LECTURE NOTES OF WILLIAM CHEN
MISCELLANEOUS TOPICS IN FIRST YEAR MATHEMATICS
As the title suggests, this is a small collection of topics which do not fit in easily with either calculus or linear algebra.
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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