Overview

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Explore a comprehensive 19-hour course on Discrete Mathematics covering fundamental concepts and advanced topics. Delve into propositional logic, set theory, functions, algorithms, number theory, mathematical induction, counting principles, probability, relations, graphs, and trees. Learn through detailed lectures, problem sets, and practical applications using Rosen's "Discrete Mathematics and Its Applications" textbook. Master essential skills in logical reasoning, proof techniques, algorithmic thinking, and mathematical modeling. Enhance your understanding with hands-on exercises, including truth tables, logic circuits, matrix operations, and graph representations. Develop a strong foundation in discrete structures crucial for computer science, mathematics, and related fields.

Syllabus

Discrete Math - 1.1.1 Propositions, Negations, Conjunctions and Disjunctions.
Discrete Math - 1.1.2 Implications Converse, Inverse, Contrapositive and Biconditionals.
Discrete Math - 1.1.3 Constructing a Truth Table for Compound Propositions.
Discrete Math 1.2.1 - Translating Propositional Logic Statements.
Discrete Math - 1.2.2 Solving Logic Puzzles.
Discrete Math - 1.2.3 Introduction to Logic Circuits.
Discrete Math - 1.3.1 “Proving” Logical Equivalences with Truth Tables.
Discrete Math - 1.3.2 Key Logical Equivalences Including De Morgan’s Laws.
Discrete Math - 1.3.3 Constructing New Logical Equivalences.
Discrete Math - 1.4.1 Predicate Logic.
Discrete Math - 1.4.2 Quantifiers.
Discrete Math - 1.4.3 Negating and Translating with Quantifiers.
Discrete Math - 1.5.1 Nested Quantifiers and Negations.
Discrete Math - 1.5.2 Translating with Nested Quantifiers.
Discrete Math - 1.6.1 Rules of Inference for Propositional Logic.
Discrete Math - 1.6.2 Rules of Inference for Quantified Statements.
Discrete Math - 1.7.1 Direct Proof.
Discrete Math - 1.7.2 Proof by Contraposition.
Discrete Math - 1.7.3 Proof by Contradiction.
Discrete Math - 1.8.1 Proof by Cases.
Discrete Math - 1.8.2 Proofs of Existence And Uniqueness.
Discrete Math - 2.1.1 Introduction to Sets.
Discrete Math - 2.1.2 Set Relationships.
Discrete Math - 2.2.1 Operations on Sets.
Discrete Math - 2.2.2 Set Identities.
Discrete Math - 2.2.3 Proving Set Identities.
Discrete Math - 2.3.1 Introduction to Functions.
Discrete Math - 2.3.2 One to One and Onto Functions.
Discrete Math - 2.3.3 Inverse Functions and Composition of Functions.
Discrete Math - 2.3.4 Useful Functions to Know.
Discrete Math - 2.4.1 Introduction to Sequences.
Discrete Math - 2.4.2 Recurrence Relations.
Discrete Math - 2.4.3 Summations and Sigma Notation.
Discrete Math - 2.4.4 Summation Properties and Formulas.
Discrete Math - 2.6.1 Matrices and Matrix Operations.
Discrete Math - 2.6.2 Matrix Operations on your TI-84.
Discrete Math - 2.6.3 Zero-One Matrices.
Discrete Math - 3.1.1 Introduction to Algorithms and Pseudo Code.
Discrete Math - 3.1.2 Searching Algorithms.
Discrete Math - 3.1.3 Sorting Algorithms.
Discrete Math - 3.1.4 Optimization Algorithms.
Discrete Math - 4.1.1 Divisibility.
Discrete Math - 4.1.2 Modular Arithmetic.
Discrete Math - 4.2.1 Decimal Expansions from Binary, Octal and Hexadecimal.
Discrete Math - 4.2.2 Binary, Octal and Hexadecimal Expansions From Decimal.
Discrete Math - 4.2.3 Conversions Between Binary, Octal and Hexadecimal Expansions.
Discrete Math - 4.2.4 Algorithms for Integer Operations.
Discrete Math - 4.3.1 Prime Numbers and Their Properties.
Discrete Math - 4.3.2 Greatest Common Divisors and Least Common Multiples.
Discrete Math - 4.3.3 The Euclidean Algorithm.
Discrete Math - 4.3.4 Greatest Common Divisors as Linear Combinations.
Discrete Math - 4.4.1 Solving Linear Congruences Using the Inverse.
Discrete Math - 5.1.1 Proof Using Mathematical Induction - Summation Formulae.
Discrete Math - 5.1.2 Proof Using Mathematical Induction - Inequalities.
Discrete Math - 5.1.3 Proof Using Mathematical Induction - Divisibility.
Discrete Math - 5.2.1 The Well-Ordering Principle and Strong Induction.
Discrete Math - 5.3.1 Revisiting Recursive Definitions.
Discrete Math - 5.3.2 Structural Induction.
Discrete Math - 5.4.1 Recursive Algorithms.
Discrete Math - 6.1.1 Counting Rules.
Discrete Math - 6.3.1 Permutations and Combinations.
Discrete Math - 6.3.2 Counting Rules Practice.
Discrete Math - 6.4.1 The Binomial Theorem.
Discrete Math - 7.1.1 An Intro to Discrete Probability.
Discrete Math - 7.1.2 Discrete Probability Practice.
Discrete Math - 7.2.1 Probability Theory.
Discrete Math - 7.2.2 Random Variables and the Binomial Distribution.
Discrete Math - 8.1.1 Modeling with Recurrence Relations.
Discrete Math - 8.5.1 The Principle of Inclusion Exclusion.
Discrete Math - 9.1.1 Introduction to Relations.
Discrete Math - 9.1.2 Properties of Relations.
Discrete Math - 9.1.3 Combining Relations.
Discrete Math - 9.3.1 Matrix Representations of Relations and Properties.
Discrete Math - 9.3.2 Representing Relations Using Digraphs.
Discrete Math - 9.5.1 Equivalence Relations.
Discrete Math - 10.1.1 Introduction to Graphs.
Discrete Math - 10.2.1 Graph Terminology.
Discrete Math - 10.2.2 Special Types of Graphs.
Discrete Math - 10.2.3 Applications of Graphs.
Discrete Math - 11.1.1 Introduction to Trees.