Goals

1. To help first-year students prepare for MATH courses at the 1000 and 2000 level.
2. To enhance an atmosphere that promotes the discussion of mathematics within the Department.

Activities for the First Semester 2024-25.

Two classes (`accelerated class', `non-accelerated class') are offered:---

• The accelerated class is intended for students with DSE (or equivalent) background
  • who are doing MATH1018, MATH1038.
• The non-accelerated class is intended for students with DSE (or equivalent) background
  • who are doing MATH1010 and/or MATH1030, and
  • who plan to graduate with major in mathematics.

Below is a tentative list of topics for the non-acclerated class. The schedule for the accelerated class will be adapted from this list.

• Weeks 3-7: Solving equations, mathematical induction, elementry inequalities, trigonometric functions.
• Weeks 8-13: Infinite sequence, Mean-Value Theorem, Taylor series expansion, definite integrals and indefinite integrals.

The objective of the classes is to help participants to acquire, through hands-on work and discussion on exercises, important skills and techniques needed by mathematics major students for the mastery of the content in most MATH required courses in the MATH curriculum (beyond MATH1010/1018 and MATH1030/1038, but to some extent also relevant to MATH1010/1018 and MATH1030/1038).

• The accelerated class will focus on material adapted from the old HKALE Pure Mathematics which is supplementary to MATH1018 and MATH1038.
• The non-accelerated class will start with material adapted from the old HKCEE Mathematics and Additional Mathematics and gradually move on to material in the old HKALE Pure Mathematics.

Activities for Second Semester 2024-25.

Below are the tentative arrangements:---

• Classes will be offered on Monday evenings.
• The objective is to provide participants with guided tours in selected topics in old HKALE Pure Mathematics which, in various MATH level-2000 courses, may be assumed to be elementary knowledge covered in present-day school mathematics.
• The topics are selected from: Binomial Theorem, (further applications of) mathematical induction, complex numbers, polynomials and rational functions, Taylor's Theorem, advanced results on definite integrals (including inequalities about integrals), conic sections, symmetric matrices and quadratic forms.
• A test, open to all mathematics major students, will be arranged in mid-May (very likely on the Friday immediately before the beginning of the Summer Semester.)

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