Discrete Math

Discrete Math for Science and Engineering Students

What you'll learn
Properties of numbers; Conversions among bases; Sets; Logic and truth tables
Boolean algebras; Relations and functions
The theory of counting; Combinatorial formulas; Probability
Introduction to Graph Theory
Requirements
High school mathematics needed
Description
Discrete Mathematics is the study of mathematical structures that can be considered discrete rather than continuous. The study includes integers, statements in logic, and graphs. Concepts and notations from discrete mathematics are especially useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development.This course will cover the following topics:1. Properties of Numbers: Factors and Divisors; Greatest common divisor and least common multiple; Exponents and logarithms; Converting a number from one base to another.2. Data Structures: Propositions and Logic; Truth tables; de Morgan’s laws.3. Elements of Set Theory: the union and the intersection of sets; The complement of a set; A partition of a set; Method of Truth Tables, Mathematical Induction.4. Boolean Algebras: Principle of Duality; Idempotent Laws; Absorption Laws; Nullity Laws; de Morgan’s Laws.5. Relations and Functions: Equivalence Relations; One–One and onto Functions; Inverse functions.6. The Counting Theory: Event and sample space; The Multiplication Principle; Combinatorial formulas; The Pigeonhole Principle7. Probability: Probability Measures; Repeated Experiments; Conditional Probabilities; Bayes’ Formula and Applications.8. Introduction to Graph Theory: Directed graph; Simple graph.The course is taught in a way of lectures and in-class exercises combined. So when you reach the session for in-class exercises, you should stop watching the video to do the problems. When done, continue to watch the video to check your answers.

Overview

Section 1: Course Overview

Lecture 1 Overview

Section 2: Properties of numbers

Lecture 2 Factors and divisors

Lecture 3 Exponents, logarithms, and bases

Section 3: Sets and data structures

Lecture 4 Propositions and Logic

Lecture 5 The laws of logic

Lecture 6 Elements of set theory

Lecture 7 Proof methods in set theory

Lecture 8 Mathematical induction

Section 4: Boolean algebras

Lecture 9 Definition and theorems

Section 5: Relations and functions

Lecture 10 Relations

Lecture 11 Functions

Section 6: The theory of counting

Lecture 12 Events and the multiplication principle

Lecture 13 Combinatorial formulas

Section 7: Probability

Lecture 14 Probability measures and stochastic processes

Lecture 15 Conditional probabilities

Section 8: Introduction to graph theory

Lecture 16 Graphs

Any undergraduate student