| Blank notes |
Completed notes |
Chapter 1: The Foundations: Logic and
Proofs
|
|
1.1
Propositional Logic
|
1.1
|
1.2
Applications of Propositional Logic
|
1.2
|
| 1.3
Propositional Equivalences |
1.3
|
| 1.4
Predicates and Quantifiers |
1.4
|
| 1.5
Nested Quantifiers |
1.5
|
| 1.7
Introduction to Proofs |
1.7
|
| 1.8
Proof Methods and Strategy |
1.8
|
| Chapter 2: Basic
Structures, Functions, Sequences, Sums, and Matrices
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|
| 2.1 Sets
|
2.1
|
| 2.2 Set
Operations |
2.2
|
| Test 1 (Chapters 1
and 2.1, 2.2 ) |
Test 1 |
Test 1 Review
Questions
|
Test
1 Review Questions |
| 2.3
Functions |
2.3
|
| 2.4
Sequences and Summations |
2.4
|
| Chapter 4: Number Theory and
Cryptography |
|
| 4.1
Divisibility and Modular Arithmetic |
4.1
|
| 4.3
Primes and Greatest Common Divisors |
4.3
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| 4.4
Solving Congruences |
4.4
|
| Chapter 5: Induction and Recursion |
|
| 5.1
Mathematical Induction |
5.1
|
| 5.2
Strong Induction |
5.2
|
| Test 2 (2.3, 2.4,
Chapters 4 and 5; only sections covered in class) |
Test 2
|
| Test 2 Review Questions |
Test 2 Review Questions |
| Chapter 6: Counting |
|
| 6.1 The
Basics of Counting |
6.1
|
| 6.2 The
Pigeonhole Principle |
6.2
|
| 6.3
Permutations and Combinations |
6.3
|
| 6.5
Generalized Permutations and Combinations |
6.5
|
Chapter 8: Advanced Counting Techniques
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|
| 8.5, 8.6
Inclusion - Exclusion |
8.5
|
8.1
Recurrence Relations
|
8.1
|
| Test 3 (Chapters 6
and 8; only sections covered in class) |
Test 2
|
| Test 3 Review Questions |
Test 3 Review Questions |
Graphs
|
Graphs
|