Undergraduate Courses

This page introduces our first- and second-year core courses.

Click HERE for the complete list of MATH courses to learn more about their descriptions, prerequisites, exclusions, etc. Note that not all courses in that list are offered in the current academic year.

First-Year Calculus courses

Currently, the Department of Mathematics offers the following single variable calculus courses at different levels and with different purposes. Typically, first-year students pick one course below in each semester:

Fall semester:

MATH 1023 is recommended for:

• students with strong interest in mathematics,
• students who plan to enroll in the Pure Mathematics or Pure Mathematics (Advanced) tracks in the Math program, or
• students who aspire to pursue postgraduate studies in pure/applied mathematics, statistics, and related fields.

Students are expected to learn the fundamental concepts of differentiations and limit of sequences using rigorous “epsilon-delta approach”. Students will also be trained to write logical and coherent mathematical proofs.

Minimum prerequisite is Level 5 or above in HKDSE Mathematics Module 2. Students with other qualifications such as JEE, IB, GCEAL, etc. should consult the instructor / UG Coordinator about the recommended prerequisites before taking this course.

MATH 1013 is designed for students who passed HKDSE Mathematics Module 1 or Module 2. It covers limits, differentiations, and elementary integrations using more intuitive approaches than MATH 1023. The main goal of the course is to equip students with workable knowledge and skills of single-variable calculus for further studies of science, engineering, and business. One lecture section of MATH 1013 in the Fall semester will be a special section for potential math majors. The special section, while covering similar materials as other sections, will have more emphasis on logical reasoning skills and conceptual aspects of differentiations and limits, but it is not as rigorous and challenging as MATH 1023.

MATH 1012 is designed for students without HKDSE Mathematics Module 1 nor Module 2. Its content is similar to that of MATH 1013, but an extra tutorial hour will be added each week to make up some essential knowledge taught in HKDSE M2.

MATH 1003 covers very minimal material in single variable calculus and matrix arithmetics. It is not targeted for students in the Science or Engineering programs.

Spring semester:

After the Fall semester, students from MATH 1023 may opt to continue on either MATH 1024 or MATH 1014. They are advised to self-evaluate their performance in the past semester and consult the instructor / UG coordinator when making the choice between the two. All students from MATH 1012 and MATH 1013, regardless of their performance, should continue on MATH 1014, unless they have self-studied MATH 1023 materials seriously in the Fall semester.

Only students who took MATH 1003 with A- or above will be permitted to continue on MATH 1014 after MATH 1003. Other MATH 1003 students must first take MATH 1013 before taking any other MATH courses.

Below are major topics to be covered in Spring semester Calculus courses:

MATH 1024 is the continuation of MATH 1023. It covers integrations and infinite series using rigorous approaches. It begins with the formal definition of Riemann integrals, followed by a formal proof of Newton-Leibniz formula. It then covers various integration techniques including integration by parts, by substitutions, and reduction formulae. At the discretion of instructors, some deeper topics such as the irrationality of pi, integral remainder of Taylor series, rectifiable curves, etc. will also be included. The infinite series chapter will cover both applications and formal proofs of various convergence tests.

Students in MATH 1024 are assumed to have acquired the knowledge about vectors and matrices at the level equivalent to HKDSE M2. Therefore, instead of covering vectors in the last chapter, other deeper topics such as Fourier series, isoperimetric inequality, etc. will be covered at the end of the course.

MATH 1014 is the continuation of MATH 1012/1013. Compared to MATH 1024, it covers integrations and infinite series using more intuitive approaches. It emphasizes more computational techniques, and less on conceptual aspects, than MATH 1024. Various integration techniques including integration by parts, by substitutions, and reduction formulae will be included. The infinite series chapter will cover mostly the applications of various convergence tests, while the proofs of these convergence tests are intended to be rigorous . To prepare students (especially those without HKDSE M2 background) for better transition into 2000-level MATH courses, the course will also cover basic vectors and matrices in one of the chapters. MATH 1014 will also offer one special section for potential math majors. In this special section, less computational techniques of integrals but more conceptual explanations will be taught. However, it will not be as rigorous and challenging as MATH 1024. Furthermore, as math majors will eventually study sequences and infinite series in MATH 2033 in a much more rigorous way, the coverage on infinite series may be briefer than other sections, but more and deeper coverage on vectors, matrices, complex numbers, and other topics that are essential for math majors will be taught in the special section.

