being able to carry out computations carefully and correctly, and with some innovative approaches to solving problems. B Demonstrate a good understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, but with some minor inadequacies in arguments, identifying the appropriate theorems or their applications and presentation or with some minor computational errors. C Demonstrate an acceptable understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with some inadequacies in applying the theorems through incorrectly analysing problems with poor argument and presentation or a number of minor computational errors. D Demonstrate some understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with substantial inadequacies in applying the theorems through incorrectly analysing problems with poor argument or presentation or with substantial computational errors. Fail Demonstrate poor and inadequate understanding by not being able to identify appropriate theorems or their applications, or not being able to complete the solution.
Communication-intensive Course	N
Course Type	Lecture-based course
Course Teaching & Learning Activities	Activities Details No. of Hours Lectures 36.0 Tutorials 12.0 Reading / Self study 100.0
Assessment Methods and Weighting	Methods Details Weighting in final course grade (%) Assessment Methods to CLO Mapping Assignments 10.0 1,2,3,4 Examination 50.0 1,2,3,4 Test 40.0 1,2,3,4
Required/recommended reading and online materials	Complex Analysis, Stein and Shakarchi, Princeton University Press
Course Website	http://moodle.hku.hk/
Additional Course Information

MATH3405 Differential equations (6 credits)		Academic Year	2025
Offering Department	Mathematics	Quota	---
Course Co-ordinator	Dr H Y Zhang, Mathematics < hyzhang@maths.hku.hk >
Teachers Involved	(Dr H Y Zhang,Mathematics)
Course Objectives	The standard topics in the wide field of ordinary differential equations (ODEs) included in this course are of importance to students of sciences and engineering. Our emphasis is on principles rather than routine calculations and our approach is a compromise between diversity and depth.
Course Contents & Topics	- Review of elementary differential equations. - Existence and uniqueness theorems. - Second order differential equations, Wronskian, variation of parameters. - Power series method, Legendre polynomials, Bessel functions. - Linear systems, autonomous systems. - Qualitative properties of solutions. - The Laplace transform.
Course Learning Outcomes	On successful completion of this course, students should be able to: CLO 1 solve simple first order and second order (linear or nonlinear) ODEs by various techniques, including auxiliary equations, variation of parameters, Laplace transform, and series method CLO 2 solve systems of first order linear ODEs with constant coefficients, of which the number of equations and the number of unknown functions are no more than three CLO 3 discuss qualitatively the solutions of nonlinear ODEs or systems of nonlinear ODEs by studying their linear approximations or their phase diagrams CLO 4 apply the theory of differential equations to study quantitatively/qualitatively problems arising from physical and life sciences
Pre-requisites (and Co-requisites and Impermissible combinations)	Pass in (MATH2101 and MATH2211) or MATH2014 or (MATH1821 and MATH2822)
Course Status with Related Major/Minor /Professional Core	2025 Major in Mathematics ( Disciplinary Elective ) 2025 Major in Mathematics (Intensive) ( Core/Compulsory ) 2025 Minor in Mathematics ( Disciplinary Elective ) 2025 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2024 Major in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics (Intensive) ( Core/Compulsory ) 2024 Minor in Mathematics ( Disciplinary Elective ) 2024 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2023 Major in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics (Intensive) ( Core/Compulsory ) 2023 Minor in Mathematics ( Disciplinary Elective ) 2023 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2022 Major in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics (Intensive) ( Core/Compulsory ) 2022 Minor in Mathematics ( Disciplinary Elective ) 2022 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2021 Major in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics (Intensive) ( Core/Compulsory ) 2021 Minor in Mathematics ( Disciplinary Elective ) 2021 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective )
Course to PLO Mapping	2025 Major in Mathematics < PLO 1,2,3 > 2025 Major in Mathematics (Intensive) < PLO 1,2,3 > 2024 Major in Mathematics < PLO 1,2,3 > 2024 Major in Mathematics (Intensive) < PLO 1,2,3 > 2023 Major in Mathematics < PLO 1,2,3 > 2023 Major in Mathematics (Intensive) < PLO 1,2,3 > 2022 Major in Mathematics < PLO 1,2,3 > 2022 Major in Mathematics (Intensive) < PLO 1,2,3 > 2021 Major in Mathematics < PLO 1,2,3 > 2021 Major in Mathematics (Intensive) < PLO 1,2,3 >
Offer in 2025 - 2026	Y        2nd sem	Examination	May
Offer in 2026 - 2027	Y
Course Grade	A+ to F
Grade Descriptors	A Demonstrate an excellent understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and argumentation and being able to carry out computations carefully and correctly, and with some innovative approaches to solving problems. B Demonstrate a good understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, but with some minor inadequacies in arguments, identifying the appropriate theorems or their applications and presentation or with some minor computational errors. C Demonstrate an acceptable understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with some inadequacies in applying the theorems through incorrectly analysing problems with poor argument and presentation or a number of minor computational errors. D Demonstrate some understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with substantial inadequacies in applying the theorems through incorrectly analysing problems with poor argument or presentation or with substantial computational errors. Fail Demonstrate poor and inadequate understanding by not being able to identify appropriate theorems or their applications, or not being able to complete the solution.
Communication-intensive Course	N
Course Type	Lecture-based course
Course Teaching & Learning Activities	Activities Details No. of Hours Lectures 36.0 Tutorials 12.0 Reading / Self study 100.0
Assessment Methods and Weighting	Methods Details Weighting in final course grade (%) Assessment Methods to CLO Mapping Assignments 10.0 1,2,3,4 Examination 50.0 1,2,3,4 Test 40.0 1,2,3,4
Required/recommended reading and online materials	On-line textbook of William F. Trench: Elementary Differential Equations with Boundary Value Problems (2013) url: http://aimath.org/textbooks/approved-textbooks/trench-de/ R. Nagle, E. Saff and A. Snider: Fundamentals of Differential Equations and Boundary Value Problems (Pearson, 6th edition) W.E. Boyce and R.C. DiPrima: Elementary Differential Equations and Boundary Value Problems (John Wiley, 6th edition) E.A. Coddington: An Introduction to Ordinary Differential Equations (Prentice-Hall)
Course Website	http://moodle.hku.hk/
Additional Course Information

