Discovering Mathematics,
2nd Edition

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.

• Richard N. Aufmann

  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.

• NEW AND REFRESHED APPLICATION PROBLEMS DEMONSTRATE THE RELEVANCE OF EACH TOPIC. Updated applications include recent data from the U.S. Census Bureau and technology students constantly use.

• MORE EXPLANATION OF FAIR DIVISION GUIDES STUDENT LEARNING: More detail was added to examples to help students understand this interesting, yet challenging, topic.

• MORE EMPHASIS ON PRACTICAL APPLICATION OF NONLINEAR FUNCTIONS: CHAPTER 6, Nonlinear Functions, has been revised to put more emphasis on the practical applications of those functions to provide relevancy to students' lives.

• EXCEL HAS BEEN INTEGRATED INTO WEBASSIGN: Students can use this tool to solve problems for finance and statistics exercises. Spreadsheet templates are provided to the student for exercises that are data intensive.

• REIMAGINED PROBLEM TYPES PROVIDE RELEVANCE AND EMPOWER STUDENTS: Traditional skill-building problems are recreated as word problems, providing context to the content and allowing students to practice interpreting and extracting data from sentences. This integration of skill-building and applications establishes the importance of mathematics in everyday life.

• PRELIMINARY EXERCISES PROVIDE ADDITIONAL PRACTICE: Located at the beginning of each problem set, Preliminary Exercises provide an opportunity for the student to practice an exercise that is very similar to a worked example in the text. A complete solution for each Preliminary Exercise can be found in a solution section of the text.

• NEW END OF CHAPTER, MULTI-PART EXERCISES DEMONSTRATE "MATH AT WORK": Math in Practice exercises expand on chapter learning objectives with real-world, applicable situations students can relate to in their daily lives, or their intended career tracks.

• NEW LEARN IT MODULES ADDRESS STUDENTS’ KNOWLEDGE GAPS: Offering scaffolded help, Learn It modules provide just-in-time instruction that meets students’ diverse learning styles. Learn Its provide immediate, targeted instruction and practice for a topic. Explanations include clear narratives, videos and tutorials—all in one place.

Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.

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