Math in Our World 13 9780073519678
Math in Our World

Math in Our World

Grade Levels: 13
By David Sobecki and Allan Bluman
Copyright: 2015
Publication Date: January 7, 2014
MHID: 0073519677
ISBN 13: 9780073519678

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Math in Our World

Mathematics in Our World, Third Edition

Chapter 1: Problem Solving

1-1 The Nature of Mathematical Reasoning

1-2 Estimation and Interpreting Graphs

1-3 Problem Solving Strategies

Chapter 1 Summary

Chapter 2: Sets

2-1 The Nature of Sets

2-2 Subsets and Set Operations

2-3 Using Venn Diagrams to Study Set Operations

2-4 Using Sets to Solve Problems

2-5 Infinite Sets

Chapter 2 Summary

Chapter 3: Logic

3-1 Statements and Quantifiers

3-2 Truth Tables

3-3 Types of Statements

3-4 Logical Arguments

3-5 Euler Circles

Chapter 3 Summary

Chapter 4: Numeration Systems

4-1 Early and Modern Numeration Systems

4-2 Tools and Algorithms in Arithmetic

4-3 Base Number Systems

4-4 Operations in Base Number Systems

Chapter 4 Summary

Chapter 5: The Real Number System

5-1 The Natural Numbers

5-2 The Integers

5-3 The Rational Numbers

5-4 The Irrational Numbers

5-5 The Real Numbers

5-6 Exponents and Scientific Notation

5-7 Arithmetic and Geometric Sequences

Chapter 5 Summary

Chapter 6: Topics in Algebra

6-1 The Fundamentals of Algebra

6-2 Solving Linear Equations

6-3 Applications of Linear Equations

6-4 Ratio, Proportion, and Variation

6-5 Solving Linear Inequalities

6-6 Solving Quadratic Equations

Chapter 6 Summary

Chapter 7: Additional Topics in Algebra

7-1 The Rectangular Coordinate System and Linear Equations in Two Variables

7-2 Systems of Linear Equations

7-3 Linear Inequalities

7-4 Linear Programming

7-5 Functions

7-6 Quadratic, Exponential, and Logarithmic Functions

7-7 Available Online: Solving Systems of Linear Equations Using Matrices

Chapter 7 Summary

Chapter 8: Consumer Mathematics

8-1 Percents

8-2 Simple Interest

8-3 Compound Interest

8-4 Installment Buying

8-5 Student Loans and Home Buying

8-6 Investing in Stocks and Bonds

Chapter 8 Summary

Chapter 9: Measurement

9-1 Measures of Length: Converting Units and the Metric System

9-2 Measures of Area, Volume, and Capacity

9-3 Measures of Weight and Temperature

Chapter 9 Summary

Chapter 10: Geometry

10-1 Points, Lines, Planes and Angles

10-2 Triangles

10-3 Polygons and Perimeter

10-4 Areas of Polygons and Circles

10-5 Volume and Surface Area

10-6 Right Triangle Trigonometry

10-7 A Brief Survey of Non-Euclidean and

Transformational Geometries

Chapter 10 Summary

Chapter 11: Probability and Counting Techniques

11-1 The Fundamental Counting Rule and Permutations

11-2 Combinations

11-3 Basic Concepts of Probability

11-4 Tree Diagrams, Tables, and Sample Spaces

11-5 Probability Using Permutations and Combinations

11-6 Odds and Expectation

11-7 The Addition Rules for Probability

11-8 The Multiplication Rules and Conditional


11-9 The Binomial Distribution

Chapter 11 Summary

Chapter 12: Statistics

12-1 Gathering and Organizing Data

12-2 Picturing Data

12-3 Measures of Average

12-4 Measures of Variation

12-5 Measures of Position

12-6 The Normal Distribution

12-7 Applications of the Normal Distribution

12-8 Correlation and Regression Analysis

Supplement: Misuses of Statistics

Chapter 12 Summary

Chapter 13: Voting Methods

13-1 Preference Tables and the Plurality Method

13-2 The Borda Count Method and the Plurality-with-Elimination Method

13-3 The Pairwise Comparison Method and Approval Voting

13-4 Apportionment

13-5 Apportionment Flaws

Chapter 13 Summary

Chapter 14: Graph Theory

14-1 Basic Concepts of Graph Theory

14-2 Euler’s Theorem

14-3 Hamilton Paths and Circuits

14-4 Trees

Chapter 14 Summary

Chapter 15-Available online: Other Mathematical Systems