MATH3408 Computational methods and differential equations with applications (6 credits)		Academic Year	2025
Offering Department	Mathematics	Quota	---
Course Co-ordinator	Prof W K Ching, Mathematics < wching@hku.hk >
Teachers Involved	(Prof W K Ching,Mathematics)
Course Objectives	This course covers topics in the fields of differential equations, mathematical modelling and numerical analysis which are of importance to sciences students. The emphasis is practical applications of basic principles.
Course Contents & Topics	- Solution of linear difference equations. - Mathematical modelling and dynamical systems. - Numerical differentiation and integration.   - LU factorization for solving linear system of equations. - Matrix norms and iterative solutions of matrix equations. - Solution of nonlinear systems of equations.   - Elementary differential equations and power series method. - Numerical solutions of ordinary and partial differential equations. - Numerical solutions of systems of first-order ordinary differential equations.
Course Learning Outcomes	On successful completion of this course, students should be able to: CLO 1 construct and implement numerical methods for numerical integration and differentiation, and the solution of linear and nonlinear system of equations CLO 2 explain mathematical ideas of numerical methods and mathematical modelling in solving linear difference equations, ordinary and partial differential equations CLO 3 construct one-step and linear multistep methods for the numerical solution of initial-value problems for ordinary differential equations and systems of such equations and analyze their stability and accuracy properties CLO 4 construct finite difference methods for the numerical solution of partial differential equations and analyze their stability and accuracy properties CLO 5 implement numerical methods for solving initial and boundary value problems by software packages like MATLAB
Pre-requisites (and Co-requisites and Impermissible combinations)	Pass in (MATH2101 and MATH2211) or MATH2014 or (MATH1821 and MATH2822)
Course Status with Related Major/Minor /Professional Core	2025 Major in Mathematics ( Disciplinary Elective ) 2025 Minor in Computational & Financial Mathematics ( Disciplinary Elective ) 2025 Minor in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics ( Disciplinary Elective ) 2024 Minor in Computational & Financial Mathematics ( Disciplinary Elective ) 2024 Minor in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics ( Disciplinary Elective ) 2023 Minor in Computational & Financial Mathematics ( Disciplinary Elective ) 2023 Minor in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics ( Disciplinary Elective ) 2022 Minor in Computational & Financial Mathematics ( Disciplinary Elective ) 2022 Minor in Mathematics ( Disciplinary Elective ) 2021 Major in Decision Analytics ( Disciplinary Elective ) 2021 Major in Mathematics ( Disciplinary Elective ) 2021 Minor in Computational & Financial Mathematics ( Disciplinary Elective ) 2021 Minor in Mathematics ( Disciplinary Elective )
Course to PLO Mapping	2025 Major in Mathematics < PLO 1,2,3 > 2024 Major in Mathematics < PLO 1,2,3 > 2023 Major in Mathematics < PLO 1,2,3 > 2022 Major in Mathematics < PLO 1,2,3 > 2021 Major in Decision Analytics < PLO 1,3 > 2021 Major in Mathematics < PLO 1,2,3 >
Offer in 2025 - 2026	Y        1st sem	Examination	Dec
Offer in 2026 - 2027	Y
Course Grade	A+ to F
Grade Descriptors	A Demonstrate an excellent understanding of key concepts and ideas by being able to identify the appropriate theorems and computational methods and their applications through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and argumentation and being able to carry out computations carefully and correctly, and with some innovative approaches to solving problems. B Demonstrate a good understanding of key concepts and ideas by being able to identify the appropriate theorems and computational methods and their applications through correctly analysing problems, but with some minor inadequacies in arguments, identifying the appropriate theorems and computational methods or their applications and presentation or with some minor computational errors. C Demonstrate an acceptable understanding of key concepts and ideas by being able to correctly identify appropriate theorems and computational methods, but with some inadequacies in applying them through incorrectly analysing problems with poor argument and presentation or a number of minor computational errors. D Demonstrate some understanding of key concepts and ideas by being able to correctly identify appropriate theorems and computational methods, but with substantial inadequacies in applying them through incorrectly analysing problems with poor argument or presentation or with substantial computational errors. Fail Demonstrate poor and inadequate understanding by not being able to identify appropriate theorems and computational methods or their applications, or not being able to complete the solution.
Communication-intensive Course	N
Course Type	Lecture-based course
Course Teaching & Learning Activities	Activities Details No. of Hours Lectures 36.0 Tutorials 12.0 Reading / Self study 100.0
Assessment Methods and Weighting	Methods Details Weighting in final course grade (%) Assessment Methods to CLO Mapping Examination 50.0 1,2,3,4,5 Test 50.0 1,2,3,4,5
Required/recommended reading and online materials	D.F. Parkhurst: Introduction to Applied Mathematics for Environmental Science (Springer) E.A. Coddington: An Introduction to Ordinary Differential Equations (Prentice-Hall) A. Ralston and P. Rabinowitz: A First Course in Numerical Analysis (McGraw-Hill) C. F. Gerald and P.O. Wheatley: Applied Numerical Analysis (Addison Wesley) K.E. Atkinson, An Introduction to Numerical Analysis (Wiley).
Course Website	http://moodle.hku.hk/
Additional Course Information

MATH3541 Introduction to topology (6 credits)		Academic Year	2025
Offering Department	Mathematics	Quota	---
Course Co-ordinator	Prof Z Hua, Mathematics < huazheng@maths.hku.hk >
Teachers Involved	(Prof Z Hua,Mathematics)
Course Objectives	This course covers the basics on general topology and prepares students for more advanced topics in mathematics and other subjects in which topology finds applications.
Course Contents & Topics	Topics will be chosen among the following: (i) Basic concepts: topological spaces; constructing new topologies from old; compactness; connectedness; (ii) Topological manifolds; (iii) Topological groups and orbit spaces; (iv) Fundamental groups and covering spaces; (v) Classification of compact surfaces.
Course Learning Outcomes	On successful completion of this course, students should be able to: CLO 1 state the basic definitions and understand some basic constructions in general topology CLO 2 give examples and counterexamples of basic concepts in general topology CLO 3 compute fundamental groups of examples and understand the classification theorem on compact surfaces
Pre-requisites (and Co-requisites and Impermissible combinations)	Pass in MATH2101 and MATH2241. Pass or have already enrolled in MATH3301 and MATH3401.
Course Status with Related Major/Minor /Professional Core	2025 Major in Mathematics ( Disciplinary Elective ) 2025 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2025 Minor in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2024 Minor in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2023 Minor in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2022 Minor in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2021 Minor in Mathematics ( Disciplinary Elective )
Course to PLO Mapping	2025 Major in Mathematics < PLO 1,2,3 > 2025 Major in Mathematics (Intensive) < PLO 1,2,3 > 2024 Major in Mathematics < PLO 1,2,3 > 2024 Major in Mathematics (Intensive) < PLO 1,2,3 > 2023 Major in Mathematics < PLO 1,2,3 > 2023 Major in Mathematics (Intensive) < PLO 1,2,3 > 2022 Major in Mathematics < PLO 1,2,3 > 2022 Major in Mathematics (Intensive) < PLO 1,2,3 > 2021 Major in Mathematics < PLO 1,2,3 > 2021 Major in Mathematics (Intensive) < PLO 1,2,3 >
Offer in 2025 - 2026	Y        1st sem	Examination	Dec
Offer in 2026 - 2027	Y
Course Grade	A+ to F
Grade Descriptors	A Demonstrate an excellent understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and argumentation and being able to carry out computations carefully and correctly, and with some innovative approaches to solving problems. B Demonstrate a good understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, but with some minor inadequacies in arguments, identifying the appropriate theorems or their applications and presentation or with some minor computational errors. C Demonstrate an acceptable understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with some inadequacies in applying the theorems through incorrectly analysing problems with poor argument and presentation or a number of minor computational errors. D Demonstrate some understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with substantial inadequacies in applying the theorems through incorrectly analysing problems with poor argument or presentation or with substantial computational errors. Fail Demonstrates poor and inadequate understanding by not being able to identify appropriate theorems or their applications, or not being able to complete the solution.
Communication-intensive Course	N
Course Type	Lecture-based course
Course Teaching & Learning Activities	Activities Details No. of Hours Lectures 36.0 Tutorials 12.0 Reading / Self study 100.0
Assessment Methods and Weighting	Methods Details Weighting in final course grade (%) Assessment Methods to CLO Mapping Assignments 10.0 1,2,3 Examination 50.0 1,2,3 Test 40.0 1,2,3
Required/recommended reading and online materials	1. M. A. Armstrong: Basic topology; 2. S. W. MasseyL A basic course on Algebraic Topology (Chapter 1), 1991. 3. J. Munkres: Topology, 2000.
Course Website	http://moodle.hku.hk/
Additional Course Information

