Lecture 2: Precalculus

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Reminder: This class will meet on Friday in room 420 of the Fretwell building. A representative of computer services will help you access your Eudora account. You will need a 3 1/2 diskett for that class meeting. Come to my office before class to buy one for 50 cents or borrow one from a friend. Also, expect a quiz on Friday.
In the lecture we talked a little more about absolute value, then about whle number, fractional and negative exponents.

Brief review of the lecture

Preliminary Stuff. There are three important types of objects in our study of algebra: 1. Numbers, 2. Algebraic Expressions, and 3. Functions. By numbers we mean real numbers. We need to understand how to represent them, how to convert from one representation to another, and how to do arithmetic-that is, how to combine numbers using the arithmetic operations plus, minus, times, divide, exponentiate, etc. We also learn about ordering numbers. We learn rules of arithmetic and order. This is what chapter P is about. The next few chapters do the same thing with algrebraic expressions that the first one does with numbers. There are a few more things we can do with these expressions than we can do with numbers. For example, we can evaluate them. For example, the expression 4xy^2 has the value 3 when x=3 and y=1/2. The third part of our study of algebra will involve functions. A function is a relationship between two sets of numbers. Functions are ofter defined using algebraic expressions. Functions from the real numbers to the real numbers have graphs which we use to understand the `behavior' of the function.

1. The need for numbers. Our number systems have grown as the need for new numbers grew. Cave men had only two numbers, few and many. Irrational numbers were `invented' to solve equations like x times x-2=0.
2. Exponents and radicals. The meaning of exponential notation.
3. The need to distinguish two aspects of number. Each (real) number has a value, and a representation (in fact each number has many representations). When we say two numbers are equal, we mean they have the same value.
4. The real number system. This will have to wait until the third lecture.

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