I am pleased to announce the latest edition of Discrete Math, An Inquiry Based Approach. This latest edition includes additional guided practice, clarifies tasks, and corrects grammatical errors. The structure and contents remains essentially the same as before. Below is the table of contents. If you are interested in using the book or would like to have the book approved for use in your district or state, please contact me.
Table of Contents 0. Introduction ..................................................................................… page 7 1.
Counting and Discrete Probability …………………………………………………….… page 10
1.1. Initial Investigations …………………………………..…..………………………… page 10
1.2. Figurate Numbers ……………………………….………..……………….………… page 11
1.3. Finite Differences ……………………………….………..………………..…………page 12
1.4. Polygonal Numbers ………..……………………………..………………..…………page 14
1.5. Combinations and Permutations ……………………...………………...........………page 15
1.6. The Pigeonhole Principle ……………………………………..……….....…………. page 18
1.7. Advanced Counting ……………………………………..……………..…………..…page 19
1.8. Discrete Probability ……………………………………..………..…...…………..… page 20
1.9. Conditional Probability …………………………..……..………....…………………page 22
1.10. Probability Practice and Mastery Quiz ………………………….........…………….page 25
2. Graph Theory ……………………………………..…………………...……………… page 28
2.1. Introduction to Graphs ………………………………..………………....…..……… page 28
2.2. Graph Theorems ………...………………………………..………………………… page 33
2.3. Mail Route Practice ……………..……………..………..……..…………………… page 37
2.4. Hamilton Paths and Circuits …………..……………..……….......………………… page 38
2.5. Planar Graphs …………….………………………………..……..………………… page 41
2.6. Complete and Complementary Graphs …………………………............………….. page 45
2.7. Graph Coloring …………………………………………..………………………… page 49
2.8. Edge Coloring …..……………………………………......………………………… page 54
3. Elementary Number Theory ………..……………………...………………………… page 57
3.1. Prime Numbers …………………………..………………..……………..………… page 57
3.2. Prime Number Distribution ………...………………..………………......………… page 60
3.3. Prime Number Sequences ……………...……………..……………....…………… page 64
3.4. Relative Primes ………..………………………………...………………………… page 66
3.5. Prime Sums ………………………………………….…..………………………… page 69
3.6. Prime Factorization ……….……………………………..………………………… page 70
3.7. Perfect Numbers ………………………...……………….………………………… page 73
3.8. Mersenne Primes and Prime Formulas ……...…..………….............……………… page 76
3.9. Euclidean Algorithm ………………………………..…..……..…………………… page 78
4. Cryptography ……………………………………..………....……………………..… page 81
4.1. Caesar Ciphers ……………………...……………………....……………………… page 81
4.2. Cipher Functions …………..……………………………..………………………… page 83
4.3. Affine Ciphers …………………....………………………....……………………… page 87
4.4. Chinese Remainder Theorem ……….………………..……......…………………… page 88
4.5. Congruences ……………………………….……………...………………………... page 90
4.6. Solving Congruences ……………………………………..………………………... page 94
4.7. Congruences and Divisibility ………………..………..…….....………...………… page 97
4.8. Modular Arithmetic …………….………………………..………………………… page 100
4.9. Primality Tests ……………………………………...……..……………..………… page 101
4.10. Cryptography Revisited ………………………………...………………………… page 103
4.11. Diffie-Hellman Exchange ……….……………………..……………….………… page 104
4.12. Cracking the Diffie-Hellman Exchange ……………...…………………............... page 108
4.13. RSA Protocol ……………………………...……………………………………… page 110
4.14. RSA Practice ………………………….……………………..………………....… page 112
5. Set Theory and Boolean Algebra ……...………………………..…………….……… page 114
5.1. Understanding Sets ……………………..………………..……………………...… page 114
5.2. Set Operations ……………………………….……………..………………….…… page 117
5.3. Venn Diagrams ……………………………...……………..………………..……… page 121
5.4. DeMorgan’s Laws …………….……………………………………..……...……… page 122
5.5. Cartesian Products ……………………………………….…….…………...……… page 123
5.6. Boolean Algebra …………………………..………………..……..…………..…… page 124
5.7. Boolean Functions ……………….………………………..………....……..……… page 126
5.8. Boolean Identities ……………..…………………………..……………………..… page 129
5.9. Truth Tables ……………………………………..…………..…….……..………… page 131
5.10. Logic Gates ……………………………………………….…..………………..… page 134
6. Logic and Proof …………………………………………………….....………..…… page 139
6.1. Statements and Negation ………………..……………..…………......…………… page 139
6.2. The Language of Logic …………………………….……..…………….....……… page 141
6.3. Showing Truth …………………………….………………..…………..………… page 143
6.4. Methods of Proof ……………………...…………………..……………………… page 146
7. Citations …………………………………………………….....………...………….. page 152
Copyright 2016-2021 Michael G. Pugliese
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