## 1.2 Outline

- Magic squares
- A pattern of nines
- Order of operations (see below)
- Inductive reasoning (see below)
- conjecture
- exponentiation
*b*^{2}*; b*squared*b*^{3}*; b*cubed

- Deductive reasoning (see below)
- undefined terms
- axioms or premises
- conclusion
- syllogism
- invalid reasoning
- Euler circles (see below)

## 1.2 Essential Ideas

**Order of Operations**

*The order of operations in this section permeates almost all types of mathematical calculations. You should remember these steps:*

*First*, perform any operations enclosed in parentheses.

*Next*, perform multiplication and divisions as they occur by working from left to right.

*Finally*, perform additions and subtractions as they occur by working from left to right.

**Inductive Reasoning**

The type of reasoning in which you first observe a pattern, and then predict outcomes for future occurrences.

**Deductive Reasoning** The type of reasoning involves reaching a conclusion by using a formal structure based on a set of undefined terms and a set of accepted unproved axioms or premises.

**Euler Circles** Test the validity of a syllogism by using Euler circles.