MAT 310 Bridge to Advanced Mathematics

by Richard Hammack

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This book will initiate you into an esoteric world. You will learn and apply the methods of thought that mathematicians use to verify theorems, explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics.

Description from LibreTexts.

Publisher
Virginia Commonwealth University
Subjects
Mathematics
Licence
CC BY-NC-ND, as LibreTexts states it. Non-commercial use only, and no changed versions.
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: Sets
  7. 1.1: Introduction to Sets
  8. 1.2: The Cartesian Product
  9. 1.3: Subsets
  10. 1.4: Power Sets
  11. 1.5: Union, Intersection, Difference
  12. 1.6: Complement
  13. 1.7: Venn Diagrams
  14. 1.8: Indexed Sets
  15. 1.8: Sets That Are Number Systems
  16. 1.9: Russell’s Paradox
  17. 2: Logic
  18. 2.0: Statement
  19. 2.1: And, Or, Not
  20. 2.2: Conditional Statements
  21. 2.3: Biconditional Statements
  22. 2.4: Truth Tables for Statements
  23. 2.5: Logical Equivalence
  24. 2.6: Quantifiers
  25. 2.7: More on Conditional Statements
  26. 2.8: Translating English to Symbolic Logic
  27. 2.9: Negating Statements
  28. 2.10: Logical Inference
  29. 2.11: An Important Note
  30. 3: Counting
  31. 3.0: Lists
  32. 3.1: The Multiplication Principle
  33. 3.2: The Addition and Subtraction Principles
  34. 3.3: Factorials and Permutations
  35. 3.4: Counting Subsets
  36. 3.5: Pascal’s Triangle and the Binomial Theorem
  37. 3.6: The Inclusion-Exclusion Principle
  38. 3.7: Counting Multisets
  39. 3.8: New Page
  40. 3.9: New Page
  41. 4: Direct Proof
  42. 4.1: Section 1-
  43. 4.2: Section 2-
  44. 4.3: Section 3-
  45. 4.4: Section 4-
  46. 4.5: Section 5-
  47. 4.6: Section 6-Exercises
  48. 5: Contrapositive Proof
  49. 5.1: Section 1-
  50. 5.2: Section 2-
  51. 5.3: Section 3-
  52. 5.4: Section 4-
  53. 5.5: Section 5-
  54. 5.6: Section 6-
  55. 6: Proof by Contradiction
  56. 6.0: Section 1-
  57. 6.1: Section 2-
  58. 6.2: Section 3-
  59. 6.3: Section 4-
  60. 6.4: Section 5-
  61. 6.5: Section 6-
  62. 7: Proving Non-Conditional Statements
  63. 7.0: Section 1-
  64. 7.1: Section 2-
  65. 7.2: Section 3-
  66. 7.3: Section 4-
  67. 7.4: Section 5-
  68. 7.5: Section 6-
  69. 8: Proofs Involving Sets
  70. 8.0: Section 1-
  71. 8.1: Section 2-
  72. 8.2: Section 3-
  73. 8.3: Section 4-
  74. 9: Disproof
  75. 9.0: Section 1-
  76. 9.1: Section 2-
  77. 9.2: Section 3-
  78. 9.3: Section 4-
  79. 9.4: Section 5-
  80. 9.5: Section 6-
  81. 10: Mathematical Induction
  82. 10.0: Section 1-
  83. 10.1: Section 2-
  84. 10.2: Section 3-
  85. 10.3: Section 4-
  86. 10.4: Section 5-
  87. 10.5: Section 6-
  88. 11: Relations
  89. 11.0: Section 1-
  90. 11.1: Section 2-
  91. 11.2: Section 3-
  92. 11.3: Section 4-
  93. 11.4: Section 5-
  94. 11.5: Section 6-
  95. 12: Functions
  96. 12.0: Section 1-
  97. 12.1: Section 2-
  98. 12.2: Section 3-
  99. 12.3: Section 4-
  100. 12.4: Section 5-
  101. 12.5: Section 6-
  102. 13: Proofs in Calculus
  103. 13.0: Section 1-
  104. 13.1: Section 2-
  105. 13.2: Section 3-
  106. 13.3: Section 4-
  107. 13.4: Section 5-
  108. 13.5: Section 6-
  109. 14: Cardinality of Sets
  110. 14.0: Section 1-
  111. 14.1: Section 2-
  112. 14.2: Section 3-
  113. 14.3: Section 4-
  114. 14.4: Section 5-
  115. 14.5: Section 6-
  116. Back Matter
  117. Index
  118. Glossary
  119. Detailed Licensing