Enquiry for Science Major/Minor/Programme Requirements
MATH1853 Linear algebra, probability and statistics (6 credits) Academic Year 2025
Offering Department Mathematics Quota 700
Course Co-ordinator Dr F L Tsang, Mathematics < f.l.tsang@hku.hk >
Teachers Involved (Dr F L Tsang,Mathematics)
(Dr V Bhat,Mathematics)
(Prof J Yu,Civil Engineering)
(Prof N Wong,Electrical & Electronic Engineering)
(Prof SH Cheung,Civil Engineering)
Course Objectives As the complementary course of MATH1851, students will be introduced to more topics of mathematics commonly applied in engineering so that students could be further enhanced with a concrete skill in mathematics underpinned for different engineering subjects. The course emphasizes mathematical concepts, principles, analysis, and their relationship to the modelling of engineering systems.  Students could be furnished with the essential mathematical skills to analytically tackle some typical engineering problems to prepare for all the engineering subjects.
Course Contents & Topics - Linear algebra [vectors and scalars, inner product, vector projection, linear dependence and independence, matrix, determinant, matrix inverse, system of linear equations, matrix equation, Gaussian elimination, Cramer's rule, matrix rank, eigenvalue, eigenvector, matrix diagonalization, positive, negative and semi-definiteness, and their applications]
- Elementary complex variables [arithmetics of complex numbers, representations of complex numbers, De Moivre's theorem, roots of unity, complex functions, and their applications]
- Basic probability theory [axioms of probability, conditional probability, Bayes' theorem, the total probability formula, random variable, (joint) probability distribution, expectation, variance, independence, and their applications]
- Commonly used distributions [Bernoulli, Binomial, Geometric, Negative Binomial, Exponential, Poisson and Normal distribution, and their applications]
- Basic statistics [point estimates, sample mean, sample variance with known or unknown mean, confidence interval for a population mean with known or unknown population variances, inference for proportion, and their applications]
Course Learning Outcomes
On successful completion of this course, students should be able to:

CLO 1 demonstrate knowledge and understanding of linear algebra, complex numbers, probability theory and statistics as well as their relationship with some typical physical/engineering applications: unerringly perform the calculation details for the solution, and accurately correlate the solution approach with the fundamental concepts involved
CLO 2 apply such knowledge and understanding to solve certain practical problems that are relevant to physical/engineering applications: analyze the given problem, identify the appropriate mathematical skills, articulate a convincing rationale for the approach used, and clearly give the mathematical formulation, and correctly find the solution
CLO 3 be well prepared to cope with a higher level of engineering mathematics required in different engineering disciplines
Pre-requisites
(and Co-requisites and
Impermissible combinations)		 Level 2 or above in Module 1, or Module 2 of HKDSE Mathematics or equivalent, or Pass in MATH1011, or take MATH1011 and MATH1853 concurrently in the same semester. (This course is exclusively for Engineering students.)
Course to PLO Mapping
Offer in 2025 - 2026 Y        1st sem    2nd sem    Examination Dec    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 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 methods and their applications through correctly analysing problems, but with some minor inadequacies in arguments, identifying the appropriate theorems and 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 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 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 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
Assignments 20.0 1,2,3
Examination 80.0 1,2,3
Required/recommended reading
and online materials		 D.C. Lay: Linear Algebra and its Applications (Addison-Wesley, 2012, 4th ed.)
S.J. Leon: Linear Algebra with Applications (Pearson Education, 2006, 7th ed.)
G. James, et al.: Modern Engineering Mathematics (Pearson Education, 2008, 4th ed.)
C. Rorres and H. Anton: Applications of Linear Algebra (Wiley, 1984, 3rd ed.)
E. Kreyzig: Advanced Engineering Mathematics (Wiley, 2006, 9th ed.)
K. L. Chung and F. AitSahlia. Elementary Probability Theory, 4th Edition. Springer, 2003.
R. V. Hogg, J. W. McKean, and A. T. Craig. Introduction to Mathematical Statistics, 8th Edition. Pearson, 2019.
H. P. Hsu. Schaum’s outline of theory and problems of probability, random variables, and random processes. McGraw-Hill, 1997.
Course Website http://moodle.hku.hk/
Additional Course Information There will be no 'make-up' for a missed quiz or assignment under normal circumstances.
Students are advised not to take MATH1851 and MATH1853 together in the same semester.
This course is offered by the Department of Mathematics and the Faculty of Engineering.


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