Learning Algebra

To help with a few of my projects and learning Fusion, I thought I'd brush up on some basic maths - I've been using the Openstax textbooks (access for free at openstax.org) to learn a bit of algebra, trigonometry and geometry. I'm going to record what I've learned here, with an eye on using the Feynman technique to help me understand it.

Classifying Numbers

• Natural numbers

The numbers we use to count real life things {1, 2, 3, ...}

• Whole numbers

Zero plus the natural numbers {0, 1, 2, 3, ...}

• Integers

Negative and postive whole numbers including 0 {..., -3, -2, -1, 0, 1, 2, 3, ...}

• Rational numbers

Fractions m/n where m and n are integers and n ≠ 0

Whole numbers can be represented with the whole number as a numerator and 1 as denominator.

• Irrational numbers

A fraction is a ratio. In this sense, irrational means it can't be written as a ratio.

Essentially an irrational number can't be written as a fraction. A clue to this is a non-repeating decimal.

π is an irrational number, it will never fit into a neat fraction. 22/7 is close, but not exactly right.

The set of rational numbers contains all of the integers, the set of integers contains the whole numbers, the set of whole numbers contains all the natural numbers. Irrational numbers are those outside the rational set. See diagram below:

PEMDAS

• P - Parentheses
• E - Exponents
• M - Multiplication
• D - Division
• A - Addition
• S - Subtraction

1. Simplify any expressions within grouping symbols e.g. (), {}, [], etc.
2. Simplify any expressions containing exponents or radicals (see below).
3. Perform any multiplication and division in order, from left to right.
4. Perform any addition and subtraction in order, from left to right.

Exponents

Exponents are a shorthand way of writing repeated multiplication. For example, 2³ is 2 x 2 x 2 = 8.

Radicals

A radical is a root. The square root of 9 is 3 because 3 x 3 = 9. The cube root of 27 is 3 because 3 x 3 x 3 = 27.

The radical symbol is the one that people call the sqrt or square root (√) but actually refers to any root and the index number above the radical symbol indicates this. People tend to leave the 2 off when they refer to square root.

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