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Discrete Mathematics
Discrete Mathematics
Fall 2025: CSE-20110
Lecture Notes
Lecture 2: Logic
Lecture 3: Logic
Lecture 4: Logic
Lecture 5: Logic
Lecture 6: Introduction to Proofs
Lecture 7: Proof by Contradiction
Lecture 8: Proof Examples and Cartesian Products
Lecture 9: Functions and Cardinality of Infinite Sets
Lecture 10: Binary Relations and Composition of Relations
Lecture 11: Graph Powers and Matrix Multiplication
Lecture 12: Orders and Algorithmic Time Complexities
Lecture 13: Proving Time Complexities and Analyzing Pseudocode
Lecture 14: Analyzing Pseudocode and Mathematical Induction
Lecture 15: Strong Induction, Structural Induction, and Recursive Definitions
Lecture 16: Recursive Algorithms
Lecture 17: (Linear) Homogeneous and Non-Homogeneous Recurrences
Lecture 18: Integer Properties and Modular Arithmetic
Lecture 19: Sum Rule and Permutations
Lecture 20: R-Combinations and Counting Examples
Lecture 21: Counting Examples
Lecture 22: Probability
Lecture 23: Conditional Probability and Bayes Theorem
Lecture 24: Random Variables and Expected Value
Lecture 25: Graphs and Networks
Lecture 26: Trees
Reading Assignment Notes
RA 1: Logic
RA 2: Logic
RA 3: Logic
RA 4: Logic
RA 5: Proofs
RA 6: Proof by Contradictions and Sets
RA 7: Set Properties and Cartesian Products
RA 8: Properties of Functions and Boolean Algebra
RA 9: Relations, Matrix Representations, and Directed Graphs
RA 10: Graph Powers, Orders, and Equivalence Relations
RA 11: Introduction to Algorithmic Growth Analysis
RA 13: Mathematic Induction
RA 14: Summations and Recursive Definitions
RA 15: Divide and Conquer Algorithms
RA 16: Solving (linear) Homogeneous and Non-Homogeneous Recurrences
RA 18: Sum Rule, Product Rule, Counting Subsets
RA 19: Permutations and Counting by Complement
RA 20: Counting Multisets
RA 21: Probability
RA 22: Bayes Theorem, Random Variables, Linearity of Expectations
RA 24: Graphs
RA 25: Trees