Miscellaneous Topics in First Year Mathematics
by WWL Chen
This set of notes has been compiled over the last few years. All 4 chapters have been in use at Macquarie University since 1999, and cover material in first year mathematics that does not fall neatly into either calculus or linear algebra.
The following is the suggested order for the presentation of the material:
MATH135:
MATH132:
MATH136:
MATH133:
To read the notes, click the chapters below for connection to the appropriate PDF files.
The material is available free to all individuals, on the understanding that it is not to be used for financial gain, and may be downloaded and/or photocopied, with or without permission from the author. However, the documents may not be kept on any information storage and retrieval system without permission from the author, unless such system is not accessible to any individuals other than its owners.
Chapter 1: REVIEW ON TRIGONOMETRY (written with XT Duong)
 Radian and Arc Length
 The Trigonometric Functions
 Some Trigonometric Identities
Chapter 2: POLYNOMIALS
 Introduction
 Polynomial Equations
 Division of Polynimials
 Roots of Polynomials
 Fundamental Theorem of Algebra
 Roots of Real Polynomials
 Rational Functions
 Greatest Common Divisor
Chapter 3: CONGRUENCES
 Introduction
 Arithmetic of Congruences
 Linear Congruences
 Special Divisibility Rules
 Further Discussion
Chapter 4: INTRODUCTION TO GROUP THEORY
 Some Examples
 Formal Definition
 Subgroups
 Order
 Cyclic Groups
 Further Discussion
 Groups of Small Order
