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Discrete Structures

U1
Mathematical Reasoning
topic 1
1 topics
01
Mathematical Reasoning: Propositional and Predicate Logic
U2
Propositional Logic
topic 2 to 4
3 topics
02
Propositional Logic: Logical Operators
03
Translations Between Symbolic Expressions and Formal English Expression
04
Logical Equivalences
U3
Predicate Logic
topic 5 to 8
4 topics
05
Predicate Logic: Quantifiers
06
Nested Quantification
07
Equivalences in Predicate Logic
08
Translations Between Symbolic Forms and Formal English
U4
Rules of Inference
topic 9 to 17
9 topics
09
Rules of Inference: Proof Methods and Strategies
10
Direct Proof
11
Proof by Contraposition
12
Proof by Induction
13
Proof by Implication
14
Existence Proof
15
Uniqueness Proofs
16
Trivial Proofs
17
Vacuous Proofs
U5
Sets
topic 18 to 20
3 topics
18
Sets: Notations and Set Operations
19
Venn Diagrams
20
Countable and Uncountable Sets
U6
Relations
topic 21 to 53
6 topics
21
Relations: Equivalence Relations and Partitions
22
Partial Orderings
23
Recurrence Relations
51
Relations: Reflexive, Symmetric, Transitive, and Antisymmetric
52
Equivalence Relations and Equivalence Classes
53
Partial Orders
U7
Functions
topic 24 to 29
6 topics
24
Functions: Injective, Surjective, Bijective
25
Special Types of Functions
26
Function Composition
27
Inverse Functions
28
Recursive Functions
29
Compositions
U8
Number Theory
topic 30
1 topics
30
Number Theory: Sequences and Series
U9
Counting
topic 31 to 50
8 topics
31
Counting: Inclusion and Exclusion Principle
32
Pigeonhole Principle
33
Permutations and Combinations
46
Counting: Product Rule and Sum Rule
47
Principle of Inclusion-Exclusion
48
Binomial Coefficients
49
Pascal's Identity and Pascal’s Triangle
50
Binomial Theorem
U10
Integers and Divisibility
topic 34 to 38
5 topics
34
Integers and Divisibility: Division Theorem
35
Modular Arithmetic
36
LCM and GCD
37
Euclidean and Extended Euclidean Method
38
Finding Solutions to Congruence
U11
Primes
topic 39 to 41
3 topics
39
Primes: Fundamental Theorem of Arithmetic
40
Characterizations of Primes
41
Mersenne Primes
U12
Induction
topic 42 to 43
2 topics
42
Induction: Weak Induction
43
Strong Induction
U13
Recursion and Recurrences
topic 44 to 45
2 topics
44
Recursion and Recurrences: Formulation of Recurrences
45
Closed Formulas
U14
Graph Theory
topic 54 to 67
14 topics
54
Graph Theory: Terminologies
55
Elements of Graph Theory
56
Planar Graphs
57
Graph Coloring
58
Euler Graph
59
Hamiltonian Path
60
Rooted Trees
61
Graph Traversals
62
Handshaking Lemma and Corollary
63
Special Families of Graphs
64
Graph Isomorphism
65
Planarity in Graphs
66
Eulerian and Hamiltonian Graphs
67
Trees in Graph Theory

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