A little outside help would be much obliged even though this is not a wiki.
Mental Mathematics
This project is not a computer program. Rather it is a program for the computer that you take with you everywhere that you go: your brain.
It should be shocking to know that in our American education system, there are students who do not know how to calculate the four basic arithmetic operations (addition, subtraction, multiplication, and division) without the aid of a calculator. Many of them graduate high school still unable to add simple integers and yet they are accepted into college. This is unacceptable.
And the problem doesn't stop there. There are studies that link brain aliments such as Alzheimer's, dementia, and other cognitive diseases due to the fact that in our developmental years, we need to exercise our brains with numbers, puzzles, patterns, logic, and calculations.
It is never too late to learn mathematics and to learn how to complete math problems without the aid of a calculator. And if your profession requires that you use math at a moments notice, it is vital to your career.
This project will be on going and developing. While most of you should take advantage of the arithmetic section, this project will also cover other sections of mathematics including algebra, geometry, trigonometry, calculus, vector calculus, and numerical analysis.
This project will be organized into categories and into smaller sections such that it is informative and not overwhelming. Learn as much as you'd like at your own pace. The more you understand it, the better, especially if you are a parent with kids who needs help with their math or science homework and you weren't so great in math class.
For the most part, this page will serve as a directory of resources to a lot of content while there will also be some stuff I will write myself.
Table of contents
- Arithmetic
- Addition and Subtraction
- Multiplication with Lattices
- Division and Modulus with with Rulers
- Multiples and Factors - Lowest Common Multiple and Greatest Common Denominator
- Fractions and Decimals
- Adding and Subtracting Fractions
- Multiplying and Dividing Fractions
- Converting Fractions into Decimals
- Adding and Subtracting Decimals
- Multiplying and Dividing Decimals
- Inverses - How Division with Decimals becomes Multiplication with Decimals.
- Logic - There is a good reason this chapter is here
- The rules of logic, and how from this point onward you'll need them for math
- Venn Diagrams
- Statements and Expressions
- Algebra
- Introduction to Polynomials
- Multiples and Factors II
- Absolute Values and Negative Numbers
- Introduction to Imaginary and Complex Numbers
- Equations
- Linear Equations
- Quadratic Equations
- Cubic Equations and Beyond
- Logarithms, Exponents, and Roots
- Geometry
- Shapes
- Circles and an introduction to π
- A short introduction to ellipses
- Polygons
- Regular Polygons
- Triangles
- Quadrilaterals: Squares, Rectangles, Rombuses, Paralleograms, and Trapezoids
- Trigonometry
- Angles
- An introduction to trigonometic functions
- Calculus
- Derivatives
- Integrals
- Math in Physics
- MacClauren and Fourier Series
- Analytical Geometry
- Polar Equations
- Parametric Equations
- Advanced Logic - "A psychologist, a mathematician, and a computer scientist walk into a bar..."
- Predicate Logic: How Everybody is Somebody and Nobody is nothing.
- Numerical Analysis
- Inverses II: The real reason Division is just multiplying with decimals
- Newton's Method: Why it took you this long to learn how to do square roots.
- Combinatorics: How not to waste your time with the factorial operator.
- Statistical Numerical Analysis or How that Hurricane may or may not hit your house next week.
- A short bit about actuarial science, or how to make sure that your house is insured properly.
- Vector Calculus
- Vectors
- Vectors in Physics
- Partial Derivatives or why your math teacher keep skilling this chapter.
- Double and Triple Integrals
- Beizer and Hermite Curves
- Discrete Mathematics
- Paths: Why it takes two hours to take the bus to work.
- Russian Peasants and Traveling Salesmen
- Fair Elections: How America got stuck with George W. Bush and how mathematics is non-partisan.
- Estate Division: I bequeath a boot to the head!
- Automata
- Booklist - Books I recommend
- Reference List - In case I cite outside sources
- About me
Arithmetic
TOCLogic
TOCAlgebra
TOCGeometry
TOCTrigonometry
TOCCalculus
TOCAdvanced Logic
TOCNumerical Analysis
TOCVector Calculus
TOC
