Academic Year 
2014 
Offering Department 
Mathematics 
Quota 


Course Coordinator 
Prof W S Cheung, Mathematics

Course Aim

This course extends to more general situations some basic results covered in Calculus and introduces some fundamental concepts which are essential for advanced studies in mathematical analysis.

Course Contents 
Basic properties of metric spaces; openness; closedness; interior point; adherent point; accumulation point; boundary point; compactness; completeness; continuity; connectedness; pathwise connectedness; uniform continuity; uniform convergence; Banach's fixed point theorem.

Learning Outcomes 
On successful completion of the course, students should be able to:  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);  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);  think creatively and laterally to generate innovative examples and solutions to nonstandard problems (e.g., able to provide counterexamples to inaccurate mathematical statements).

Prerequisites 
Pass in (MATH1201 and MATH1202) or MATH1211 or MATH1803 or or MATH1804 or MATH1805 or MATH1811 or MATH1812 or MATH1813; and Pass in MATH2201, or already enrolled in this course.

Offer in 2014  2015

Y
1st sem

Examination 
Dec

Offer in 2015  2016
 Y 
Teaching Hours 
36 hours of lectures and studentcentered learning. Tutorials will also be arranged if necessary.

Assessment Method 
One 2.5hour written examination (50% weighting) together with coursework assessment (50% weighting)

Course Grade 
A+ to F

Textbooks 
To be decided by the course instructor.

References 
Apostol: Mathematical Analysis Rudin: Principles of Mathematical Analysis

Course Website 
http://hkumath.hku.hk/course/MATH2401/

Remarks 
NIL
