Enquiry for Science Major/Minor/Programme Requirements
MATH2241 Introduction to mathematical analysis (6 credits) Academic Year 2025
Offering Department Mathematics Quota ---
Course Co-ordinator Prof K Y Chan (1st sem); Prof C Y Hui (2nd sem), Mathematics < kychan@maths.hku.hk; chhui@maths.hku.hk >
Teachers Involved (Prof C Y Hui,Mathematics)
(Prof K Y Chan,Mathematics)
Course Objectives To introduce students to the basic ideas and techniques of mathematical analysis.
Course Contents & Topics - The real number system: the real numbers as an ordered field, supremum and infimum, the completeness axiom, denseness of the rational numbers.
- Sequences and series of real numbers: limits of sequences, properties of convergent sequences, monotone sequences and Cauchy sequences, subsequences, series, tests of convergence for series.
- Continuity of real-valued functions: properties of continuous functions, the extreme value theorem, the intermediate value theorem, uniform continuity, limits of functions.
- Differentiation: properties of differentiable functions, the mean value theorem, Taylor's theorem and its applications.
- Integration: construction of the Riemann integral using Darboux sums and Riemann sums, the fundamental theorem of calculus.
Course Learning Outcomes
On successful completion of this course, students should be able to:

CLO 1 comprehend and use abstract mathematical arguments such as the epsilon-delta argument
CLO 2 demonstrate convergence or non-convergence of a sequence/series using properties of convergent sequences/series
CLO 3 elucidate important properties of continuous functions such as the extreme value theorem and the intermediate value theorem
CLO 4 elucidate important properties of differentiable functions such as the mean value theorem, and to understand and apply Taylor's Theorem
CLO 5 articulate the construction of the Riemann integral and its relation to differentiation
Pre-requisites
(and Co-requisites and
Impermissible combinations)		 Pass in MATH1013 or MATH1851 or MATH1821.
Course Status with Related Major/Minor /Professional Core 2025 Major in Mathematics ( Core/Compulsory )
2025 Major in Mathematics (Intensive) ( Core/Compulsory )
2024 Major in Mathematics ( Core/Compulsory )
2024 Major in Mathematics (Intensive) ( Core/Compulsory )
2023 Major in Mathematics ( Core/Compulsory )
2023 Major in Mathematics (Intensive) ( Core/Compulsory )
2022 Major in Mathematics ( Core/Compulsory )
2022 Major in Mathematics (Intensive) ( Core/Compulsory )
2021 Major in Mathematics ( Core/Compulsory )
2021 Major in Mathematics (Intensive) ( Core/Compulsory )
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    2nd sem    Examination Dec    May     
Offer in 2026 - 2027 Y
Course Grade A+ to F
Grade Descriptors
A Demonstrate a thorough mastery of the mathematical notions and proof techniques taught in the course by being able to handle abstract mathematical arguments, to apply appropriate theorems correctly, and to make use of those proof techniques in novel situations. Ability to present solutions clearly and logically, and the use of innovative ideas in solving problems are expected.
B Demonstrate a substantial command of the mathematical notions and proof techniques taught in the course by being able to handle abstract mathematical arguments, to apply appropriate theorems correctly, and, with guidance, to make use of those proof techniques in novel situations. Ability to present solutions clearly and logically, and evidence of innovative ideas in solving problems are expected.
C Demonstrate a good understanding of the mathematical notions and proof techniques taught in the course by being able to handle abstract mathematical arguments and to apply appropriate theorems correctly. Ability to present solutions clearly and logically is expected.
D Demonstrate some understanding of the mathematical notions taught in the course by being able to correctly identify appropriate theorems for applications and to carry out logical arguments that are leading to complete solutions.
Fail Demonstrate poor and inadequate understanding by not being able to identify appropriate theorems for applications, or not being able to apply the theorems correctly.
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
Examination 50.0 1,2,3,4,5
Test 40.0 1,2,3,4,5
Required/recommended reading
and online materials		 Robert G. Bartle, Donald R. Sherbert: Introduction to Real Analysis (Wiley, 2011, Fourth Edition)
Kenneth A. Ross: Elementary Analysis: The Theory of Calculus (Springer, 2013, Second Edition)
Course Website http://moodle.hku.hk/
Additional Course Information


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