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, Applied 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

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  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Problem Solving
  7. 1.1: Introduction
  8. 1.2: Percents
  9. 1.3: Proportions and Rates
  10. 1.4: Geometry
  11. 1.5: Problem Solving and Estimating
  12. 1.6: Exercises
  13. 1.7: Extension - Taxes
  14. 1.8: Income Taxation
  15. 2: Voting Theory
  16. 2.1: Introduction
  17. 2.2: Preference Schedules
  18. 2.3: Plurality
  19. 2.4: What’s Wrong with Plurality?
  20. 2.5: Insincere Voting
  21. 2.6: Instant Runoff Voting
  22. 2.7: What’s Wrong with IRV?
  23. 2.8: Borda Count
  24. 2.9: What’s Wrong with Borda Count?
  25. 2.10: Copeland’s Method (Pairwise Comparisons)
  26. 2.11: What’s Wrong with Copeland’s Method?
  27. 2.12: So Where’s the Fair Method?
  28. 2.13: Approval Voting
  29. 2.14: What’s Wrong with Approval Voting?
  30. 2.15: Voting in America
  31. 2.16: Exercises
  32. 2.17: Concepts
  33. 2.18: Exploration
  34. 3: Weighted Voting
  35. 3.1: Introduction
  36. 3.2: Beginnings
  37. 3.3: A Look at Power
  38. 3.4: Calculating Power- Banzhaf Power Index
  39. 3.5: Calculating Power- Shapley-Shubik Power Index
  40. 3.6: Exercises(Skills)
  41. 3.7: Exercises(Concepts)
  42. 3.8: Exercises(Exploration)
  43. 4: Apportionment
  44. 4.1: Introduction
  45. 4.2: Hamilton’s Method
  46. 4.3: Jefferson’s Method
  47. 4.4: Webster’s Method
  48. 4.5: Huntington-Hill Method
  49. 4.6: Lowndes’ Method
  50. 4.7: Apportionment of Legislative Districts
  51. 4.8: Exercises
  52. 5: Fair Division
  53. 5.1: Introduction
  54. 5.2: Divider-Chooser
  55. 5.3: How not to divide with 3 parties
  56. 5.4: Lone Divider
  57. 5.5: Last Diminisher
  58. 5.6: Moving Knife
  59. 5.7: Sealed Bids Method
  60. 5.8: Exercises-1- Skills
  61. 5.9: Exercise-2- Exploration
  62. 6: Graph Theory
  63. 6.1: Introduction
  64. 6.2: Graphs
  65. 6.3: Shortest Path
  66. 6.4: Euler Circuits and the Chinese Postman Problem
  67. 6.5: Eulerization and the Chinese Postman Problem
  68. 6.6: Hamiltonian Circuits and the Traveling Salesman Problem
  69. 6.7: Spanning Trees
  70. 6.8: Exercise
  71. 7: Scheduling
  72. 7.1: Introduction
  73. 7.2: Getting Started
  74. 7.3: Adding an algorithm
  75. 7.4: Choosing a Priority List
  76. 7.5: Exercises
  77. 8: Growth Models
  78. 8.1: Introduction
  79. 8.2: Linear (Algebraic) Growth
  80. 8.3: When good models go bad
  81. 8.4: Exponential (Geometric) Growth
  82. 8.5: Solving Exponentials for Time- Logarithms
  83. 8.6: Logistic Growth
  84. 8.7: Exercises
  85. 9: Finance
  86. 9.1: Introduction
  87. 9.2: Simple Interest
  88. 9.3: Compound Interest
  89. 9.4: Annuities
  90. 9.5: Payout Annuities
  91. 9.6: Loans
  92. 9.7: Remaining Loan Balance
  93. 9.8: Which equation to use?
  94. 9.9: Solving for time
  95. 9.10: Exercises
  96. 10: Statistics
  97. 10.1: Introduction
  98. 10.2: Populations and Samples
  99. 10.3: Categorizing data
  100. 10.4: Sampling methods
  101. 10.5: How to mess things up before you start
  102. 10.6: Experiments
  103. 10.7: Exercise
  104. 11: Describing Data
  105. 11.2: Presenting Categorical Data Graphically
  106. 11.3: Presenting Quantitative Data Graphically
  107. 11.4: Numerical Summaries of Data
  108. 11.5: Measures of Central Tendency
  109. 11.6: Measures of Variation
  110. 11.7: Exercises
  111. 12: Probability
  112. 12.1: Introduction to Probability
  113. 12.2: Basic Concepts
  114. 12.3: Working with Events
  115. 12.4: Bayes Theorem
  116. 12.5: Counting
  117. 12.6: Expected Value
  118. 12.7: Exercises
  119. 13: Sets
  120. 13.1: Basics of Sets
  121. 13.2: Union, Intersection, and Complement
  122. 13.3: Venn Diagrams
  123. 13.4: Cardinality
  124. 13.5: Exercises
  125. 14: Historical Counting Systems
  126. 14.1: Introduction and Basic Number and Counting Systems
  127. 14.2: The Number and Counting System of the Inca Civilization
  128. 14.3: The Hindu-Arabic Number System
  129. 14.4: The Development and Use of Different Number Bases
  130. 14.5: The Mayan Numeral System
  131. 14.6: Exercise
  132. 15: Fractals
  133. 15.1: Fractals
  134. 15.2: Iterated Fractals
  135. 15.3: Fractal Dimension
  136. 15.4: Complex Numbers
  137. 15.5: Complex Recursive Sequences
  138. 15.6: Exercises
  139. 16: Cryptography
  140. 16.1: Cryptography
  141. 16.2: Substitution Ciphers
  142. 16.3: Transposition Ciphers
  143. 16.4: Advanced shared symmetric-key methods
  144. 16.5: Public Key Cryptography
  145. 16.6: Other Secret Keeping Methods
  146. 16.7: The One-Way Function
  147. 16.8: The key exchange
  148. 17: Logic
  149. 17.1: Logic
  150. 17.2: Boolean Logic
  151. 17.3: Conditional Statements
  152. 17.4: Quantified Statements
  153. 17.5: Truth Tables: Conjunction (and), Disjunction (or), Negation (not)
  154. 17.6: Truth Tables: Conditional, Biconditional
  155. 17.10: Evaluating Deductive Arguments with Truth Tables
  156. 17.11: Forms of Valid Arguments
  157. 17.12: Logical Fallacies in Common Language
  158. 17.13: Exercises
  159. 17.7: De Morgan’s Laws
  160. 17.8: Arguments
  161. 17.9: Evaluating Deductive Arguments with Euler Diagrams
  162. 18: Solutions to Selected Exercises
  163. 18.1: Problem Solving
  164. 18.2: Voting Theory
  165. 18.3: Weighted Voting
  166. 18.4: Fair Division
  167. 18.5: Apportionment
  168. 18.6: Graph Theory
  169. 18.10: Statistics
  170. 18.11: Describing Data
  171. 18.12: Probability
  172. 18.13: Sets
  173. 18.14: Historical Counting
  174. 18.15: Fractals
  175. 18.16: Cryptography
  176. 18.17: Logic
  177. 18.7: Scheduling
  178. 18.8: Growth Models
  179. 18.9: Finance
  180. Back Matter
  181. Index
  182. Index
  183. Detailed Licensing