Remarks:

• MATH 1020 (Accelerated Calculus) was offered many years ago. It covers MATH 1013 and MATH 1014 material in one single semester. Currently, Math Department is not offering MATH 1020 as a regular course. It is now used only for credit transfer purposes. Students with top scores in HKDSE M2 should consider taking MATH 1023 (Honors Calculus I).
• Students who took IB Further Math, GCEAL Further/Pure Math, AP Calculus can get credit transfer into either MATH 1003 or MATH 1013 – according to the scores obtained in these international exams (see HERE for detail). However, students who plan to declare Math as their major are NOT recommended to transfer these qualifications into MATH 1013, and should instead take our single-variable Calculus courses such as MATH 1013 (especially the Math major section) or MATH 1023 to build up a better mathematical foundation.
• IRE students who plan to declare Math as their major MUST take MATH 1023 and MATH 1024 in their first year.
• The S.S. Chern class scholarship program typically only considers applicants who took MATH 1023 and MATH 1024.

Summer break:

After the major declaration exercise at the end of the first year, math majors without HKDSE M2 background should make up their knowledge of vectors and matrices during the summer break - as the coverage of these topics in MATH 1014 could be very minimal because of the time constraint. There are a lot of free online lecture videos on these topics. Students with HKDSE M2 background should also consider reviewing the materials about vectors and matrices before Fall semester starts. Both required courses of Year 2: MATH 2023 (Multivariable Calculus), and MATH 2121 (Linear Algebra) require solid conceptual understanding and computational skills about vectors and matrices.

Second-Year Required courses

There are three Math courses required for MATH students in all tracks in the second year:

• MATH 2023 - Multivariable Calculus
• MATH 2121 - Linear Algbera, or MATH 2131 - Honors Linear Algebra
• MATH 2033 - Mathematical Analysis, or MATH 2043 - Honors Mathematical Analysis

Both Multivariable Calculus and Linear Algebra have corresponding courses offered mainly for students in the School of Engineering, namely MATH 2011 and MATH 2111. However, students with MATH as the first major should take MATH 2023 and MATH 2121/2131.

MATH 2001 - Foundation of Mathematics

The course MATH 2033 (Mathematical Analysis) - usually taken in Year 2 Spring - is known to be difficult to many, but not all, students. It is partly because many students feel there is a wide gap between high school / first-year mathematics (which could be mostly about computations), and this proof-oriented course.

To get a preparation of the required course MATH 2033 in Year 2 Spring, MATH majors are advised to take MATH 2001 (Foundation of Mathematics), offered in Fall semester, to get trained on understanding set notations, logics, writing formal proofs, etc. MATH 2001 is currently a required course for Pure Mathematics and Pure Mathematics (Advanced) tracks, and is also recognized as an elective for other tracks. Students in the CS-track may also consider taking COMP2711 in Year 2 Fall. It could also serve as a bridging course for MATH 2033.

Honors Courses

The honors versions of Linear Algebra and Mathematical Analysis are recommended for mathematically talented students. Students who plan to pursue postgraduate studies (Master/PhD) in Pure/Applied Mathematics, Statistics, and related areas are strongly recommended to take the honors versions if they have successfully completed MATH 1023 and MATH 1024. Students from MATH 1012/1013 and MATH 1014 are NOT recommended to take these honors versions, as they require the knowledge and skills developed in MATH 1023 and MATH 1024.

In addition, the honors versions of Abstract Algebra, Real Analysis, and Probability are also offered for mathematically talented and motivated students who want to pursue postgraduate degrees after graduation.

Enquiries

For any academic enquiries about the above-mentioned courses, please contact course instructors or the UG Coordinator, Prof. Frederick Fong at frederick.fong@ust.hk