MATH3600 Discrete mathematics (6 credits)		Academic Year	2025
Offering Department	Mathematics	Quota	---
Course Co-ordinator	Dr K H Law, Mathematics < lawkaho@connect.hku.hk >
Teachers Involved	(Dr K H Law,Mathematics)
Course Objectives	To introduce students to the basic ideas and techniques of discrete mathematics.
Course Contents & Topics	- Counting: combinations, permutations, pigeonhole principle, inclusion-exclusion, recurrence relations, and generating functions. - Graph theory: paths, circuits, trees, connectivity, planarity, etc. - Applications of counting techniques and graph theory.
Course Learning Outcomes	On successful completion of this course, students should be able to: CLO 1 demonstrate knowledge and understanding of the basic ideas and techniques of discrete mathematics CLO 2 solve various real-world problems by using counting techniques and graph theory CLO 3 develop their ability to read, comprehend, and create mathematical arguments
Pre-requisites (and Co-requisites and Impermissible combinations)	Pass in (MATH1013 and any 1 of Level 2 MATH courses) or (MATH1851 and MATH1853 and any 1 of level 2 MATH courses) or MATH2014 or (MATH1821 and MATH2822)
Course Status with Related Major/Minor /Professional Core	2025 Major in Mathematics ( Disciplinary Elective ) 2025 Major in Mathematics (Intensive) ( Core/Compulsory ) 2025 Minor in Mathematics ( Disciplinary Elective ) 2025 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2024 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2024 Major in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics (Intensive) ( Core/Compulsory ) 2024 Minor in Mathematics ( Disciplinary Elective ) 2024 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2023 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2023 Major in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics (Intensive) ( Core/Compulsory ) 2023 Minor in Mathematics ( Disciplinary Elective ) 2023 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2022 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2022 Major in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics (Intensive) ( Core/Compulsory ) 2022 Minor in Mathematics ( Disciplinary Elective ) 2022 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2021 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2021 Major in Decision Analytics ( Disciplinary Elective ) 2021 Major in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics (Intensive) ( Core/Compulsory ) 2021 Minor in Mathematics ( Disciplinary Elective ) 2021 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective )
Course to PLO Mapping	2025 Major in Mathematics < PLO 1,2,3 > 2025 Major in Mathematics (Intensive) < PLO 1,2,3 > 2024 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2 > 2024 Major in Mathematics < PLO 1,2,3 > 2024 Major in Mathematics (Intensive) < PLO 1,2,3 > 2023 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2 > 2023 Major in Mathematics < PLO 1,2,3 > 2023 Major in Mathematics (Intensive) < PLO 1,2,3 > 2022 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2 > 2022 Major in Mathematics < PLO 1,2,3 > 2022 Major in Mathematics (Intensive) < PLO 1,2,3 > 2021 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2 > 2021 Major in Decision Analytics < PLO 1,3 > 2021 Major in Mathematics < PLO 1,2,3 > 2021 Major in Mathematics (Intensive) < PLO 1,2,3 >
Offer in 2025 - 2026	Y        1st sem	Examination	Dec
Offer in 2026 - 2027	Y
Course Grade	A+ to F
Grade Descriptors	A Demonstrate an excellent understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and argumentation and being able to carry out computations carefully and correctly, and with some innovative approaches to solving problems. B Demonstrate a good understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, but with some minor inadequacies in arguments, identifying the appropriate theorems or their applications and presentation or with some minor computational errors. C Demonstrate an acceptable understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with some inadequacies in applying the theorems through incorrectly analysing problems with poor argument and presentation or a number of minor computational errors. D Demonstrate some understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with substantial inadequacies in applying the theorems through incorrectly analysing problems with poor argument or presentation or with substantial computational errors. Fail Demonstrate poor and inadequate understanding by not being able to identify appropriate theorems or their applications, or not being able to complete the solution.
Communication-intensive Course	Y
Course Type	Lecture-based course
Course Teaching & Learning Activities	Activities Details No. of Hours Lectures 36.0 Tutorials 12.0 Reading / Self study Students are expected to watch videos online before classes. 100.0
Assessment Methods and Weighting	Methods Details Weighting in final course grade (%) Assessment Methods to CLO Mapping Assignments Tutorials, assignments, participation, etc. 10.0 1,2,3 Examination 50.0 1,2,3 Test 40.0 1,2,3
Required/recommended reading and online materials	Richard A. Brualdi: Introductory Combinatorics (Pearson)
Course Website	http://moodle.hku.hk/
Additional Course Information

MATH3601 Numerical analysis (6 credits)		Academic Year	2025
Offering Department	Mathematics	Quota	---
Course Co-ordinator	Dr F L Tsang, Mathematics < f.l.tsang@hku.hk >
Teachers Involved	(Dr F L Tsang,Mathematics)
Course Objectives	This course covers both the theoretical and practical aspects of numerical analysis. Emphasis will be on basic principles and numerical methods of solution, using high speed computers.
Course Contents & Topics	- Different types of errors, condition number, and convergence order. - Polynomial interpolation and function approximation. - Solution of equations of one variable. - Direct  and iterative methods for solving linear systems. - Numerical differentiation and integration. - Simple initial value problems for Ordinary Differential Equations.
Course Learning Outcomes	On successful completion of this course, students should be able to: CLO 1 construct and implement algorithms to find the zeros of functions, apply the bisection, Newton, Secant and fixed point iteration methods; and construct and implement Newton's method to solve a system of nonlinear equations CLO 2 apply direct and iterative methods for solving linear equation systems CLO 3 construct interpolation polynomials in Lagrange, Newton, Hermite and spline forms; and construct function approximations in the least-square sense CLO 4 understand the basic numerical integration and differentiation methods CLO 5 apply Euler methods and Runge-Kutta methods to solve initial value problems CLO 6 use software package such as Scilab or Matlab or Python to solve numerical problems
Pre-requisites (and Co-requisites and Impermissible combinations)	Pass in (MATH2101 and MATH2211) or MATH2014 or (MATH1821 and MATH2822)
Course Status with Related Major/Minor /Professional Core	2025 Major in Mathematics ( Disciplinary Elective ) 2025 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2025 Minor in Computational & Financial Mathematics ( Core/Compulsory ) 2025 Minor in Mathematics ( Disciplinary Elective ) 2024 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2024 Major in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2024 Minor in Computational & Financial Mathematics ( Core/Compulsory ) 2024 Minor in Mathematics ( Disciplinary Elective ) 2023 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2023 Major in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2023 Minor in Computational & Financial Mathematics ( Core/Compulsory ) 2023 Minor in Mathematics ( Disciplinary Elective ) 2022 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2022 Major in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2022 Minor in Computational & Financial Mathematics ( Core/Compulsory ) 2022 Minor in Mathematics ( Disciplinary Elective ) 2021 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2021 Major in Decision Analytics ( Disciplinary Elective ) 2021 Major in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2021 Minor in Computational & Financial Mathematics ( Core/Compulsory ) 2021 Minor in Mathematics ( Disciplinary Elective )
Course to PLO Mapping	2025 Major in Mathematics < PLO 1,2,3 > 2025 Major in Mathematics (Intensive) < PLO 1,2,3 > 2024 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,3,4 > 2024 Major in Mathematics < PLO 1,2,3 > 2024 Major in Mathematics (Intensive) < PLO 1,2,3 > 2023 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,3,4 > 2023 Major in Mathematics < PLO 1,2,3 > 2023 Major in Mathematics (Intensive) < PLO 1,2,3 > 2022 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,3,4 > 2022 Major in Mathematics < PLO 1,2,3 > 2022 Major in Mathematics (Intensive) < PLO 1,2,3 > 2021 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,3,4 > 2021 Major in Decision Analytics < PLO 1,3 > 2021 Major in Mathematics < PLO 1,2,3 > 2021 Major in Mathematics (Intensive) < PLO 1,2,3 >
Offer in 2025 - 2026	Y        1st sem	Examination	Dec
Offer in 2026 - 2027	Y
Course Grade	A+ to F
Grade Descriptors	A Demonstrate an excellent understanding of key concepts and methods by being able to identify the appropriate theorems/algorithms and their applications through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and argumentation and being able to carry out numerical procedures carefully and correctly, and with some innovative approaches to solving problems. B Demonstrate a good understanding of key concepts and methods by being able to identify the appropriate theorems/algorithms and their applications through correctly analysing problems, but with some minor inadequacies in arguments, identifying the appropriate algorithms or their applications or with some minor computational errors. C Demonstrate an acceptable understanding of key concepts and methods by being able to correctly identify appropriate theorems/algorithms, but with some inadequacies in applying the theorems/methods through incorrectly analysing problems with poor argument and presentation or with a number of minor computational errors. D Demonstrate some understanding of key concepts and methods by being able to correctly identify appropriate theorems/algorithms, but with substantial inadequacies in applying the theorems/methods through incorrectly analysing problems with poor argument and presentation or with substantial computational errors. Fail Demonstrate poor and inadequate understanding by not being able to identify appropriate theorems/algorithms or their applications, or not being able to complete the solution.
Communication-intensive Course	N
Course Type	Lecture-based course
Course Teaching & Learning Activities	Activities Details No. of Hours Lectures 36.0 Tutorials 12.0 Reading / Self study 100.0
Assessment Methods and Weighting	Methods Details Weighting in final course grade (%) Assessment Methods to CLO Mapping Assignments 20.0 1,2,3,4,5,6 Examination 50.0 1,2,3,4,5,6 Test 30.0 1,2,3,4,5,6
Required/recommended reading and online materials	Instructor's Lecture Notes A. Ralston and P. Rabinowitz: A First Course in Numerical Analysis (McGraw-Hill) K. E. Atkinson: An Introduction to Numerical Analysis (Wiley, 1989) D. Kincaid and W. Cheney. Numerical Analysis: Mathematics of Scientific Computing. 3rd Edition. AMS, 2009. R. L. Burden and J. D. Faires. Numerical Analysis. 10th Edition. Cengage, 2016. E. Isaacson and H. B. Keller. Analysis of Numerical Methods. Dover, 1994. S. D. Conte and C. de Boor. Elementary Numerical Analysis - An Algorithmic Approach. Third Edition. SIAM, 2017.
Course Website	http://moodle.hku.hk/
Additional Course Information

