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Summary
The author team of Dave Sobecki and Allan Bluman created an engaging text and digital program aimed at meeting the needs of today’s liberal arts math students, resulting in the third edition of Math in Our World. This revision focused on further development of critical thinking skills through several hundred revised exercises and examples, still presented within the hallmark style of the Math in Our World program. Carefully chosen questions help students to form a connection between relevant examples and the mathematical concepts of the chapter. Using the engaging writing style characteristic of the text, the authors support concepts through abundant examples, helpful practice problems, and rich exercise sets. The author team was also deeply engaged in the development of the Connect and LearnSmart online content
to help ensure a consistent experience for students regardless of medium. The result is an exceptionally engaging program that is able to both effectively and creatively convey the fundamental concepts of a liberal arts math curriculum to even the most hesitant student.
Table of Contents
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
Probability
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