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Contemporary Mathematics

A liberal-arts tour of mathematics in use: logic, sets, number systems, personal finance, probability, statistics, geometry, voting and apportionment, and graph theory. The exercises practice quantitative reasoning on everyday questions of money, fairness, risk, and data.

Contemporary Mathematics

611 exercises94 sections

Status

Sections

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Sets

29

1.1 Basic Set Concepts10

1.3 Understanding Venn Diagrams1

1.4 Set Operations with Two Sets10

1.5 Set Operations with Three Sets1

Logic

33

2.1 Statements and Quantifiers7

2.2 Compound Statements4

2.3 Constructing Truth Tables6

2.4 Truth Tables for the Conditional and Biconditional4

2.5 Equivalent Statements4

2.6 De Morgan’s Laws5

2.7 Logical Arguments3

Real Number Systems and Number Theory

135

3.1 Prime and Composite Numbers23

3.2 The Integers13

3.3 Order of Operations8

3.4 Rational Numbers33

3.5 Irrational Numbers12

3.6 Real Numbers4

3.7 Clock Arithmetic5

3.8 Exponents10

3.9 Scientific Notation15

3.10 Arithmetic Sequences6

3.11 Geometric Sequences6

Number Representation and Calculation

36

4.1 Hindu-Arabic Positional System3

4.2 Early Numeration Systems2

4.3 Converting with Base Systems15

4.4 Addition and Subtraction in Base Systems10

4.5 Multiplication and Division in Base Systems6

Algebra

59

5.1 Algebraic Expressions11

5.2 Linear Equations in One Variable with Applications9

5.3 Linear Inequalities in One Variable with Applications3

5.4 Ratios and Proportions10

5.5 Graphing Linear Equations and Inequalities1

5.6 Quadratic Equations In One Variable with Applications9

5.8 Graphing Functions1

5.9 Systems of Linear Equations in Two Variables5

5.10 Systems of Linear Inequalities in Two Variables1

5.11 Linear Programming4

Money Management

119

6.1 Understanding Percent9

6.2 Discounts, Markups, and Sales Tax17

6.3 Simple Interest12

6.4 Compound Interest10

6.5 Making a Personal Budget6

6.6 Methods of Savings7

6.7 Investments14

6.8 The Basics of Loans3

6.9 Understanding Student Loans10

6.10 Credit Cards6

6.11 Buying or Leasing a Car12

6.12 Renting and Homeownership4

6.13 Income Tax9

Probability

30

7.1 The Multiplication Rule for Counting2

7.2 Permutations4

7.3 Combinations4

7.4 Tree Diagrams, Tables, and Outcomes3

7.5 Basic Concepts of Probability4

7.6 Probability with Permutations and Combinations2

7.7 What Are the Odds?2

7.8 The Addition Rule for Probability2

7.9 Conditional Probability and the Multiplication Rule2

7.10 The Binomial Distribution3

7.11 Expected Value2

Statistics

37

8.1 Gathering and Organizing Data4

8.2 Visualizing Data3

8.3 Mean, Median and Mode9

8.4 Range and Standard Deviation4

8.5 Percentiles3

8.6 The Normal Distribution6

8.7 Applications of the Normal Distribution2

8.8 Scatter Plots, Correlation, and Regression Lines6

Metric Measurement

47

9.1 The Metric System9

9.2 Measuring Area9

9.3 Measuring Volume11

9.4 Measuring Weight9

9.5 Measuring Temperature9

Geometry

11

10.4 Polygons, Perimeter, and Circumference3

10.7 Volume and Surface Area1

Voting and Apportionment

43

11.1 Voting Methods12

11.2 Fairness in Voting Methods5

11.3 Standard Divisors, Standard Quotas, and the Apportionment Problem7

11.4 Apportionment Methods11

11.5 Fairness in Apportionment Methods8

Graph Theory

10

12.1 Graph Basics2

12.2 Graph Structures2

12.5 Euler Circuits1

12.7 Hamilton Cycles3

12.9 Traveling Salesperson Problem2

Math and...

22

13.1 Math and Art4

13.2 Math and the Environment7

13.3 Math and Medicine4

13.4 Math and Music5

13.5 Math and Sports2

Adapted from Contemporary Mathematics © 2023 Rice University. Licensed under CC BY 4.0. Source: Contemporary Mathematics. Imported at revision fa7c1a1.