MATH3603 Probability theory (6 credits)		Academic Year	2025
Offering Department	Mathematics	Quota	---
Course Co-ordinator	Prof Z Bao, Mathematics < zgbao@hku.hk >
Teachers Involved	(Prof Z Bao,Mathematics)
Course Objectives	The emphasis of this course will be on probability models and their applications. The primary aim is to elucidate the fundamental principles of probability theory through examples and to develop the ability of the students to apply what they have learned from this course to widely divergent concrete problems.
Course Contents & Topics	-Basic probability theory: random variable, discrete and continuous probability distributions, expectation, variance, moment generating function, strong law of large numbers, central limit theorem. -Conditional probability theory: conditional probability, Bayes theorem, conditional expectation, conditional variance, compound random variable, Polya's urn model, Bose-Einstein statistics. -Markov chain theory: concepts of states and transition probability, irreducibility, stationary distribution, limiting probabilities, reversibility, hidden Markov chain, applications in marketing and genetic problems, branching process, Markov decision process. -Poisson process and reliability theory: exponential distribution, memoryless property, Poisson process, concepts of reliability, applications to server queue problems.
Course Learning Outcomes	On successful completion of this course, students should be able to: CLO 1 understand and recognize the fundamental principles of probability theory CLO 2 explain the typical proofs and computational techniques in probability theory and apply them to concrete problems CLO 3 demonstrate knowledge and understanding of various types of probability models
Pre-requisites (and Co-requisites and Impermissible combinations)	Pass in (MATH2101 and MATH2211) or MATH2014 or (MATH1821 and MATH2822)
Course Status with Related Major/Minor /Professional Core	2025 Major in Mathematics ( Disciplinary Elective ) 2025 Major in Mathematics (Intensive) ( Core/Compulsory ) 2025 Minor in Computational & Financial Mathematics ( Disciplinary Elective ) 2025 Minor in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics (Intensive) ( Core/Compulsory ) 2024 Minor in Computational & Financial Mathematics ( Disciplinary Elective ) 2024 Minor in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics (Intensive) ( Core/Compulsory ) 2023 Minor in Computational & Financial Mathematics ( Disciplinary Elective ) 2023 Minor in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics (Intensive) ( Core/Compulsory ) 2022 Minor in Computational & Financial Mathematics ( Disciplinary Elective ) 2022 Minor in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics (Intensive) ( Core/Compulsory ) 2021 Minor in Computational & Financial Mathematics ( Disciplinary Elective ) 2021 Minor in Mathematics ( Disciplinary Elective )
Course to PLO Mapping	2025 Major in Mathematics < PLO 1,2,3 > 2025 Major in Mathematics (Intensive) < PLO 1,2,3 > 2024 Major in Mathematics < PLO 1,2,3 > 2024 Major in Mathematics (Intensive) < PLO 1,2,3 > 2023 Major in Mathematics < PLO 1,2,3 > 2023 Major in Mathematics (Intensive) < PLO 1,2,3 > 2022 Major in Mathematics < PLO 1,2,3 > 2022 Major in Mathematics (Intensive) < PLO 1,2,3 > 2021 Major in Mathematics < PLO 1,2,3 > 2021 Major in Mathematics (Intensive) < PLO 1,2,3 >
Offer in 2025 - 2026	Y        2nd sem	Examination	May
Offer in 2026 - 2027	Y
Course Grade	A+ to F
Grade Descriptors	A Demonstrate an excellent understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and argumentation and being able to carry out computations carefully and correctly, and with some innovative approaches to solving problems. B Demonstrate a good understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, but with some minor inadequacies in arguments, identifying the appropriate theorems or their applications and presentation or with some minor computational errors. C Demonstrate an acceptable understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with some inadequacies in applying the theorems through incorrectly analysing problems with poor argument and presentation or a number of minor computational errors. D Demonstrate some understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with substantial inadequacies in applying the theorems through incorrectly analysing problems with poor argument or presentation or with substantial computational errors. Fail Demonstrate poor and inadequate understanding by not being able to identify appropriate theorems or their applications, or not being able to complete the solution.
Communication-intensive Course	N
Course Type	Lecture-based course
Course Teaching & Learning Activities	Activities Details No. of Hours Lectures 36.0 Tutorials 12.0 Reading / Self study 100.0
Assessment Methods and Weighting	Methods Details Weighting in final course grade (%) Assessment Methods to CLO Mapping Assignments Coursework assessment 10.0 1,2,3 Examination 50.0 1,2,3 Test Two midterm tests 40.0 1,2,3
Required/recommended reading and online materials	S.M. Ross: Introduction to Probability Models (Academic Press, 2007, 9th ed.)
Course Website	http://moodle.hku.hk/
Additional Course Information

