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Discrete Mathematics
Sets
Introduction (0:19)
Defenition of a Set (8:41)
Number Sets (10:07)
Set Equality (9:16)
Set-Builder Notation (9:56)
Types of Sets (11:49)
Subsets (10:27)
Power Set (5:06)
Ordered Pairs (4:59)
Cartesian Products (14:08)
Cartesian Plane (3:38)
Venn Diagrams (3:13)
Set Operations (Union, Intersection) (14:35)
Properties of Union and Intersection (10:16)
Set Operations (Difference, Complement) (11:34)
Properties of Difference and Complement (7:29)
De Morgan’s Law (8:17)
Partition of Sets (15:49)
Logic
Introduction (0:22)
Statments (7:13)
Compound Statements (13:10)
Truth Tables (9:20)
Examples (13:03)
Logical Equivalence (6:39)
Tautologies and Contradictions (6:15)
De Morgan’s Laws in Logic (11:34)
Logical Equivalence Laws (3:23)
Conditional Statements (12:58)
Negation of Conditional Statements (9:31)
Converse and Inverse (7:25)
Biconditional Statements (8:46)
Examples (11:50)
Digital Logic Circuits (12:54)
Black Boxes and Gates (15:18)
Boolean Expressions (6:23)
Truth Tables and Circuits (9:24)
Equivalent Circuits (6:37)
NAND and NOR Gates (7:12)
Quantified Statements-ALL (7:36)
Quantified Statements-ANY (6:39)
Negations of Quantified Statements (8:28)
Number Theory
Introduction (0:35)
Parity (12:43)
Divisibility (10:45)
44-Prime Numbers (8:03)
45-Prime Factorization (8:33)
GCD, LCM (17:23)
Proofs
Proofs (5:40)
Terminologies (7:37)
Direct Proofs (8:45)
Proof by Contraposition (11:26)
Proofs by Contradiction (17:16)
Proofs by Exhaustion (13:36)
Existence & Uniqueness Proofs (15:57)
Proofs by Induction (11:41)
Induction Examples (18:46)
Functions
Introduction (0:24)
Functions (15:05)
Evaluating a Function (12:29)
Domain (15:56)
Range (5:29)
Function Composition (9:43)
Function Combination (9:00)
Even and Odd function (8:19)
One-to-One Function (8:18)
Inverse Functinos (10:10)
Relations
Introduction (0:25)
The Language of Relations (10:26)
Relations on Sets (12:44)
The Inverse of a Relation (6:05)
Reflexivity, Symmetry, and Transitivity (13:07)
Examples (7:31)
Properties of Equality & Less Than (7:48)
Equivalence Relation (6:42)
Equivalence Class (6:30)
Graph Theory
Introduction (0:28)
Graphs (11:25)
Subgraphs (8:32)
Degree (9:52)
Sum of Degrees of Vertices Theorem (23:22)
Adjacency and Incidence (9:15)
Adjacency Matrix (16:16)
Incidence Matrix (8:04)
Isomorphisms (8:23)
Walks, Trails, Paths, and Circuits (12:41)
Examples (10:18)
Eccentricity, Diameter, and Radius (6:47)
Connectedness (20:03)
Euler Trails and Circuits (17:36)
Fleury’s Algorithm (10:15)
Hamiltonian Paths and Circuits (5:46)
Ore's Theorem (14:08)
The Shortest Path Problem (12:58)
Statistics
Introduction (0:19)
Terminologies (3:05)
Mean (3:31)
Median (3:11)
Mode (3:01)
Range (8:00)
Outlier (4:18)
Variance (9:25)
Standard Deviation (4:14)
Combinatorics
Introduction (3:29)
Factorials! (7:46)
The Fundamental Counting Principle (13:24)
Permutations (12:50)
Combinations (12:01)
Pigeonhole Principle (6:10)
Pascal's Triangle (8:20)
Sequence and Series
Introduction (0:19)
Sequnces (6:37)
Arithmatic Sequance (12:19)
Geometric Sequances (8:57)
Partial Sums of Arithamtics Sequance (11:56)
Partial Sum of Geometric Sequance (6:31)
Series (12:32)
Defenition of a Set
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