Discovering Mathematics

Richard Aufmann is the lead author of two best-selling DEVELOPMENTAL MATH series and a best-selling COLLEGE ALGEBRA AND TRIGONOMETRY series, as well as several derivative math texts. Mr. Aufmann taught math, computer science and physics at Palomar College in California, where he was on the faculty for 28 years. His textbooks are highly recognized and respected among college mathematics professors. Today, Mr. Aufmann's professional interests include quantitative literacy, the developmental math curriculum and the impact of technology on curriculum development. He holds a Bachelor of Arts in Mathematics from the University of California, Irvine and a Master of Arts degree in Mathematics from California State University, Long Beach.

Module 1: VALIDITY STUDIES.
1. An Introduction to Problem Solving.
Inductive and Deductive Reasoning. Estimation and Graphs. Problem-Solving Strategies. Fair Division.
2. Sets and Logic.
Sets, Set Operations, and Applications. Categorical Logic. Propositional Logic. Investigating Fallacies.
3. Proportions and Variation.
Ratios and Rates. Measurement. Proportions. Percent. Variation.
Module 2: FINANCIAL LITERACY.
4. Managing Your Finances.
Simple Interest. Compound Interest. Future and Present Value of an Annuity. Credit Cards. Student Loans. Financial Considerations of Car Ownership. Financial Considerations of Home Ownership. Stocks, Bonds, and Mutual Funds.
Module 3: MODELING.
5. Linear Functions.
Introduction to Functions. Properties of Linear Functions. Linear Models.
6. Nonlinear Functions.
Exponential Models. Logarithmic Functions. Quadratic Functions.
Module 4: PROBABILITY AND STATISTICS.
7. Introduction to Probability.
The Counting Principle. Permutations and Combinations. Probability and Odds. Addition and Complement Rules. Conditional Probability. Expectations.
8. Introduction to Statistics.
Measures of Central Tendency. Measures of Dispersion. Measures of Relative Position. Normal Distributions. Linear Regression and Correlation.
Module 5: ADDITIONAL TOPICS.
9. Voting and Apportionment.
Introduction to Apportionment. Introduction to Voting. Weighted Voting Systems.
10. Circuits and Networks.
Graphs and Euler Circuits. Weighted Graphs. Planarity and Euler’s Formula. Graph Coloring.
11. Geometry.
Measurement. Basic Concepts of Euclidean Geometry. Perimeter and Area of Plane Figures. Volume and Surface Area. Properties of Triangles. Right Triangle Trigonometry. Non-Euclidean Geometry. Fractals.
APPENDICES (AVAILABLE UPON REQUEST. CHECK WITH YOUR CENGAGE LEARNING SALES REPRESENTATIVE).
Appendix A: A Review of Integers, Rational Numbers, and Percents.
Appendix B: Variable Expressions and Equations.
Appendix C: Review of the Rectangular Coordinates and Graphing.
SELECTED ANSWERS.
SOLUTIONS TO PRELIMINARY EXERCISES.
INDEX.