MATH3901 Operations research I (6 credits)		Academic Year	2025
Offering Department	Mathematics	Quota	---
Course Co-ordinator	Prof L Lai, Mathematics < lai.lexiao@hku.hk >
Teachers Involved	(Prof L Lai,Mathematics)
Course Objectives	The objective is to provide a fundamental account of the basic results and techniques of Linear Programming (LP) and its related topics in operations research. The topics include the simplex method, the dual simplex method, parametric programming, decomposition methods and interior point methods.
Course Contents & Topics	- Linear programming - Duality theory - Sensitivity analysis and parametric linear programming - Ellipsoid methods - Interior point methods
Course Learning Outcomes	On successful completion of this course, students should be able to: CLO 1 understand the fundamental concept and approach of linear programming appropriate to the further study of operations research CLO 2 demonstrate knowledge and understanding of the underlying techniques of the simplex method and its extensions such as the dual simplex algorithm and the decomposition method CLO 3 understand and apply the theory of integer programming
Pre-requisites (and Co-requisites and Impermissible combinations)	Pass in MATH2014 or MATH2101 or MATH2102
Course Status with Related Major/Minor /Professional Core	2025 Major in Mathematics ( Disciplinary Elective ) 2025 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2025 Minor in Mathematics ( Disciplinary Elective ) 2025 Minor in Operations Research & Mathematical Programming ( Core/Compulsory ) 2024 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2024 Major in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2024 Minor in Mathematics ( Disciplinary Elective ) 2024 Minor in Operations Research & Mathematical Programming ( Core/Compulsory ) 2023 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2023 Major in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2023 Minor in Mathematics ( Disciplinary Elective ) 2023 Minor in Operations Research & Mathematical Programming ( Core/Compulsory ) 2022 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2022 Major in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2022 Minor in Mathematics ( Disciplinary Elective ) 2022 Minor in Operations Research & Mathematical Programming ( Core/Compulsory ) 2021 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2021 Major in Decision Analytics ( Disciplinary Elective ) 2021 Major in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2021 Minor in Mathematics ( Disciplinary Elective ) 2021 Minor in Operations Research & Mathematical Programming ( Core/Compulsory )
Course to PLO Mapping	2025 Major in Mathematics < PLO 1,2,3 > 2025 Major in Mathematics (Intensive) < PLO 1,2,3 > 2024 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,3,5 > 2024 Major in Mathematics < PLO 1,2,3 > 2024 Major in Mathematics (Intensive) < PLO 1,2,3 > 2023 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,3,5 > 2023 Major in Mathematics < PLO 1,2,3 > 2023 Major in Mathematics (Intensive) < PLO 1,2,3 > 2022 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,3,5 > 2022 Major in Mathematics < PLO 1,2,3 > 2022 Major in Mathematics (Intensive) < PLO 1,2,3 > 2021 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,3,5 > 2021 Major in Decision Analytics < PLO 1,3,4 > 2021 Major in Mathematics < PLO 1,2,3 > 2021 Major in Mathematics (Intensive) < PLO 1,2,3 >
Offer in 2025 - 2026	Y        2nd sem	Examination	May
Offer in 2026 - 2027	Y
Course Grade	A+ to F
Grade Descriptors	A Demonstrate an excellent understanding of key concepts and ideas by being able to identify basic principles, appropriate theorems, algorithms and their applications through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and argumentation and being able to carry out computations carefully and correctly, and to solve problems with some innovative approaches. B Demonstrate a good understanding of key concepts and ideas by being able to identify basic principles, appropriate theorems, algorithms and their applications through correctly analysing problems, but with some minor inadequacies in arguments, identifying the appropriate theorems or their applications and presentation or with some minor computational errors. C Demonstrate an acceptable understanding of key concepts and ideas by being able to identify basic principles, appropriate theorems, algorithms and their applications but with some inadequacies in applying the theorems through incorrectly analysing problems with poor argument and presentation or a number of minor computational errors. D Demonstrate some understanding of key concepts and ideas by being able to identify basic principles, appropriate theorems, algorithms and their applications but with substantial inadequacies in applying the theorems through incorrectly analysing problems with poor argument or presentation or with substantial computational errors. Fail Demonstrate poor and inadequate understanding by not being able to identify basic principles, appropriate theorems, algorithms or their applications, or not being able to complete or compute the solution.
Communication-intensive Course	N
Course Type	Lecture-based course
Course Teaching & Learning Activities	Activities Details No. of Hours Lectures 36.0 Tutorials 12.0 Reading / Self study 100.0
Assessment Methods and Weighting	Methods Details Weighting in final course grade (%) Assessment Methods to CLO Mapping Assignments Coursework assessment 10.0 1,2,3 Examination 50.0 1,2,3 Test Two midterm tests 40.0 1,2,3
Required/recommended reading and online materials	J.P. Ignizio and T.M. Cavalier: Linear Programming (Prentice-Hall International, 1994) D. Bertsimas and J.N. Tsitsiklis: Introduction to Linear Optimization (Athena Scientific, 1997) W.L. Winston: Introduction to Mathematical Programming (Duxbury 4/e 2003)
Course Website	http://moodle.hku.hk/
Additional Course Information

MATH3904 Introduction to optimization (6 credits)		Academic Year	2025
Offering Department	Mathematics	Quota	---
Course Co-ordinator	Prof W Zang, Mathematics < wzang@maths.hku.hk >
Teachers Involved	(Prof W Zang,Mathematics)
Course Objectives	This course introduces students to the theory and techniques of optimization, aiming at preparing them for further studies in operations research, mathematical economics and related subject areas.
Course Contents & Topics	- Unconstrained and constrained optimization. - Necessary conditions and sufficient conditions for optimality, convexity, duality. - Algorithms and numerical examples.
Course Learning Outcomes	On successful completion of this course, students should be able to: CLO 1 demonstrate knowledge and understanding of the basic theory and techniques of optimization CLO 2 solve various optimization problems encountered in practice CLO 3 understand the connection between the purely analytical character of an optimization problem and the behavior of algorithms for solving it
Pre-requisites (and Co-requisites and Impermissible combinations)	Pass in (MATH2101 and MATH2211) or MATH2014 or (MATH1821 and MATH2822)
Course Status with Related Major/Minor /Professional Core	2025 Major in Mathematics ( Disciplinary Elective ) 2025 Major in Mathematics (Intensive) ( Core/Compulsory ) 2025 Minor in Computational & Financial Mathematics ( Disciplinary Elective ) 2025 Minor in Mathematics ( Disciplinary Elective ) 2025 Minor in Operations Research & Mathematical Programming ( Core/Compulsory ) 2024 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Core/Compulsory ) 2024 Major in Decision Analytics ( Core/Compulsory ) 2024 Major in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics (Intensive) ( Core/Compulsory ) 2024 Minor in Computational & Financial Mathematics ( Disciplinary Elective ) 2024 Minor in Mathematics ( Disciplinary Elective ) 2024 Minor in Operations Research & Mathematical Programming ( Core/Compulsory ) 2023 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Core/Compulsory ) 2023 Major in Decision Analytics ( Core/Compulsory ) 2023 Major in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics (Intensive) ( Core/Compulsory ) 2023 Minor in Computational & Financial Mathematics ( Disciplinary Elective ) 2023 Minor in Mathematics ( Disciplinary Elective ) 2023 Minor in Operations Research & Mathematical Programming ( Core/Compulsory ) 2022 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Core/Compulsory ) 2022 Major in Decision Analytics ( Core/Compulsory ) 2022 Major in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics (Intensive) ( Core/Compulsory ) 2022 Minor in Computational & Financial Mathematics ( Disciplinary Elective ) 2022 Minor in Mathematics ( Disciplinary Elective ) 2022 Minor in Operations Research & Mathematical Programming ( Core/Compulsory ) 2021 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Core/Compulsory ) 2021 Major in Decision Analytics ( Core/Compulsory ) 2021 Major in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics (Intensive) ( Core/Compulsory ) 2021 Minor in Computational & Financial Mathematics ( Disciplinary Elective ) 2021 Minor in Mathematics ( Disciplinary Elective ) 2021 Minor in Operations Research & Mathematical Programming ( Core/Compulsory )
Course to PLO Mapping	2025 Major in Mathematics < PLO 1,2,3 > 2025 Major in Mathematics (Intensive) < PLO 1,2,3 > 2024 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,3,4,5 > 2024 Major in Decision Analytics < PLO 1,3,4 > 2024 Major in Mathematics < PLO 1,2,3 > 2024 Major in Mathematics (Intensive) < PLO 1,2,3 > 2023 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,3,4,5 > 2023 Major in Decision Analytics < PLO 1,3,4 > 2023 Major in Mathematics < PLO 1,2,3 > 2023 Major in Mathematics (Intensive) < PLO 1,2,3 > 2022 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,3,4,5 > 2022 Major in Decision Analytics < PLO 1,3,4 > 2022 Major in Mathematics < PLO 1,2,3 > 2022 Major in Mathematics (Intensive) < PLO 1,2,3 > 2021 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,3,4,5 > 2021 Major in Decision Analytics < PLO 1,3,4 > 2021 Major in Mathematics < PLO 1,2,3 > 2021 Major in Mathematics (Intensive) < PLO 1,2,3 >
Offer in 2025 - 2026	Y        1st sem	Examination	Dec
Offer in 2026 - 2027	Y
Course Grade	A+ to F
Grade Descriptors	A Demonstrate an excellent understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and argumentation and being able to carry out computations carefully and correctly, and with some innovative approaches to solving problems. B Demonstrate a good understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, but with some minor inadequacies in arguments, identifying the appropriate theorems or their applications and presentation or with some minor computational errors. C Demonstrate an acceptable understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with some inadequacies in applying the theorems through incorrectly analysing problems with poor argument and presentation or a number of minor computational errors. D Demonstrate some understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with substantial inadequacies in applying the theorems through incorrectly analysing problems with poor argument or presentation or with substantial computational errors. Fail Demonstrate poor and inadequate understanding by not being able to identify appropriate theorems or their applications, or not being able to complete the solution.
Communication-intensive Course	N
Course Type	Lecture-based course
Course Teaching & Learning Activities	Activities Details No. of Hours Lectures 36.0 Tutorials 12.0 Reading / Self study 100.0
Assessment Methods and Weighting	Methods Details Weighting in final course grade (%) Assessment Methods to CLO Mapping Examination 50.0 1,2,3 Test 50.0 1,2,3
Required/recommended reading and online materials	Instructor's lecture notes
Course Website	http://moodle.hku.hk/
Additional Course Information