15-1 Mathematical Systems and Groups

15-2 Clock Arithmetic

15-3 Modular Systems

Chapter 15 Review

Appendix A: Area Under the Standard Normal Distribution

Appendix B-Available Online: Using the TI-84 Plus Graphing Calculator

Selected Answers

Additional Exercise Sets

Answers to Additional Exercise Sets

Photo Credits


About the Author

David Sobecki

I was born and raised in Cleveland, and started college at Bowling Green State University in 1984 majoring in creative writing. Eleven years later, I walked across the graduation stage to receive a PhD in math, a strange journey indeed. After two years at Franklin and Marshall College in Pennsylvania, I came home to Ohio, accepting a tenure-track job at the Hamilton campus of Miami University. I’ve won a number of teaching awards in my career, and while maintaining an active teaching schedule, I now spend an inordinate amount of time writing textbooks and course materials. I’ve written or co-authored either seven or twelve textbooks, depending on how you count them, as well as several solutions manuals and interactive CD-ROMS. After many years as developmental math coordinator at Miami Hamilton, I share the frustration that goes along with low pass rates in the developmental math curriculum. Far too many students end up on the classic Jetson’s-style treadmill, with the abstract nature of the traditional algebra curriculum keeping them from reaching their goals. Like so many instructors across the country, I believe the time is right to move beyond the one-size-fits-all curriculum that treats students the same whether they hope to be an engineer or a pastry chef. “Because we’ve always done it that way” is NOT a good reason to maintain the status quo in our curriculum. Let’s work together to devise alternate pathways that help students to learn more and learn better while hastening their trip into credit-bearing math courses. Since my book (Math in Our World) is written for the Liberal Arts Math and Quantitative Literacy market, I think I’m in the right place at the right time to make a difference in the new and exciting pathways course. I’m in a very happy place right now: my love of teaching meshes perfectly with my childhood dream of writing. (Don’t tell my publisher this – they think I spend 20 hours a day working on textbooks – but I’m working on my first novel in the limited spare time that I have.) I’m also a former coordinator of Ohio Project NExT, as I believe very strongly in helping young college instructors focus on high-quality teaching as a primary career goal. I live in Fairfield, Ohio with my lovely wife Cat and fuzzy dogs Macleod and Tessa. When not teaching or writing, my passions include Ohio State football, Cleveland Indians baseball, heavy metal music, travel, golf, and home improvement.

Allan Bluman

Allan G. Bluman is a professor emeritus at the Community College of Allegheny County, South Campus, near Pittsburgh. He has taught mathematics and statistics for over 35 years. He received an Apple for the Teacher award in recognition of his bringing excellence to the learning environment at South Campus. He has also taught statistics for Penn State University at the Greater Allegheny (McKeesport) Campus and at the Monroeville Center. He received his master's and doctor's degrees from the University of Pittsburgh.

In addition to Elementary Statistics: A Step by Step Approach (Eighth Edition ©2012) and Elementary Statistics: A Brief Version (Fifth Edition ©2010), Al is a co-author on a liberal arts mathematics text published by McGraw-Hill, Math in Our World (2nd Edition ©2011). Al also the author of for mathematics books in the McGraw-Hill DeMystified Series. They are Pre-Algebra, Math Word Problems, Business Math, and Probability.

Al Bluman is married and has two sons and a granddaughter.