This
note covers the following topics: The Laws of Algebra, Coordinates,The Cartesian
Coordinate Plane, Graphs of Equations, Three Interesting Curves, Functions,
Function Notation, Linear and Quadratic Functions, Polynomial Functions,
Rational Functions, Function Composition, Exponential and Logarithmic Functions,
Systems of Equations, Sequences and Series, Complex Numbers and the Fundamental
Theorem of Algebra.
The contents include:
Preliminaries About the Integers, Polynomials, and Matrices, Vector Spaces Over
Q, R, and C, Inner-product Spaces, Groups and Group Actions, Theory of a Single
Linear Transformation , Multilinear Algebra, Advanced Group Theory, .
Commutative Rings and Their Modules, Fields and Galois Theory, Modules Over
Noncommutative Rings.
The contents include: Mathematical Notation and Symbols, Indices,
Simplification and Factorisation, Arithmetic of Algebraic Fractions, Formulae
and Transposition.
Author(s): HELM, Mathematics Education Centre, Loughborough
University
The contents
include: Basic Algebraic Structures, The Integers, Other Examples of Rings,
Quotients and Isomorphisms, Finite Groups, Modules, Galois Theory, Commutative
Algebra, Set Theory.
Author(s): Rui L. Fernandes, University of Illinois
at Urbana-Champaign, Manuel Ricou, Instituto Superior Tecnico
This note describes the
following topics: Functions and Their Graphs, Intercepts, Zeros, and Solutions,
Polynomials and Rational Functions, Systems of Equations and Inequalities,
Matrices and Determinants, Sequences and Probability, Conics and Parametric
Equations.
This note covers the following topics: Symbolic
Expressions, Transcription of Verbal Information into Symbolic Language, Linear
Equations in One Variable, Linear Equations in Two Variables and Their Graphs,
Simultaneous Linear Equations, Functions and Their Graphs, Linear functions and
proportional reasoning, Linear Inequalities and Their Graphs, Exponents,
Quadratic Functions and Their Graphs, The Quadratic Formula and Application.