Math 22 Videos
Section Kimberly Brehm Trevor Bazett SMCC Math
1.1 Variables, Variables (Example)
1.2 Intro to Sets | Examples, Notation & Properties, Cartesian Product of Two Sets A x B, Set-Roster vs Set-Builder notation The Language of Sets, 1.2 (Examples)
1.3 Relations between two sets | Definition + First Examples, The intuitive idea of a function, Example: Is this relation a function? The Language of Relations and Functions, Example
2.1 Propositions, Negations, Conjunctions and Disjunctions, Constructing a Truth Table for Compound Propositions, Key Logical Equivalences Including De Morgan's Laws Intro to Logical Statements, Intro to Truth Tables | Negation, Conjunction, and Disjunction, Truth Table Example: ~p V ~q, Logical Equivalence of Two Statements, Tautologies and Contradictions, 3 Ways to Show a Logical Equivalence | Ex: DeMorgan's Laws Logical Form and Logical Equivalence, Example
2.2 Implications Converse, Inverse, Contrapositive, and Biconditionals, Translating Propositional Logic Statements, ``Proving" Logical Equivalences with Truth Tables Conditional Statements: if p then q, Vacuously True Statements, Negating a Conditional Statement, Contrapositive of a Conditional Statement, The converse and inverse of a conditional statement, Biconditional Statements | "if and only if" Conditional Statements, Example
2.3 Solving Logic Puzzles, Rules of Inference for Propositional Logic Logical Arguments - Modus Ponens & Modus Tollens, Logical Argument Forms: Generalizations, Specialization, Contradiction, Analyzing an argument for validity Valid and Invalid Arguments, Examples
3.1 Quantifiers Predicates and their Truth Sets, Universal and Existential Quantifiers, "For All" and "There Exists" Predicates and Quantified Statements I, Examples
3.2 Negating and Translating with Quantifiers Negating Universal and Existential Quantifiers, Universal Conditionals P(x) implies Q(x), Necessary and Sufficient Conditions Predicates and Quantified Statements II, Examples
3.3 Nested Quantifiers and Negations, Translating with Nested Quantifiers Negating Logical Statements with Multiple Quantifiers Statements with Multiple Quantifiers, Examples
3.4 Rules of Inference for Quantified Statements Arguments with Quantified Statements, Examples
4.1 Direct Proof Formal Definitions in Math | Ex: Even & Odd Integers, How to Prove Math Theorems | 1st Ex: Even + Odd = Odd, Step-By-Step Guide to Proofs | Ex: product of two evens is even, Disproving implications with Counterexamples Direct Proof and Counterexample I, Examples
4.2 Rational Numbers | Definition + First Proof Direct Proof and Counterexample II: Rational Numbers, Examples
4.3 Divisibility, Prime Numbers and Their Properties Proving that divisibility is transitive Direct Proof and Counterexample III: Divisibility, Examples
4.4 Division Algorithm, Proof by Cases Proof by Division Into Cases, Quotient-Remainder Theorem and Modular Arithmetic Direct Proof and Counterexample IV: The Quotient-Remainder Theorem, Examples
4.5 Proof by Contraposition, Proof by Contradiction Proof by Contradiction | Method & First Example, Proof by Contrapositive | Method & First Example Indirect Argument, Examples
4.6 Proof: There are infinitely many primes numbers
5.1 Introduction to Sequences, Summations and Sigma Notation, Summation Properties and Formulas Introduction to sequences, The formal definition of a sequence., The sum and product of finite sequences 5.1 Sequences (Part 1), 5.1 Sequences (Part 2)
5.2 Proof Using Mathematical Induction - Summation Formulae Intro to Mathematical Induction Mathematical Induction I
5.3 Proof Using Mathematical Induction - Inequalities, Proof Using Mathematical Induction - Divisibility Induction Proofs Involving Inequalities. Mathematical Induction II
5.4 Decimal Expansions from Binary, Octal and Hexadecimal, Binary, Octal and Hexadecimal Expansions From Decimal, Conversions Between Binary, Octal and Hexadecimal Expansions, The Well-Ordering Principle and Strong Induction Strong Induction
5.5 Recurrence Relations, Revisiting Recursive Definitions, Modeling with Recurrence Relations Recursive Sequences, The Miraculous Fibonacci Sequence Defining Sequences Recursively, Examples
5.6 Solving Recurrence Relations Solving Recurrence Relations by Iteration, Examples
6.1 Introduction to Sets, Set Relationships, Operations on Sets Prove A is a subset of B with the ELEMENT METHOD, Proving equalities of sets using the element method, The union of two sets, The Intersection of Two Sets, Universes and Complements in Set Theory, Using the Element Method to prove a Set Containment w/ Modus Tollens, Power Sets and the Cardinality of the Continuum, The summation rule for disjoint unions Set Theory Definitions and the Element Method of Proof
6.2 Set Identities, Proving Set Identities The Empty Set & Vacuous Truth Properties of Sets
6.3
6.4
7.1 Introduction to Functions Formal Definition of a Function using the Cartesian Product Functions Defined on General Sets
7.2 One-to-One and Onto Functions, Inverse Functions and Composition of Functions One to One and Onto, Inverse Functions
7.3 Composition of Functions Composition of Functions
7.4
8.1 Introduction to Relations Relations and their Inverses
8.2 Properties of Relations Reflexive, Symmetric, and Transitive Relations on a Set, You need to check EVERY spot for reflexivity, symmetry, and transitivity
8.3 Equivalence Relations Equivalence Relations - Reflexive, Symmetric, and Transitive
8.5 Greatest Common Divisors and Least Common Multiples, The Euclidean Algorithm, Greatest Common Divisors as Linear Combinations, Solving Linear Congruences Using the Inverse
9.1 An Intro to Discrete Probability, Discrete Probability Practice, Probability Theory Introduction to probability // Events, Sample Space, Formula, Independence, Example: Computing Probabilities using P(E)=N(E)/N(S) Introduction to Counting and Probability
9.2 Counting Rules Permutations and Combinations What is the probability of guessing a 4 digit pin code?, How many ways to rearrange the letters in a word? Possibility Trees and the Multiplication Rule
9.3 Counting Rules, The Principle of Inclusion-Exclusion Counting with Triple Intersections // Example & Formula, Counting formula for two intersecting sets: N(A union B)=N(A)+N(B)-N(A intersect B) Counting Elements of Disjoint Sets: The Addition Rule
9.4 The Pigeonhole Principle | A Pigeonhole Proof The Pigeonhole Principle
9.5 Permutations and Combinations, Counting Rules Practice Combinations Formula: Counting the number of ways to choose r items from n items., How many ways are there to reorder the word MISSISSIPPI? // Choose Formula Example, Counting and Probability Walkthrough Counting Subsets of a Set: Combinations
9.6 The Binomial Theorem, Random Variables and the Binomial Distribution
10.1 Representing Relations Using Digraphs, Introduction to Graphs, Graph Terminology, Special Types of Graphs, Applications of Graphs Intro to Graph Theory | Definitions & Ex: 7 Bridges of Konigsberg, Properties in Graph Theory: Complete, Connected, Subgraph, Induced Subgraph, Degree of Vertices | Definition, Theorem & Example | Graph Theory
10.2 Euler Paths and Circuits, Hamilton Paths and Circuits Euler Paths & the 7 Bridges of Konigsberg | Graph Theory
10.3 Introduction to Trees
10.4 Trees