   <<< This course is not offered in 2025-2026. Course details are subject to change. >>>

MATH3905 Queueing theory and simulation (6 credits)		Academic Year	2025
Offering Department	Mathematics	Quota	---
Course Co-ordinator	Dr G Han, Mathematics < ghan@maths.hku.hk >
Teachers Involved
Course Objectives	This course introduces students to the models and theory of queueing system, as well as the technique of simulation as a practical tool of analysis.
Course Contents & Topics	- Markov, birth-and-death, and Poisson processes, exponential models. - Markovian queueing networks. Imbedded Markov-chain queueing models. - Simulation of queueing models and discrete-event systems. - Introduction of the Monte Carlo (MC) method and Markov Chain Monte Carlo (MCMC) method.
Course Learning Outcomes	On successful completion of this course, students should be able to: CLO 1 understand the terminology and nomenclature appropriate to queueing theory CLO 2 demonstrate knowledge and understanding of various queueing models CLO 3 formulate concrete problems using queueing theoretical approaches CLO 4 become familiar with fundamental principles of simulation and compare different simulation techniques CLO 5 use Monte Carlo method and Markov Chain Monte Carlo method to conduct numerical simulations
Pre-requisites (and Co-requisites and Impermissible combinations)	Pass in (MATH2101 and MATH2211) or MATH2014 or (MATH1821 and MATH2822)
Course Status with Related Major/Minor /Professional Core	2025 Major in Mathematics ( Disciplinary Elective ) 2025 Minor in Mathematics ( Disciplinary Elective ) 2025 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2024 Major in Mathematics ( Disciplinary Elective ) 2024 Minor in Mathematics ( Disciplinary Elective ) 2024 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2023 Major in Mathematics ( Disciplinary Elective ) 2023 Minor in Mathematics ( Disciplinary Elective ) 2023 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2022 Major in Mathematics ( Disciplinary Elective ) 2022 Minor in Mathematics ( Disciplinary Elective ) 2022 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2021 Major in Mathematics ( Disciplinary Elective ) 2021 Minor in Mathematics ( Disciplinary Elective ) 2021 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective )
Course to PLO Mapping	2025 Major in Mathematics < PLO 1,2,3 > 2024 Major in Mathematics < PLO 1,2,3 > 2023 Major in Mathematics < PLO 1,2,3 > 2022 Major in Mathematics < PLO 1,2,3 > 2021 Major in Mathematics < PLO 1,2,3 >
Offer in 2025 - 2026	N	Examination
Offer in 2026 - 2027	N
Course Grade	A+ to F
Grade Descriptors	A Demonstrate an excellent understanding of key concepts and ideas by being able to identify appropriate theorems and their applications through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and argumentation and being able to carry out computations carefully and correctly, and to solve problems with some innovative approaches. B Demonstrate a good understanding of key concepts and ideas by being able to identify appropriate theorems and their applications through correctly analysing problems, but with some minor inadequacies in arguments, identifying the appropriate theorems or their applications and presentation or with some minor computational errors. C Demonstrate an acceptable understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with some inadequacies in applying the theorems through incorrectly analysing problems with poor argument and presentation or a number of minor computational errors. D Demonstrate some understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with substantial inadequacies in applying the theorems through incorrectly analysing problems with poor argument or presentation or with substantial computational errors. Fail Demonstrate poor and inadequate understanding by not being able to identify appropriate theorems or their applications, or not being able to complete the solution.
Communication-intensive Course	N
Course Type	Lecture-based course
Course Teaching & Learning Activities	Activities Details No. of Hours Lectures 36.0 Tutorials 12.0 Reading / Self study 100.0
Assessment Methods and Weighting	Methods Details Weighting in final course grade (%) Assessment Methods to CLO Mapping Examination 50.0 1,2,3,4,5 Test 50.0 1,2,3,4,5
Required/recommended reading and online materials	R.B. Cooper: Introduction to Queueing Theory (Edward Arnold, 1981, 2nd ed.) S.M. Ross: Introduction to Probability Models (Academic Press, 1993, 7th ed., San Diego, California) S.M. Ross: A Course in Simulation (Macmillan, 1991) P. Glasserman: Monte Carlo Methods in Financial Engineering (Springer Science & Business Media, 2004)
Course Website	http://moodle.hku.hk/
Additional Course Information

MATH3906 Financial calculus (6 credits)		Academic Year	2025
Offering Department	Mathematics	Quota	---
Course Co-ordinator	Prof G Li, Mathematics < lotusli@maths.hku.hk >
Teachers Involved	(Prof G Li,Mathematics)
Course Objectives	This course gives an elementary treatment for the modeling of financial derivatives, asset pricing and market risks from an applied mathematician's point of view. Stochastic calculus and solution methods will be introduced.
Course Contents & Topics	- An introduction to financial instruments: stocks, bonds, options, forward and future contracts. - Asset pricing: risk neutral relationship, no arbitrage principle. Brownian motion, stochastic calculus, Ito's Lemma, Black-Scholes model and its pricing partial differential equation. - Variations on the Black-Scholes model, American options, path dependent options. Binomial tree Models. Discrete Martingale.
Course Learning Outcomes	On successful completion of this course, students should be able to: CLO 1 understand the terminology and nature of bonds, interest rates, forwards, futures, stocks, options, and the no-arbitrage-principle CLO 2 demonstrate knowledge on using binomial tree models to find option prices via the risk-neutral concept CLO 3 describe basic properties of a Brownian motion and the Black-Scholes stock price model CLO 4 implement stochastic calculus (such as Ito's Lemma) to derive Black-Scholes pricing partial differential equation on various type of options; and find a solution to this partial differential equation CLO 5 apply Euler methods and Runge-Kutta methods to solve initial value problems, and apply finite difference methods to solve boundary value problems CLO 6 use software packages such as Matlab or Python to solve numerical problems
Pre-requisites (and Co-requisites and Impermissible combinations)	Pass in  MATH2211 or MATH2014 or MATH2822. Students are strongly recommended to have passed or already enrolled in MATH3603 or STAT2601.
Course Status with Related Major/Minor /Professional Core	2025 Major in Mathematics ( Disciplinary Elective ) 2025 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2025 Minor in Computational & Financial Mathematics ( Core/Compulsory ) 2025 Minor in Mathematics ( Disciplinary Elective ) 2025 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2024 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2024 Major in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2024 Minor in Computational & Financial Mathematics ( Core/Compulsory ) 2024 Minor in Mathematics ( Disciplinary Elective ) 2024 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2023 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2023 Major in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2023 Minor in Computational & Financial Mathematics ( Core/Compulsory ) 2023 Minor in Mathematics ( Disciplinary Elective ) 2023 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2022 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2022 Major in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2022 Minor in Computational & Financial Mathematics ( Core/Compulsory ) 2022 Minor in Mathematics ( Disciplinary Elective ) 2022 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2021 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2021 Major in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2021 Minor in Computational & Financial Mathematics ( Core/Compulsory ) 2021 Minor in Mathematics ( Disciplinary Elective ) 2021 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective )
Course to PLO Mapping	2025 Major in Mathematics < PLO 1,2,3 > 2025 Major in Mathematics (Intensive) < PLO 1,2,3 > 2024 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,5 > 2024 Major in Mathematics < PLO 1,2,3 > 2024 Major in Mathematics (Intensive) < PLO 1,2,3 > 2023 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,5 > 2023 Major in Mathematics < PLO 1,2,3 > 2023 Major in Mathematics (Intensive) < PLO 1,2,3 > 2022 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,5 > 2022 Major in Mathematics < PLO 1,2,3 > 2022 Major in Mathematics (Intensive) < PLO 1,2,3 > 2021 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,5 > 2021 Major in Mathematics < PLO 1,2,3 > 2021 Major in Mathematics (Intensive) < PLO 1,2,3 >
Offer in 2025 - 2026	Y        2nd sem	Examination	May
Offer in 2026 - 2027	Y
Course Grade	A+ to F
Grade Descriptors	A Demonstrate an excellent understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and argumentation and being able to carry out computations carefully and correctly, and with some innovative approaches to solving problems. B Demonstrate a good understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, but with some minor inadequacies in arguments, identifying the appropriate theorems or their applications and presentation or with some minor computational errors. C Demonstrate an acceptable understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with some inadequacies in applying the theorems through incorrectly analysing problems with poor argument and presentation or a number of minor computational errors. D Demonstrate some understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with substantial inadequacies in applying the theorems through incorrectly analysing problems with poor argument or presentation or with substantial computational errors. Fail Demonstrate poor and inadequate understanding by not being able to identify appropriate theorems or their applications, or not being able to complete the solution.
Communication-intensive Course	N
Course Type	Lecture-based course
Course Teaching & Learning Activities	Activities Details No. of Hours Lectures 36.0 Tutorials 12.0 Reading / Self study 100.0
Assessment Methods and Weighting	Methods Details Weighting in final course grade (%) Assessment Methods to CLO Mapping Examination 50.0 1,2,3,4,5,6 Test 50.0 1,2,3,4,5,6
Required/recommended reading and online materials	A. Etheridge: A Course in Financial Calculus (Cambridge University Press) M. Baxter and A. Rennie: Financial Calculus: An Introduction to Derivative Pricing (Cambridge University Press, 1996) P. Wilmott, S. Howison, J. Dewynne: The Mathematics of Financial Derivatives (Cambridge University Press, 1995) R. Jarrow and S. Turnbull: Derivative Securities (South-Western College Publishing, 1994)
Course Website	http://moodle.hku.hk/
Additional Course Information

