Overview

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Explore the foundations of discrete mathematics in this comprehensive 12-hour course covering set theory, logic, counting, permutations and combinations, functions, relations, number theory, proofs, and formal grammar. Dive into topics such as Cartesian products, subsets, power sets, set operations, propositional logic, truth tables, logic laws, conditionals, rules of inference, predicate logic, quantifier negation, factorials, binomial theorem, Pascal's triangle, direct proofs, proof by contraposition and contradiction, mathematical induction, partial orders, injective, surjective, and bijective functions, pigeonhole principle, divisibility, modular arithmetic, Euclidean algorithm, formal languages, and finite state machines. Gain practical experience through numerous examples and problem-solving exercises, including midterm solutions, to solidify your understanding of these essential discrete mathematics concepts.

Syllabus

INTRODUCTION to SET THEORY - DISCRETE MATHEMATICS.
CARTESIAN PRODUCTS and ORDERED PAIRS - DISCRETE MATHEMATICS.
SUBSETS AND POWER SETS - DISCRETE MATHEMATICS.
[Discrete Mathematics] Subsets and Power Sets Examples.
THREE EXERCISES IN SETS AND SUBSETS - DISCRETE MATHEMATICS.
SET OPERATIONS - DISCRETE MATHEMATICS.
[Discrete Mathematics] Set Operations Examples #2.
[Discrete Mathematics] Symmetric Difference Example.
[Discrete Mathematics] Indexed Sets and Well Ordering Principle.
INTRODUCTION to PROPOSITIONAL LOGIC - DISCRETE MATHEMATICS.
[Discrete Mathematics] Statement Identification and Translation Examples.
TRUTH TABLES - DISCRETE MATHEMATICS.
PROOFS with TRUTH TABLES - DISCRETE MATHEMATICS.
[Discrete Mathematics] Truth Tables Examples.
[Discrete Mathematics] Exclusive Or Example.
[Discrete Mathematics] Sheffer Stroke Examples.
LOGIC LAWS - DISCRETE MATHEMATICS.
[Discrete Mathematics] Logic Laws Examples.
[Discrete Mathematics] Logic Laws Examples 2.
CONDITIONALS - DISCRETE MATHEMATICS.
[Discrete Mathematics] Conditional Examples.
RULES of INFERENCE - DISCRETE MATHEMATICS.
PREDICATE LOGIC and QUANTIFIER NEGATION - DISCRETE MATHEMATICS.
[Discrete Mathematics] Negating Quantifiers and Translation Examples.
[Discrete Mathematics] Unique Quantifier Examples.
RULE of SUM and RULE of PRODUCT - DISCRETE MATHEMATICS.
[Discrete Mathematics] Rule of Sum and Rule of Product Examples.
FACTORIALS and PERMUTATIONS - DISCRETE MATHEMATICS.
[Discrete Mathematics] Permutation Practice.
COMBINATIONS - DISCRETE MATHEMATICS.
[Discrete Mathematics] Permutations and Combinations Examples.
[Discrete Mathematics] Permutations and Combinations Examples 2.
[Discrete Mathematics] Binomial Theorem and Pascal's Triangle.
COMBINATIONS with REPETITION - DISCRETE MATHEMATICS.
[Discrete Mathematics] Combinations with Repetition Examples.
[Discrete Mathematics] Counting Practice.
[Discrete Mathematics] Midterm 1 Solutions.
DIRECT PROOFS - DISCRETE MATHEMATICS.
[Discrete Mathematics] Direct Proofs Examples.
[Discrete Mathematics] Cartesian Product Proofs Examples.
[Discrete Mathematics] Proof by Case.
[Discrete Mathematics] Proof by Cases Examples.
PROOF by CONTRAPOSITION - DISCRETE MATHEMATICS.
PROOF by CONTRADICTION - DISCRETE MATHEMATICS.
MATHEMATICAL INDUCTION - DISCRETE MATHEMATICS.
[Discrete Mathematics] Mathematical Induction Examples.
[Discrete Mathematics] Mathematical Induction with Derivatives and Matrices.
RELATIONS - DISCRETE MATHEMATICS.
[Discrete Mathematics] Relations Examples.
PARTIAL ORDERS - DISCRETE MATHEMATICS.
FUNCTIONS - DISCRETE MATHEMATICS.
INJECTIVE, SURJECTIVE, and BIJECTIVE FUNCTIONS - DISCRETE MATHEMATICS.
[Discrete Mathematics] Functions Examples.
[Discrete Mathematics] Surjective Functions Examples.
[Discrete Mathematics] Inverse Function Examples.
[Discrete Mathematics] Inverses Examples 2.
PIGEONHOLE PRINCIPLE - DISCRETE MATHEMATICS.
[Discrete Mathematics] Pigeonhole Principle Examples.
DIVISIBILITY - DISCRETE MATHEMATICS.
[Discrete Mathematics] Divisibility Examples.
[Discrete Mathematics] Floor and Ceiling Examples.
[Discrete Mathematics] Modular Arithmetic.
[Discrete Mathematics] Congruency Proof Examples.
[Discrete Mathematics] Primes and GCD.
EUCLIDEAN ALGORITHM - DISCRETE MATHEMATICS.
[Discrete Mathematics] Euclidean Algorithm and GCDs Examples.
[Discrete Mathematics] Formal Languages.
[Discrete Mathematics] Formal Languages Examples.
[Discrete Mathematics] Finite State Machines.
[Discrete Mathematics] Finite State Machines Examples.
[Discrete Mathematics] Midterm 2 Solutions.