Free online courseDiscrete Math
Duration of the online course: 9 hours and 38 minutes
New course
Master Discrete Math with this comprehensive online course. Dive into sets, logic, proofs, probability, and graph theory, building essential math skills in calculus.
Course Description
Explore the fascinating world of Discrete Mathematics, a foundational course that spans a diverse range of topics. Begin with an introduction to sets, learning about set notations like Set-Roster and Set-Builder, and grasp concepts such as the Cartesian Product of two sets, relations, and the fundamental idea of functions.
Delve into logical statements, understanding truth tables, tautologies, and the relationships between logical equivalences. Strengthen your reasoning with conditional and biconditional arguments, examining universal and existential quantifiers deeply, and not to forget, get guided through the first steps in mathematical proofs.
The course will lead you through sequences, modular arithmetic, proof strategies, and inspire confidence while tackling mathematical inductions and recursive sequences. A comprehensive exploration of set theory, including union, intersection, and power sets, equips learners with robust techniques for analyzing set relationships.
Transition into the intriguing world of probability, unveil the mystery of counting, and solidify knowledge with practical examples, like calculating permutations and Bayes' Theorem. Test probability principles with exciting questions like guessing a PIN code or understanding chess from a probabilistic viewpoint.
Advance into more technical realms such as graph theory, with topics covering complete and connected graphs, subgraphs, and the classic Euler Paths. As you reach course completion, you'll come away with holistic insight into logical reasoning, algorithmic thinking, and a mature mathematical perspective.
Course content
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Video class: Intro to Discrete Math - Welcome to the Course!
0h05m
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Exercise: What distinguishes discrete mathematics from continuous mathematics in this course context
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Video class: Intro to Sets | Examples, Notation
0h07m
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Video class: Set-Roster vs Set-Builder notation
0h05m
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Exercise: Which set builder notation matches the roster ..., -4, -2, 0, 2, 4, ...?
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Video class: The Empty Set
0h04m
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Video class: Cartesian Product of Two Sets A x B
0h07m
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Exercise: When are two ordered pairs equal
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Video class: Relations between two sets | Definition First Examples
0h06m
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Video class: The intuitive idea of a function
0h05m
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Exercise: Which statement correctly defines a function in terms of domain and range?
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Video class: Formal Definition of a Function using the Cartesian Product
0h05m
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Video class: Example: Is this relation a function?
0h05m
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Exercise: Is the relation C = {(x,y) in R×R | x^2 + y^2 = 1} a function from [-1,1] to [-1,1]?
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Video class: Intro to Logical Statements
0h06m
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Video class: Intro to Truth Tables | Negation, Conjunction, and Disjunction
0h05m
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Exercise: When is the conjunction P and Q true?
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Video class: Truth Table Example: ~p V ~q
0h03m
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Video class: Logical Equivalence of Two Statements
0h03m
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Exercise: Identify a logical equivalence using truth tables
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Video class: Tautologies and Contradictions
0h03m
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Video class: 3 Ways to Show a Logical Equivalence | Ex: DeMorgan's Laws
0h05m
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Exercise: Simplify the expression: ¬(p ∨ ¬q) ∧ T using logical equivalences
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Video class: Conditional Statements: if p then q
0h07m
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Video class: Vacuously True Statements
0h02m
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Exercise: Understanding vacuous truth in implications
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Video class: Negating a Conditional Statement
0h02m
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Video class: Contrapositive of a Conditional Statement
0h05m
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Exercise: Which statement is logically equivalent to the conditional P → Q?
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Video class: The converse and inverse of a conditional statement
0h05m
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This free course includes:
9 hours and 38 minutes of online video course
Exercises to train your knowledge
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