Math in Society

by David Lippman

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This book is a survey of contemporary mathematical topics, most non-algebraic, appropriate for a college-level quantitative literacy topics course for liberal arts majors. The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics.

Description from LibreTexts.

Publisher
Pierce College
Subjects
Mathematics
Licence
CC BY-SA 3.0, as LibreTexts states it
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. 1: Problem Solving
  2. 1.1: Introduction
  3. 1.2: Percents
  4. 1.3: Proportions and Rates
  5. 1.4: Geometry
  6. 1.5: Problem Solving and Estimating
  7. 1.6: Exercises
  8. 1.7: Extension - Taxes
  9. 1.8: Income Taxation
  10. 2: Geometry
  11. 2.1: Basic Geometric Concepts and Figures
  12. 2.2: Perimeter, Circumference, and Area
  13. 2.3: Volume of Geometric Solids
  14. 2.4: Exercises
  15. 3: Historical Counting Systems
  16. 3.1: The Evolution of Numeration Systems
  17. 3.2: The Number and Counting System of the Inca Civilization
  18. 3.3: The Hindu-Arabic Number System
  19. 3.4: The Development and Use of Different Number Bases
  20. 3.5: The Mayan Numeral System
  21. 3.6: Exercise
  22. 4: Saving
  23. 4.1: Introduction
  24. 4.2: Simple Interest
  25. 4.3: Compound Interest
  26. 5: Annuities and Loans
  27. 5.1: Annuities
  28. 5.2: Payout Annuities
  29. 5.3: Loans
  30. 5.4: Remaining Loan Balance
  31. 5.5: Which equation to use?
  32. 5.6: Solving for time
  33. 5.7: Exercises
  34. 6: Logic
  35. 6.1: Statements, Connectives, and Quantifiers
  36. 6.2: Truth Tables- Conjunction (and), Disjunction (or), Negation (not)
  37. 6.3: Truth Tables- Conditional, Biconditional
  38. 6.4: Verifying Arguments
  39. 7: Sets and Venn Diagrams
  40. 7.1: Basics of Sets
  41. 7.2: Union, Intersection, and Complement
  42. 7.3: Venn Diagrams
  43. 7.4: Cardinality
  44. 7.5: Exercises
  45. 8: Counting
  46. 8.1: The Fundamental Counting Principle
  47. 8.2: Permutations and Combinations
  48. 9: Probability
  49. 9.1: Introduction to Probability
  50. 9.2: Basic Concepts
  51. 9.3: Working with Events
  52. 9.4: Bayes Theorem
  53. 9.5: Counting
  54. 9.6: Expected Value
  55. 9.7: Exercises
  56. 10: Descriptive Statistics
  57. 10.1: Introduction
  58. 10.2: Populations and Samples
  59. 10.3: Categorizing data
  60. 10.4: Sampling methods
  61. 10.5: How to mess things up before you start
  62. 10.6: Experiments
  63. 10.7: Exercise
  64. 10.8: Presenting Categorical Data Graphically
  65. 10.9: Presenting Quantitative Data Graphically
  66. 10.10: Numerical Summaries of Data
  67. 10.11: Measures of Central Tendency
  68. 10.12: Measures of Variation
  69. 10.13: Exercises
  70. 11: Normal Distribution
  71. 11.1: The Standard Normal Probability Distribution
  72. 11.2: The Density Curve of a Normal Distribution
  73. 11.3: Application of Normal Distributions
  74. 11.4: The Central Limit Theorem
  75. 11.5: Exercises
  76. 12: Confidence Intervals and Hypothesis Tests
  77. 12.1: Confidence Intervals
  78. 12.2: Confidence Intervals and Sample Size for Proportions
  79. 12.3: Steps in Hypothesis Testing
  80. 12.3.1: Null and Alternative Hypotheses
  81. 12.3.2: Outcomes and the Type I and Type II Errors
  82. 12.3.3: Distribution Needed for Hypothesis Testing
  83. 12.3.4: Rare Events, the Sample, Decision and Conclusion
  84. 12.3.5: Additional Information on Hypothesis Tests
  85. 12.4: Hypothesis Test Examples for Proportions
  86. 12.E: Confidence Intervals (Optional Exercises)
  87. 1.E: Confidence Intervals for the Mean with Known Standard Deviation (Optional Exercises)
  88. 1.E: Hypothesis Testing (Optional Exercises)
  89. 13: Graph Theory
  90. 13.1: Introduction
  91. 13.2: Graphs
  92. 13.3: Shortest Path
  93. 13.4: Euler Circuits and the Chinese Postman Problem
  94. 13.5: Eulerization and the Chinese Postman Problem
  95. 13.6: Hamiltonian Circuits and the Traveling Salesman Problem
  96. 13.7: Spanning Trees
  97. 13.8: Exercise
  98. 14: Solutions to Selected Exercises
  99. 14.1: Problem Solving
  100. 14.2: Geometry
  101. 14.3: Historical Counting
  102. 14.4: Sets
  103. 14.5: Probability
  104. 14.6: Statistics
  105. 14.6.1: Describing Data
  106. 14.7: Saving
  107. 14.8: Annuities and Loans
  108. 14.9: Confidence Intervals and Hypothesis Tests
  109. 14.10: Graph Theory
  110. 14.11: Normal
  111. Front Matter
  112. TitlePage
  113. InfoPage
  114. Table of Contents
  115. Credit List
  116. Licensing
  117. Back Matter
  118. Index
  119. Glossary
  120. Detailed Licensing