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Math in Society

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Math in Society

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.

Applied MathematicsMathematics
Author
David Lippman
Publisher
Pierce College
Source
LibreTexts
License
CC BY-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 174 sections
  1. 01: Problem Solving
  2. 1.01: Introduction
  3. 1.02: Percents
  4. 1.03: Proportions and Rates
  5. 1.04: Geometry
  6. 1.05: Problem Solving and Estimating
  7. 1.06: Exercises
  8. 1.07: Extension - Taxes
  9. 1.08: Income Taxation
  10. 02: Voting Theory
  11. 2.01: Introduction
  12. 2.02: Preference Schedules
  13. 2.03: Plurality
  14. 2.04: Whats Wrong with Plurality
  15. 2.05: Insincere Voting
  16. 2.06: Instant Runoff Voting
  17. 2.07: Whats Wrong with IRV
  18. 2.08: Borda Count
  19. 2.09: Whats Wrong with Borda Count
  20. 2.10: Copelands Method (Pairwise Comparisons)
  21. 2.11: Whats Wrong with Copelands Method
  22. 2.12: So Wheres the Fair Method
  23. 2.13: Approval Voting
  24. 2.14: Whats Wrong with Approval Voting
  25. 2.15: Voting in America
  26. 2.16: Exercises
  27. 2.17: Concepts
  28. 2.18: Exploration
  29. 03: Weighted Voting
  30. 3.01: Introduction
  31. 3.02: Beginnings
  32. 3.03: A Look at Power
  33. 3.04: Calculating Power- Banzhaf Power Index
  34. 3.05: Calculating Power- Shapley-Shubik Power Index
  35. 3.06: Exercises(Skills)
  36. 3.07: Exercises(Concepts)
  37. 3.08: Exercises(Exploration)
  38. 04: Apportionment
  39. 4.01: Introduction
  40. 4.02: Hamiltons Method
  41. 4.03: Jeffersons Method
  42. 4.04: Websters Method
  43. 4.05: Huntington-Hill Method
  44. 4.06: Lowndes Method
  45. 4.07: Apportionment of Legislative Districts
  46. 4.08: Exercises
  47. 05: Fair Division
  48. 5.01: Introduction
  49. 5.02: Divider-Chooser
  50. 5.03: How not to divide with 3 parties
  51. 5.04: Lone Divider
  52. 5.05: Last Diminisher
  53. 5.06: Moving Knife
  54. 5.07: Sealed Bids Method
  55. 5.08: Exercises-1- Skills
  56. 5.09: Exercise-2- Exploration
  57. 06: Graph Theory
  58. 6.01: Introduction
  59. 6.02: Graphs
  60. 6.03: Shortest Path
  61. 6.04: Euler Circuits and the Chinese Postman Problem
  62. 6.05: Eulerization and the Chinese Postman Problem
  63. 6.06: Hamiltonian Circuits and the Traveling Salesman Problem
  64. 6.07: Spanning Trees
  65. 6.08: Exercise
  66. 07: Scheduling
  67. 7.01: Introduction
  68. 7.02: Getting Started
  69. 7.03: Adding an algorithm
  70. 7.04: Choosing a Priority List
  71. 7.05: Exercises
  72. 08: Growth Models
  73. 8.01: Introduction
  74. 8.02: Linear (Algebraic) Growth
  75. 8.03: When good models go bad
  76. 8.04: Exponential (Geometric) Growth
  77. 8.05: Solving Exponentials for Time- Logarithms
  78. 8.06: Logistic Growth
  79. 8.07: Exercises
  80. 09: Finance
  81. 9.01: Introduction
  82. 9.02: Simple Interest
  83. 9.03: Compound Interest
  84. 9.04: Annuities
  85. 9.05: Payout Annuities
  86. 9.06: Loans
  87. 9.07: Remaining Loan Balance
  88. 9.08: Which equation to use
  89. 9.09: Solving for time
  90. 9.10: Exercises
  91. 10: Statistics
  92. 10.01: Introduction
  93. 10.02: Populations and samples
  94. 10.03: Categorizing data
  95. 10.04: Sampling methods
  96. 10.05: How to mess things up before you start
  97. 10.06: Experiments
  98. 10.07: Exercise
  99. 11: Describing Data
  100. 11.02: Presenting Categorical Data Graphically
  101. 11.03: Presenting Quantitative Data Graphically
  102. 11.04: Numerical Summaries of Data
  103. 11.05: Measures of Central Tendency
  104. 11.06: Measures of Variation
  105. 11.07: Exercises
  106. 12: Probability
  107. 12.01: Introduction to Probability
  108. 12.02: Basic Concepts
  109. 12.03: Working with Events
  110. 12.04: Bayes Theorem
  111. 12.05: Counting
  112. 12.06: Expected Value
  113. 12.07: Exercises
  114. 13: Sets
  115. 13.01: Basics of Sets
  116. 13.02: Union Intersection and Complement
  117. 13.03: Venn Diagrams
  118. 13.04: Cardinality
  119. 13.05: Exercises
  120. 14: Historical Counting Systems
  121. 14.01: Introduction and Basic Number and Counting Systems
  122. 14.02: The Number and Counting System of the Inca Civilization
  123. 14.03: The Hindu-Arabic Number System
  124. 14.04: The Development and Use of Different Number Bases
  125. 14.05: The Mayan Numeral System
  126. 14.06: Exercise
  127. 15: Fractals
  128. 15.01: Fractals
  129. 15.02: Iterated Fractals
  130. 15.03: Fractal Dimension
  131. 15.04: Complex Numbers
  132. 15.05: Complex Recursive Sequences
  133. 15.06: Exercises
  134. 16: Cryptography
  135. 16.01: Cryptography
  136. 16.02: Substitution Ciphers
  137. 16.03: Transposition Ciphers
  138. 16.04: Advanced shared symmetric-key methods
  139. 16.05: Public Key Cryptography
  140. 16.06: Other Secret Keeping Methods
  141. 16.07: The One-Way Function
  142. 16.08: The key exchange
  143. 17: Logic
  144. 17.01: Logic
  145. 17.02: Boolean Logic
  146. 17.03: Conditional Statements
  147. 17.04: Section 4-
  148. 17.05: Section 5-
  149. 17.06: Section 6-
  150. 17.7: De Morgans Laws
  151. 17.8: Arguments
  152. 17.9: Evaluating Deductive Arguments with Euler Diagrams
  153. 17.10: Evaluating Deductive Arguments with Truth Tables
  154. 17.11: Forms of Valid Arguments
  155. 17.12: Logical Fallacies in Common Language
  156. 17.13: Exercises
  157. 18: Solutions to Selected Exercises
  158. 18.01: Section 1-
  159. 18.02: Section 2-
  160. 18.03: Section 3-
  161. 18.04: Section 4-
  162. 18.05: Section 5-
  163. 18.06: Section 6-
  164. 18.7: Scheduling
  165. 18.8: Growth Models
  166. 18.9: Finance
  167. 18.10: Statistics
  168. 18.11: Describing Data
  169. 18.12: Probability
  170. 18.13: Sets
  171. 18.14: Historical Counting
  172. 18.15: Fractals
  173. 18.16: Cryptography
  174. 18.17: Logic