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MAT 310 Bridge to Advanced Mathematics

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MAT 310 Bridge to Advanced Mathematics

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.

Mathematics
Author
Richard Hammack
Publisher
Virginia Commonwealth University
Source
LibreTexts
License
CC BY-NC-ND
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 110 sections
  1. 01: Sets
  2. 1.01: Introduction to Sets
  3. 1.02: The Cartesian Product
  4. 1.03: Subsets
  5. 1.04: Power Sets
  6. 1.05: Union Intersection Difference
  7. 1.06: Complement
  8. 1.07: Venn Diagrams
  9. 1.08: Indexed Sets
  10. 1.08: Sets That Are Number Systems
  11. 1.09: Russells Paradox
  12. 02: Logic
  13. 2.00: Statement
  14. 2.01: And Or Not
  15. 2.02: Conditional Statements
  16. 2.03: Biconditional Statements
  17. 2.04: Truth Tables for Statements
  18. 2.05: Logical Equivalence
  19. 2.06: Quantifiers
  20. 2.07: More on Conditional Statements
  21. 2.08: Translating English to Symbolic Logic
  22. 2.09: Negating Statements
  23. 2.10: Logical Inference
  24. 2.11: An Important Note
  25. 03: Counting
  26. 3.00: Lists
  27. 3.01: The Multiplication Principle
  28. 3.02: The Addition and Subtraction Principles
  29. 3.03: Factorials and Permutations
  30. 3.04: Counting Subsets
  31. 3.05: Pascals Triangle and the Binomial Theorem
  32. 3.06: The Inclusion-Exclusion Principle
  33. 3.07: Counting Multisets
  34. 3.08: New Page
  35. 3.09: New Page
  36. 04: Direct Proof
  37. 4.01: Section 1-
  38. 4.02: Section 2-
  39. 4.03: Section 3-
  40. 4.04: Section 4-
  41. 4.05: Section 5-
  42. 4.06: Section 6-Exercises
  43. 05: Contrapositive Proof
  44. 5.01: Section 1-
  45. 5.02: Section 2-
  46. 5.02: Section 3-
  47. 5.04: Section 4-
  48. 5.05: Section 5-
  49. 5.06: Section 6-
  50. 06: Proof by Contradiction
  51. 6.00: Section 1-
  52. 6.01: Section 2-
  53. 6.02: Section 3-
  54. 6.03: Section 4-
  55. 6.04: Section 5-
  56. 6.05: Section 6-
  57. 07: Proving Non-Conditional Statements
  58. 7.00: Section 1-
  59. 7.01: Section 2-
  60. 7.02: Section 3-
  61. 7.03: Section 4-
  62. 7.04: Section 5-
  63. 7.05: Section 6-
  64. 08: Proofs Involving Sets
  65. 8.00: Section 1-
  66. 8.01: Section 2-
  67. 8.02: Section 3-
  68. 8.03: Section 4-
  69. 09: Disproof
  70. 9.00: Section 1-
  71. 9.01: Section 2-
  72. 9.02: Section 3-
  73. 9.03: Section 4-
  74. 9.04: Section 5-
  75. 9.05: Section 6-
  76. 10: Mathematical Induction
  77. 10.00: Section 1-
  78. 10.01: Section 2-
  79. 10.02: Section 3-
  80. 10.03: Section 4-
  81. 10.04: Section 5-
  82. 10.05: Section 6-
  83. 11: Relations
  84. 11.00: Section 1-
  85. 11.01: Section 2-
  86. 11.02: Section 3-
  87. 11.03: Section 4-
  88. 11.04: Section 5-
  89. 11.05: Section 6-
  90. 12: Functions
  91. 12.00: Section 1-
  92. 12.01: Section 2-
  93. 12.02: Section 3-
  94. 12.03: Section 4-
  95. 12.04: Section 5-
  96. 12.05: Section 6-
  97. 13: Proofs in Calculus
  98. 13.00: Section 1-
  99. 13.01: Section 2-
  100. 13.02: Section 3-
  101. 13.03: Section 4-
  102. 13.04: Section 5-
  103. 13.05: Section 6-
  104. 14: Cardinality of Sets
  105. 14.00: Section 1-
  106. 14.01: Section 2-
  107. 14.02: Section 3-
  108. 14.03: Section 4-
  109. 14.04: Section 5-
  110. 14.05: Section 6-