# User:Whiteknight/Algebra

**This page is an outline for a proposed book or project.**This is only a planning page, not an actual book.

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This outline was last edited on **31 July 2007**. Last edit over 109 months ago. Please update.

The "algebra" section contains a number of different books, many of which are currently sharing or duplicating material between themselves. Also, some of the booknames don't correspond to any specific body of information, such as Intermediate Algebra, or Algebra I - A Verbose Approach. I would like to propose a merger and a reorganization of this section as follows:

The remaining books will be:

- Algebra I in Simple English (unchanged)
- Algebra (incorporating Algebra I - A Verbose Approach and Intermediate Algebra)
- Linear Algebra
- Abstract algebra (Incorporating Discrete mathematics, and possibly moved to Abstract Algebra)

And new books will be created from the extra material:

- Arithmetic
- Mathematical Logic
- Data Coding Theory (outline)
- Automata Theory (outline)

Also, I would like to separate out the material so that it goes more or less in a chronological order: Algebra → Linear Algebra → Abstract Algebra. This means that we will no longer be cross-linking chapters, and there will be no more redundant information in these books. Here is my outline for the three books:

## Contents

## Algebra[edit]

- Word Problems
- Polynomials
- Factoring Polynomials
- Completing the Square
- Quadratic Equation
- Absolute value

- Equalities, Inequalities
- Functions
- Graphing Functions
- Function combinations

- Graphings Lines
- Slope
- Slope-Intercept Form
- Point-Slope Form

- Conic Sections
- Parabola, Hyperbola, Circule, Elipse

- Shapes
- Area, Volume, Surface Area formulae

- Exponentials
- Square Roots (radicals)
- Logarithms
- e and Natural Log

- Imaginary Numbers

## Linear Algebra[edit]

- Systems of Equations
- Matricies, Vectors
- Diagonal Matrix
- Identity Matrix
- Triangular Matrices
- Kronecker Vectors
- Zero matrices/vectors
- Augmented Matrices

- Matrix Operations
- addition, multiplication, Transpose
- Row/Column Operations

- Determinant
- Laplace Expansion

- Cramers Rule
- Matrix Inverses
- Minors
- Cofactors
- Adjoints
- Computing Inverses

- Partitioned Matrices
- Vector Operations
- Norm
- Inner Product
- Orthogonality
- Metric
- Span

- Linear Dependance
- Basis Vectors
- Change of Basis

- System of Equation Solutions
- Matrix Rank
- Homogenous Solution
- Particular Solution
- Complete/General Solution

- Eigenvalues
- Characteristic Equation
- Eigenvectors

## Abstract Algebra[edit]

- Sets
- Compositions
- Associativity
- Commutivity

- Groups
- Semigroups
- Groups
- Abelian Groups

- Rings
- Fields
- Modules
- Isomorphisms, Homomorphisms
- Algebras
- Theoretical Linear Algebra
- Vector Spaces
- Subspaces
- Span
- Linear Independence
- Basis/Dimension
- Linear Transformations

## Pages to be moved out of Algebra books[edit]

These chapters are currently located in the algebra books, and need to be moved to a better location.

- Algebra/Trigonometry to Trigonometry
- Algebra/Proofs to Mathematical Proof
- Algebra/Logic to Mathematical Logic (new book)
- Algebra/Error Correcting Codes to Data Coding Theory (new book)
- Algebra/Arithmetic to Arithmetic (new book)
- Algebra/Further arithmetic to Arithmetic
- Algebra/Probability and Odds to Probability
- Abstract algebra/Category theory to Category theory
- Discrete mathematics/Number theory to Number Theory
- Discrete mathematics/Analytic Number Theory to Number Theory
- Discrete mathematics/Combinatory logic to Mathematical Logic
- Discrete mathematics/Finite state automata to Automata Theory (new book)
- Discrete mathematics/Sieve of Eratosthenes to Number Theory

All other pages in these books will be merged together as outlined above.

## Wikiversity and algebra[edit]

I'm trying to get something going on wikiversity on algebra, and was trying to follow the flow of the algebra wikibook- but the book seems to be in a process of being split or merged. where should I start? v:User:Rayc