Enquiry for Course Details
MATH3401 Analysis I (6 credits) Academic Year 2026
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 MATH2241.
Course Status with Related Major/Minor /Professional Core 2026 Major in Mathematics ( Core/Compulsory )
2026 Major in Mathematics (Intensive) ( Core/Compulsory )
2026 Minor in Mathematics ( Disciplinary Elective )
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 )
Course to PLO Mapping 2026 Major in Mathematics < PLO 1,2,3 >
2026 Major in Mathematics (Intensive) < PLO 1,2,3 >
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 >
Offer in 2026 - 2027 Y        1st sem    Examination Dec     
Offer in 2027 - 2028 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


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