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Discrete Mathematics
Discrete Mathematics
47 lessons across 14 topics
1. Logic and Mathematical Statements
1
Logical Equivalence
2
Propositions
3
Quantifiers
4
Truth Tables
2. Proof Techniques I
5
Contradiction
6
Contrapositive
7
Counterexamples
8
Direct Proof
3. Proof Techniques II
9
Mathematical Induction
10
Recursive Definitions
11
Strong Induction
4. Sets, Functions, and Relations
12
Equivalence Relations
13
Functions And Inverses
14
Partial Orders
15
Set Operations
5. Counting I
16
Binomial Coefficients
17
Permutations And Combinations
18
Sum And Product Rules
6. Counting II
19
Combinatorial Arguments
20
Inclusion-exclusion
21
Pigeonhole Principle
7. Recurrence Relations
22
Applications To Algorithmic Thinking
23
Linear Recurrences
24
Solving Simple Recurrences
8. Midterm 1 and Intro to Graph Theory
25
Degree, Paths, Cycles
26
Graph Terminology
27
Midterm 1
9. Graph Theory II
28
Bipartite Graphs
29
Connectivity
30
Euler And Hamilton Ideas
10. Trees
31
Applications To Data Structures
32
Rooted Trees
33
Spanning Trees
34
Tree Properties
11. Discrete Probability
35
Conditional Probability
36
Expected Value
37
Independence
38
Sample Spaces
12. Advanced Counting (SLASH) Generating Functions Overview
39
Introductory Generating Functions If Included
40
Key Themes In Advanced Counting / Generating Functions Overview
41
More Combinatorial Techniques
13. Algorithms and Discrete Structures
42
Applications
43
Basic Complexity Intuition
44
Graph Algorithms Overview
14. Final Review
45
Applying Final Review
46
Key Themes In Final Review
47
Unifying Logic, Proof, Counting, And Graph Methods
