First-Year Mathematics Honours Scheme

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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 Second 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 have done MATH1010/1018, MATH1030/1038, and are doing MATH1058, MATH2018.
  • The non-accelerated class is intended for students with DSE (or equivalent) background
    • who have done MATH1010, MATH1030, and are doing MATH1050 and/or MATH2010, and
    • who plan to graduate with major in mathematics.
Accelerated class. Non-accelerated class.
Time. Every Monday 1830-2030hrs, starting from 13/01* (tentatively). Every Monday 1830-2030hrs, starting from 13/01* (tentatively).
Venue. LSK 301. LSK 302.
(*) There is no class on 02/02, 03/03.

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, or on some afternoon in Week 1 of the Summer Semester.)

Topics for the Second Semester 2024-25.

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 2-7 Second Semester: Binomial theorem, vectors in Euclidean space, complex numbers, polynomials and rational functions, conic sections.
  • Weeks 8-13 Second Semester: advanced trigonometric functions, absolute value and inequality, basics on surfaces and solids, symmetric matrices and quadratic forms.

For reference, below is the list of topics covered in the classes for First Semester 2024-25:---
  • Weeks 3-7 First Semester: Solving equations, mathematical induction, elementry inequalities, trigonometric functions.
  • Weeks 8-13 First Semester: Infinite sequence, Mean-Value Theorem, Taylor series expansion, definite integrals and indefinite integrals.

Objective of the classes.

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, MATH1030/1038, MATH1050/1058, MATH2010/2018, but to some extent also relevant to MATH1010/1018, MATH1030/1038, MATH1050/1058, MATH2010/2018).

Some of the material will make up guided tours in selected topics in old HKALE Pure Mathematics which, in various MATH level-2000 courses, may be assumed to be background knowledge.
  • The accelerated class will focus on material adapted from the old HKALE Pure Mathematics which is supplementary to MATH1018, MATH1038, MATH1058, MATH2018.
  • 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.

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