ASU

MAT 243

Propositional and Predicate Logic

    Propositional Logic

    Conditional Statements - example

    Propositional Equivalence

    Logical Equivalences - negation example

    Logical Equivalences - tautology example

    Predicates, Quantifiers, and Nested Quantifiers - Part 1

    Predicates, Quantifiers, and Nested Quantifiers - Part 2

    Quantifiers - single quantifier example


Rules of Inference

    Rules of Inference

    Rules of Inference - conditional statement example

    Rules of Inference - quantified statement example


Introduction to Proofs

    Proofs

    For All Exists Proofs

    Direct Proofs - even integers example

    Direct Proofs - odd integers example

    Direct Proofs - divisibility example

    Direct Proofs - rational numbers example

    Proof by Contraposition - odd number example

    Proof by Contraposition - even number example

    Proof by Contraposition - irrational number example

    Proof by Contraposition - n square is odd example

    Proof by Contraposition - n square not divisible by 5 example

    Proof by Contraposition - product greater than 100 example

    Proof by Contradiction - example 1

    Proof by Contradiction - example 2

    Proof by Contradiction - example 3

    Proof by Contradiction - example 4

    Proof by Contradiction - example 5

    Proof by Contradiction - example 6

    Proof by Contradiction - example 7

    Proof by Contradiction - example 8

    Proof by Contradiction - example 9

    Proof by Contradiction - example 10

    Proof by Contradiction - example 11

    For All True - example

    For All False - example

    Exists False - example

    Exists Exist True - example

    Exists Exist False - example

    Exists for All True - example


Sets and Set Operations

    Sets

    Sets - examples

    Set Operations

    Sets - union subset example

    Sets - intersection subset example


Functions and Sequences

    Functions Part 1

    Functions Part 2

    Injective functions example

    Non-injective functions example

    Surjective functions example

    Non-surjective functions example

    Increasing functions example

    Non-increasing functions example

    Decreasing functions example

    Non-decreasing functions example

    Non-injective non-surjective non-increasing non-decreasing example

    Sequences and Summation


Algorithms

    Growth of Functions - 1

    Growth of Functions - 2

    Introduction to growth of functions

    Big-O definition example 1

    Big-O definition example 2

    Big-O definition example 3

    Big-O sum and product example

    Big-Omega definition example

    Big-Theta definition example

    Not-Big-O example


Number Theory

    Divisibility and Modular Arithmetic

    Integer Representations

    Prime Numbers, GCD, Euclidean Algorithm, and LCM


Mathematical Induction

    Mathematical Induction

    Induction - sum of even numbers

    Induction - sum of odd numbers

    Induction- sum of squares of odd numbers

    Induction - sum of squares

    Induction - sum of Fibonacci series

    Induction - sum of odd numbers of Fibonacci series

    Induction - multiplication of numbers

    Induction - Inequality sum 1 by i

    Induction - Inequality 1 by power of 2

    Induction - inequality 3 power n

    Induction - Inequality 3 power n greater than n square example

    Induction - Inequality x power n

    Induction - Inequality n power n

    Induction - Inequality quadratic equation

    Induction - Inequality n factorial example

    Induction - divisible by 2 example

    Induction - divisible by 3 example

    Induction - divisibility by 3 example

    Induction - divisible by 133 example


Recursively Defined Functions and Sets. Structural Induction

    Recursively Defined Functions and Sets, Structural Induction

    Structural Induction - Introduction

    Structural Induction - two variables example

    Structural Induction - ordered pairs example 1

    Structural Induction - ordered pairs example 2

    Structural Induction - ordered pairs example 3

    Structural Induction - ordered pairs example 4

    Structural Induction - 2 divided by 7 example

    Structural Induction - binary strings example


Counting

    Counting and the Pigeonhole Principle

    Permutations and Combinations

    Permutations and Combinations - Order car example

    Permutations and Combinations - License plate example

    Permutations and Combinations - Stack chips example

    Binomial Theorem


Probability

    Introduction to Probability


Advanced Counting Techniques

    Solving Linear Recurrence Relations

    Solving Linear Recurrence Relations - Definitions

    Linear Recurrence Relations - Closed Form example

    Linear Recurrence Relations - Polynomial example

    Linear Recurrence Relations - Recursion example

    Inclusion Exclusion


Relations

    Relations