English | MP4 | AVC 1920×1080 | AAC 44KHz 2ch | 19 Hours | 3.40 GB

Master Discrete Math for Computer Science and Mathematics Students

Discrete Mathematics (DM), or Discrete Math is the backbone of Mathematics and Computer Science. DM is the study of topics that are discrete rather than continuous, for that, the course is a MUST for any Math or CS student. The topics that are covered in this course are the most essential ones, those that will touch every Math and Science student at some point in their education. The goal of this course is to build the mathematical foundation for computer science courses such as data structures, algorithms, relational and database theory, and for mathematics courses such as linear and abstract algebra, combinatorics, probability, logic and set theory, and number theory.

Discrete Mathematics gives students the ability to understand Math language and based on that, the course is divided into the following sections:

- Sets
- Logic
- Number Theory
- Proofs
- Functions
- Relations
- Graph Theory
- Statistics
- Combinatorics
- and Sequences and Series

I know visually seeing a problem getting solved is the easiest and the most direct way for a student to learn so I designed the course keeping this in mind. The materials are delivered through videos to make complex subjects easy to comprehend. More details on certain lessons are delivered through text files to provide more explanations or examples. The course is taught in plain English, away from cloudy, complicated mathematical jargon, to help the student learn the material rather than getting stuck on fancy words.

What you’ll learn

- You will learn and develop the ability to think, read and write abstractly and Mathematically.
- You will learn the fundamentals of Set Theory including set builder notation, and set operations and properties.
- You will learn tautologies, contradictions, De Morgan’s Laws in Logic, logical equivalence, and formulating quantified statements.
- You will lear how to create truth tables and tell the falsehood and truthfulness of a compound statements.
- You will know how to write, read and prove Mathematical statements using a variety of methods.
- You will understand boolean expressions, black boxes, logical gates and digital circuits.
- You will understand the Fundamental Theorem of Arithmetics, modular arithmetic, and learn how to find GCD & LCM.
- You will acquire a solid foundation in functions, function composition & combination, bijective and inverse functions.
- You will learn how to find equivalence relations and equivalence classes.
- You will learn essential concepts in Statistics and Combinatorics.
- You will master arithmetic and geometric sequences, and partial sums.
- You will learn the fundamental concepts in Graph Theory like incidence and adjacency matrices, walks, eccentricity, hamiltonian paths and circuits, connectedness, and Ore’s Theorem.

## Table of Contents

**Sets**

1 Introduction

2 Definition of a Set

3 Number Sets

4 Set Equality

5 Set-Builder Notation

6 Types of Sets

7 Subsets

8 Power Set

9 Ordered Pairs

10 Cartesian Products

11 Cartesian Plane

12 Venn Diagrams

13 Set Operations (Union, Intersection)

14 Properties of Union and Intersection

15 Set Operations (Difference, Complement)

16 Properties of Difference and Complement

17 De Morgan’s Law

18 Partition of Sets

19 Extra Practice Problems

**Logic**

20 Introduction

21 Statements

22 Compound Statements

23 Truth Tables

24 Examples

25 Logical Equivalences

26 Tautologies and Contradictions

27 De Morgan’s Laws in Logic

28 Logical Equivalence Laws

29 Conditional Statements

30 Negation of Conditional Statements

31 Converse and Inverse

32 Biconditional Statements

33 Examples

34 Digital Logic Circuits

35 Black Boxes and Gates

36 Boolean Expressions

37 Truth Tables and Circuits

38 Equivalent Circuits

39 NAND and NOR Gates

40 Quantified Statements – ALL

41 Quantified Statements – THERE EXISTS

42 Negations of Quantified Statements

**Number Theory**

43 Introduction

44 Parity

45 Divisibility

46 Prime Numbers

47 Prime Factorization

48 GCD & LCM

**Proofs**

49 Intro

50 Terminologies

51 Direct Proofs

52 Proofs by Contrapositive

53 Proofs by Contradiction

54 Exhaustion Proofs

55 Existence & Uniqueness Proofs

56 Proofs by Induction

57 Examples

**Functions**

58 Intro

59 Functions

60 Evaluating a Function

61 Domains

62 Range

63 Graphs

64 Graphing Calculator

65 Extracting Info from a Graph

66 Domain & Range from a Graph

67 Function Composition

68 Function Combination

69 Even and Odd Functions

70 One to One (Injective) Functions

71 Onto (Surjective) Functions

72 Inverse Functions

73 Long Division

**Relations**

74 Intro

75 The Language of Relations

76 Relations on Sets

77 The Inverse of a Relation

78 Reflexivity, Symmetry and Transitivity

79 Examples

80 Properties of Equality & Less Than

81 Equivalence Relation

82 Equivalence Class

**Graph Theory**

83 Intro

84 Graphs

85 Subgraphs

86 Degree

87 Sum of Degrees of Vertices Theorem

88 Adjacency and Incidence

89 Adjacency Matrix

90 Incidence Matrix

91 Isomorphism

92 Walks, Trails, Paths, and Circuits

93 Examples

94 Eccentricity, Diameter, and Radius

95 Connectedness

96 Euler Trails and Circuits

97 Fleury’s Algorithm

98 Hamiltonian Paths and Circuits

99 Ore’s Theorem

100 The Shortest Path Problem

**Statistics**

101 Intro

102 Terminologies

103 Mean

104 Median

105 Mode

106 Range

107 Outlier

108 Variance

109 Standard Deviation

**Combinatorics**

110 Intro

111 Factorials

112 The Fundamental Counting Principle

113 Permutations

114 Combinations

115 Pigeonhole Principle

116 Pascal’s Triangle

**Sequence and Series**

117 Intro

118 Sequence

119 Arithmetic Sequences

120 Geometric Sequences

121 Partial Sums of Arithmetic Sequences

122 Partial Sums of Geometric Sequences

123 Series

124 Bonus Lecture

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