Instructor: Dr. Peter Tannenbaum
Office: Peters Business Building 343
e-mail: petert@csufresno.edu

TEXTBOOK: Algebra, by I. M. Gelfand and A. Shen (Birkhauser, 1993).


COURSE OBJECTIVES
Good mathematics teachers at all levels (but particularly for grades 6 through 12) should have an understanding of algebraic thinking and algebraic ideas that goes deeper than that provided by the typical skills oriented algebra courses. The purpose of this course is to provide this deeper understanding of algebra by looking at the "larger picture": What are the unifying ideas in algebra? How are the major themes interrelated? How and why we teach what we teach? What should and shouldn't we teach?


PREREQUISITES
This course assumes that the student is already familiar with the basic algebraic skills that are part of the traditional high school algebra curriculum. (Students who need a basic introduction to high school algebra should not enroll in this course).

TENTATIVE COURSE OUTLINE

Part 1. Arithmetic Revisited (approx 4 lectures).
Integers; Rational Numbers (Fractions and Decimals); Exponents (positive and negative integers); Square Roots; Irrational Numbers.

Part 2. Arithmetic with Symbols: The Birth of Algebra (approx. 6 lectures).
Symbolic Addition ("terms") and Symbolic Multiplication ("factors); Parsing an Algebraic Expression; A Few Fundamental Principles; The Distributive Law and its Progeny; Symbolic squaring (the square of a sum; the difference of squares); Powers of sums; The Binomial Theorem; Pascal's triangle.

Part 3: Polynomials and Rational Expressions (approx. 6 lectures).
Speaking of Polynomials; Addition and multiplication of polynomials; Factoring Polynomials; Division of polynomials (the long and the short); The Remainder Theorem; Rational Expressions.

Part 4: Equations (approx. 6 lectures).
The language of equations; Equations vs Identities; Linear Equations; Quadratic Equations; Graphing Parabolas; Higher Order Polynomial Equations.

Part 5: Miscellaneous but Important (approx. 4 lectures).
Radicals and Fractional Exponents; Arithmetic sequences; Geometric sequences.

GRADING
oThree midterm exams (20% each) [late Feb.; end of March and end of April].
oFinal exam (25%) [Monday, May 21, 3:30-5:30 PM].
oMiscellaneous and sundry assignments (15%).

GRADES
A: 85-100%; B: 75-85%; C: 65-75%; D: 50-65%; F: less than 50%.