Lecture 2: Classification of Functions

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Reminder: The class will meet in room 420 of Fretwell on Friday, January 16. A representative of computer services will help you access your Eudora account. Please bring a 3 1/2 diskette to this class.

Brief review of the lecture

This is a summary of the second lecture in Math 1100 last semester, left here because it is relevant to this course. We will spend very little time on this material since you have all studied this. 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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