MATH3911 Game theory and strategy (6 credits)		Academic Year	2025
Offering Department	Mathematics	Quota	---
Course Co-ordinator	Prof T W Ng, Mathematics < ntw@maths.hku.hk >
Teachers Involved	(Prof T W Ng,Mathematics)
Course Objectives	Game theory is the logical analysis of situations of conflict and cooperation. This course will introduce the students to the basic ideas and techniques of mathematical game theory in an interdisciplinary context.
Course Contents & Topics	- Combinatorial games and Zermelo's Theorem; Prisonner's Dilemma; pure and mixed strategies, minimax theorem; mixed Nash equilibria. - Application to biology: evolutionary stable strategies; games in coalition form; Shapley value. - Application to politics: Shapley-Shubik power index; core and von Neumann-Morgenstern solution; bargaining set.
Course Learning Outcomes	On successful completion of this course, students should be able to: CLO 1 understand the basic terminology and solution concepts in game theory CLO 2 compute explicitly different solution concepts for some simple cooperative and non-cooperative games CLO 3 apply game theoretical ideas and methods to solve some problems in economics and biology
Pre-requisites (and Co-requisites and Impermissible combinations)	Pass in (MATH2101 and MATH2211) or MATH2014 or (MATH1821 and MATH2822)
Course Status with Related Major/Minor /Professional Core	2025 Major in Mathematics ( Disciplinary Elective ) 2025 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2025 Minor in Computational & Financial Mathematics ( Disciplinary Elective ) 2025 Minor in Mathematics ( Disciplinary Elective ) 2025 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2024 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2024 Major in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2024 Minor in Computational & Financial Mathematics ( Disciplinary Elective ) 2024 Minor in Mathematics ( Disciplinary Elective ) 2024 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2023 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2023 Major in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2023 Minor in Computational & Financial Mathematics ( Disciplinary Elective ) 2023 Minor in Mathematics ( Disciplinary Elective ) 2023 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2022 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2022 Major in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2022 Minor in Computational & Financial Mathematics ( Disciplinary Elective ) 2022 Minor in Mathematics ( Disciplinary Elective ) 2022 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2021 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2021 Major in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2021 Minor in Computational & Financial Mathematics ( Disciplinary Elective ) 2021 Minor in Mathematics ( Disciplinary Elective ) 2021 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective )
Course to PLO Mapping	2025 Major in Mathematics < PLO 1,2,3 > 2025 Major in Mathematics (Intensive) < PLO 1,2,3 > 2024 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,3,5 > 2024 Major in Mathematics < PLO 1,2,3 > 2024 Major in Mathematics (Intensive) < PLO 1,2,3 > 2023 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,3,5 > 2023 Major in Mathematics < PLO 1,2,3 > 2023 Major in Mathematics (Intensive) < PLO 1,2,3 > 2022 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,3,5 > 2022 Major in Mathematics < PLO 1,2,3 > 2022 Major in Mathematics (Intensive) < PLO 1,2,3 > 2021 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,3,5 > 2021 Major in Mathematics < PLO 1,2,3 > 2021 Major in Mathematics (Intensive) < PLO 1,2,3 >
Offer in 2025 - 2026	Y        2nd sem	Examination	May
Offer in 2026 - 2027	Y
Course Grade	A+ to F
Grade Descriptors	A Demonstrate an excellent understanding of key concepts and ideas of Game Theory by being able to identify the appropriate theorems and their applications through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and being able to carry out computations carefully and correctly, and with some innovative approaches to solving problems. B Demonstrate a good understanding of key concepts and ideas of Game Theory by being able to identify the appropriate theorems and their applications through correctly analysing problems, but with some minor inadequacies in arguments, identifying the appropriate theorems or their applications and presentation or with some minor computational errors. C Demonstrate an acceptable understanding of key concepts and ideas of Game Theory by being able to correctly identify appropriate theorems, but with some inadequacies in applying the theorems through incorrectly analysing problems with poor argument and presentation or a number of minor computational errors. D Demonstrate some understanding of key concepts and ideas of Game Theory by being able to correctly identify appropriate theorems, but with substantial inadequacies in applying the theorems through incorrectly analysing problems with poor argument or presentation or with substantial computational errors. Fail Demonstrate poor and inadequate understanding by not being able to identify appropriate theorems or their applications, or not being able to complete the solution.
Communication-intensive Course	N
Course Type	Lecture-based course
Course Teaching & Learning Activities	Activities Details No. of Hours Lectures 36.0 Tutorials 12.0 Reading / Self study Students are expected to watch videos online before classes. 100.0
Assessment Methods and Weighting	Methods Details Weighting in final course grade (%) Assessment Methods to CLO Mapping Assignments Tutorials, assignments, project, participation, etc. 20.0 1,2,3 Examination 50.0 1,2,3 Test 30.0 1,2,3
Required/recommended reading and online materials	[Textbook] L.C. Thomas: Games, Theory and Applications (Dover Publications, 2003) [Reference] Alan D. Taylor and Allison M. Pacelli, Mathematics and Politics: Strategy, Voting, Power, and Proof (Springer-Verlag, 2009)
Course Website	http://moodle.hku.hk/
Additional Course Information

