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Discovering Mathematics: A Quantitative Reasoning Approach, 1st Edition

Richard Aufmann

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  • ISBN-10: 0357028112
  • ISBN-13: 9780357028117
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Overview

Aufmann’s DISCOVERING MATHEMATICS: A QUANTITATIVE REASONING APPROACH with WebAssign is designed for today’s Quantitative Reasoning course. This series focuses on topics relevant to students’ lives and develops critical-thinking skills they can apply beyond the course. Flexible for all teaching models--from lecture, hybrid or fully online to flipped and active-learning environments--DISCOVERING MATHEMATICS: A QUANTITATIVE REASONING APPROACH will empower you to accomplish all your course objectives.

Richard Aufmann, Palomar College

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.

WebAssign is a flexible and fully customizable online instructional solution that puts powerful tools in the hands of teachers, enabling you to realize your teaching goals and instantly assess individual student performance to help students learn math, not just do online homework.

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  • NOTE: This title is also available in WebAssign with Corequisite Support that provides the flexibility to match any corequisite implementation model and empowers you to deliver high quality content at the right time for your students at an affordable price.
  • CHAPTER OPENER. Organized to give students mathematical context for the material they are about to learn, the Chapter Opener provides an at-a-glance preview of the main ideas and topics in a concise, easy-to-navigate way.
  • INFOGRAPHICS. An engaging alternative to photos and art in the margins, Infographics combine a visual break in the narrative with illustrated concepts that are purposeful, informative and that take concepts beyond the course.
  • SHORT PROJECTS & INVESTIGATIONS. Perfect for group work and class discussion, these activities guide students on how to navigate and organize their work. Select projects are coded and assignable in WebAssign.
  • EXAMPLES. Practice problems at the beginning of the exercise set tie directly into examples from the preceding section, helping students build skills and preparing them for more robust applications of the material.

Discovering Mathematics: A Quantitative Reasoning Approach

TABLE OF CONTENTS

MODULE 1: VALIDITY STUDIES.
1. An Introduction to Problem Solving.
Inductive and Deductive Reasoning. Estimation of Graphs. Problem-Solving Strategies. Fair Division.
2. Sets and Logic.
Sets, Set Operations, and Applications. Categorical Logic. Prepositional 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. Linear Regression and Correlation.
6. Nonlinear Functions.
Exponential Models. Logarithmic Functions. Quadratic Functions.
MODULE 4: OPTIONAL CHAPTERS (AVAILABLE UPON REQUEST. CHECK WITH YOUR CENGAGE LEARNING SALES REPRESENTATIVE.)
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.
9. Voting 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).
A: A Review of Integers, Rational Numbers, and Percents
B: Variable Expressions and Equations
C: Review of the Rectangular Coordinates and Graphing

SELECTED ANSWERS
SOLUTIONS TO PRELIMINARY EXERCISES
INDEX

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FOR INSTRUCTORS

Instructor's Toolkit with Complete Solutions Manual

ISBN: 9780357028292
Resource manual containing lesson plans, discussion topics, and support for all teaching models. Also contains a complete solutions manual.

Instructor's Website with PowerPoint, Image Library

ISBN: 9780357028070
Microsoft® PowerPoint slides let you incorporate images from the book right into your lectures.

Cengage Testing, powered by Cognero® Instant Access

ISBN: 9780357025642
Cengage Testing, Powered by Cognero® is a flexible online system that allows you to author, edit and manage test bank content; create multiple test versions in an instant; and deliver tests from your LMS, your classroom or wherever you want. Available online at login.cengage.com.