Today's soundtrack is 2nd Chapter of Acts: Very Best Of.
This morning I'm continuing The Bedside Book of Algebra; I've finished reading the introduction, and I'm now on the first chapter: "Algebra Basics."
There are several number sets: natural numbers (positive numbers other than 0), whole numbers (positive numbers including 0), integers (positive and negative whole numbers, including 0), rational numbers (fractions/repeating decimals), and irrational numbers (endless non-repeating fractions).
There are also several types of integers: prime numbers (numbers that can only be divided by 1 and itself), composite numbers (numbers that can be divided by at least three natural divisors), square numbers (numbers times themselves that can also be arranged as dots into a square), triangular numbers (numbers that can be arranged as dots into a triangle), and perfect numbers (numbers whose divisors, when added together, equal the number itself).
Pi is "the ratio of the circumference of a circle to its diameter"; either the circumference or the diameter will be irrational: "we know π to billions of digits" (p. 19).
The order of operations tells us in what order to solve an equation if it has multiple parts. We follow BEDMAS: First we solve the brackets, then exponents, then division and multiplication, and lastly, addition and subtraction.
Expressions indicate to us which numbers are greater, lesser, or equal when compared to other numbers. "> means 'greater than'; ≥ means 'greater than or equal to'; < means 'less than'; ≤ means 'less than or equal to'" (p. 24), and = of course means "equal to."
To solve an equation for x that includes an equals sign, we simply apply the same operation to both sides of the equation to remove everything except x and the number on the other side of the equals sign.
Polynomials are collections of terms ("a 'term' is a collection of variables raised to exponents and multiplied by a coefficient" (p. 32)). Polynomials "are important because they are used to model real-world problems" (p. 32) such as business optimization, gravity, and the economy.
NOTE: Here, the book discusses multiplying polynomials; however, this section is far above my current understanding of mathematics, and I do not feel qualified to attempt to paraphrase this section. I will need to revisit this after I have completed my Math For Dummies lessons.
Trigonometry is used in surveying, mapping, navigation, and even models of financial markets. The Babylonians' form of trigonometry gives us our understanding of the 360° circle. The Greeks developed the first trigonometric tables. The Indians and Persians developed "trigonometric tables for sine, cosine, and tangent" (p. 37). These ratios "refer to the ratios [...] of the three sides of the triangle" (p. 37), and we can use two of these to find the third.