MATH3943 Network models in operations research (6 credits)		Academic Year	2025
Offering Department	Mathematics	Quota	---
Course Co-ordinator	Dr K H Law, Mathematics < lawkaho@connect.hku.hk >
Teachers Involved	(Dr K H Law,Mathematics)
Course Objectives	The objective is to provide a fundamental account of the basic results and techniques of network models in operations research. There is an equal emphasis on all three aspects of understanding, algorithms and applications. The course serves, together with a course on linear programming, to provide essential concept and background for more advanced studies in operations research.
Course Contents & Topics	- Graphs and algorithms. - Trees, matchings and paths. - Network models of transportation and assignment problems. - Ford-Fulkerson network flow theory and computation for maximum flow and minimum cost flow algorithms. - Applications to combinatorial optimization problems such as allocation, location and sequencing. - Project networks, if time permits.
Course Learning Outcomes	On successful completion of this course, students should be able to: CLO 1 understand the fundamental concept and approach of graphs and network models appropriate to the further study of operations research CLO 2 demonstrate knowledge and understanding of the underlying techniques of the various graph and network algorithms and their extensions CLO 3 understand the theory of network flows and the duality aspects in such methods of flow computations
Pre-requisites (and Co-requisites and Impermissible combinations)	Pass in (MATH2101 and MATH2211) or MATH2014.
Course Status with Related Major/Minor /Professional Core	2025 Major in Mathematics ( Disciplinary Elective ) 2025 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2025 Minor in Mathematics ( Disciplinary Elective ) 2025 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2024 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2024 Major in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2024 Minor in Mathematics ( Disciplinary Elective ) 2024 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2023 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2023 Major in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2023 Minor in Mathematics ( Disciplinary Elective ) 2023 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2022 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2022 Major in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2022 Minor in Mathematics ( Disciplinary Elective ) 2022 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective ) 2021 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective ) 2021 Major in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2021 Minor in Mathematics ( Disciplinary Elective ) 2021 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective )
Course to PLO Mapping	2025 Major in Mathematics < PLO 1,2,3 > 2025 Major in Mathematics (Intensive) < PLO 1,2,3 > 2024 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,5 > 2024 Major in Mathematics < PLO 1,2,3 > 2024 Major in Mathematics (Intensive) < PLO 1,2,3 > 2023 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,5 > 2023 Major in Mathematics < PLO 1,2,3 > 2023 Major in Mathematics (Intensive) < PLO 1,2,3 > 2022 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,5 > 2022 Major in Mathematics < PLO 1,2,3 > 2022 Major in Mathematics (Intensive) < PLO 1,2,3 > 2021 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,5 > 2021 Major in Mathematics < PLO 1,2,3 > 2021 Major in Mathematics (Intensive) < PLO 1,2,3 >
Offer in 2025 - 2026	Y        1st sem	Examination	Dec
Offer in 2026 - 2027	Y
Course Grade	A+ to F
Grade Descriptors	A Demonstrate an excellent understanding of key concepts and ideas by being able to identify basic principles, appropriate theorems, algorithms and their applications through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and argumentation and being able to carry out computations carefully and correctly, and to solve problems with some innovative approaches. B Demonstrate a good understanding of key concepts and ideas by being able to identify basic principles, appropriate theorems, algorithms and their applications through correctly analysing problems, but with some minor inadequacies in arguments, identifying the appropriate theorems or their applications and presentation or with some minor computational errors. C Demonstrate an acceptable understanding of key concepts and ideas by being able to identify basic principles, appropriate theorems, algorithms and their applications but with some inadequacies in applying the theorems through incorrectly analysing problems with poor argument and presentation or a number of minor computational errors. D Demonstrate some understanding of key concepts and ideas by being able to identify basic principles, appropriate theorems, algorithms and their applications but with substantial inadequacies in applying the theorems through incorrectly analysing problems with poor argument or presentation or with substantial computational errors. Fail Demonstrate poor and inadequate understanding by not being able to identify basic principles, appropriate theorems, algorithms or their applications, or not being able to complete or compute the solution.
Communication-intensive Course	Y
Course Type	Lecture-based course
Course Teaching & Learning Activities	Activities Details No. of Hours Lectures 36.0 Tutorials 12.0 Reading / Self study Students are expected to watch videos online before classes. 100.0
Assessment Methods and Weighting	Methods Details Weighting in final course grade (%) Assessment Methods to CLO Mapping Assignments Tutorials, assignments, participation, etc. 10.0 1,2,3 Examination 50.0 1,2,3 Test 40.0 1,2,3
Required/recommended reading and online materials	Bondy, J. A., and U. S. R. Murty. Graph Theory with Applications. London: Macmillan, 1976. Print.
Course Website	http://moodle.hku.hk/
Additional Course Information

MATH3999 Directed studies in mathematics (6 credits)		Academic Year	2025
Offering Department	Mathematics	Quota	---
Course Co-ordinator	Dr K H Law, Mathematics < lawkaho@connect.hku.hk >
Teachers Involved	(All teaching staff,Mathematics)
Course Objectives	This course is designed for students who would like to have early experiences on research related independent studies.
Course Contents & Topics	The subject matter of the project will be determined by consultation between the student and the supervisor. The student must achieve good standing and get the approval from both the prospective supervisor and the course coordinator to take this course.
Course Learning Outcomes	On successful completion of this course, students should be able to: CLO 1 study independently a topic that is not available in the regular curriculum CLO 2 understand how mathematical theories are applied and/or extended in problem-solving CLO 3 gain experience in project writing and oral presentation
Pre-requisites (and Co-requisites and Impermissible combinations)	This capstone course is for Mathematics / Mathematics (Intensive), and Mathematics/Physics Majors students only. The earliest that a student is allowed to take this capstone course is their year 3 study. Pass in at least 24 credits of advanced level disciplinary core/elective mathematics courses (MATH3XXX, MATH4XXX or MATH7XXX) in the Mathematics/ Mathematics (Intensive), and Mathematics/Physics Majors; and subject to approval by the Department.
Course Status with Related Major/Minor /Professional Core	2025 Major in Mathematics ( Disciplinary Elective ) 2025 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2024 Major in Mathematics ( Disciplinary Elective ) 2024 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2023 Major in Mathematics ( Disciplinary Elective ) 2023 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2022 Major in Mathematics ( Disciplinary Elective ) 2022 Major in Mathematics (Intensive) ( Disciplinary Elective ) 2021 Major in Mathematics ( Disciplinary Elective ) 2021 Major in Mathematics (Intensive) ( Disciplinary Elective )
Course to PLO Mapping	2025 Major in Mathematics < PLO 3,4,5 > 2025 Major in Mathematics (Intensive) < PLO 3,4,5 > 2024 Major in Mathematics < PLO 3,4,5 > 2024 Major in Mathematics (Intensive) < PLO 3,4,5 > 2023 Major in Mathematics < PLO 3,4,5 > 2023 Major in Mathematics (Intensive) < PLO 3,4,5 > 2022 Major in Mathematics < PLO 3,4,5 > 2022 Major in Mathematics (Intensive) < PLO 3,4,5 > 2021 Major in Mathematics < PLO 3,4,5 > 2021 Major in Mathematics (Intensive) < PLO 3,4,5 >
Offer in 2025 - 2026	Y        1st sem    2nd sem	Examination	No Exam
Offer in 2026 - 2027	Y
Course Grade	A+ to F
Grade Descriptors	A Demonstrate thorough grasp of the subject. Show strong analytical and critical abilities and logical thinking, with evidence of original thought. Insightful use and critical evaluation of information drawn from a broad range of high quality sources and to reference aptly. Critical use of data and results to draw appropriate and insightful conclusions. Apply highly effective organizational and presentational skills. B Demonstrate substantial grasp of the subject. Evidence of analytical and critical abilities and logical thinking. Critical use of relevant information from sources, showing ability to make meaningful comparisons between different secondary interpretations and to reference aptly. Correct use of data of results to draw appropriate conclusions. Apply effective organizational and presentational skills. C Demonstrate general but incomplete grasp of the subject. Evidence of some analytical and critical abilities and logical thinking. Use of relevant information from sources, showing ability to make comparisons between different interpretations and to reference aptly. Mostly correct but some erroneous use of data and results to draw appropriate conclusions. Apply moderately effective organizational and presentational skills. D Demonstrate partial but limited grasp, with retention of some relevant information, of the subject. Evidence of some coherent and logical thinking, but with limited analytical and critical abilities. Demonstrate use and reference of several sources, but mainly through summary rather than analysis and comparison. Limited ability to use data and results to draw appropriate conclusions. Apply limited or barely effective organizational and presentational skills. Fail Demonstrate evidence of little or no grasp of the knowledge and understanding of the subject. Evidence of little or lack of analytical and critical abilities, logical and coherent thinking. Limited use of secondary sources and no critical comparison of them. Misuse of data and results and/or unable to draw appropriate conclusions. Organization and presentational skills are minimally effective or ineffective.
Communication-intensive Course	Y
Course Type	Project-based course
Course Teaching & Learning Activities	Activities Details No. of Hours Reading / Self study independent work & to attend meetings & seminars 120.0
Assessment Methods and Weighting	Methods Details Weighting in final course grade (%) Assessment Methods to CLO Mapping Dissertation Written report plus oral presentation 100.0 1,2,3
Required/recommended reading and online materials	NIL
Course Website	NIL
Additional Course Information	The offered topics and application procedure are released by email from the Department. Sophomore or above students who have declared Major in Mathematics/Mathematics (Intensive) will receive emails in June. The application results will be announced in late July or early August. For enquiry, please contact the Department. The final report must be submitted by the end of the semester. The deadline for submission will be announced in the due course.

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