access

Lifetime

content

17.0 Hours

enrolled

234

**Description**

Discrete Mathematics is the backbone of Mathematics and Computer Science. It's the study of topics that are discrete rather than continuous, for that, the course is a MUST for any Math or SC student. This course covers the most essential topics that will touch every Math and Science student at some point in their education. Discrete Mathematics gives students the ability to understand Math language and based on that, the course is divided into 8 sections: Sets, Logic, Number Theory, Proofs, Functions, Relations, Graph Theory, Statistics, and Combinatorics. You might think that this is another "non-applicable, complex math", it's the actual opposite. What you'll learn from this course is essential in the real world and is very important in the Computer Science field.

- Access 116 lectures & 17 hours of content 24/7
- Learn the language of Mathematics & Mathematical symbols
- Construct, read & prove Mathematical statements using a variety of methods
- Understand the fundamental topics in Logic, how to construct truth tables, & tell the falsehood or truthfulness of compound statements
- Understand Boolean Expressions, black boxes, logical gates, digital circuits & many related topics
- Master fundamentals of Set Theory, equivalence relations & equivalence classes
- Learn the fundamental theorem of arithmetic
- Find incidence & adjacency matrices, and identify walks trails, paths and circuits
- Learn essential concepts in Statistics & Combinatorics

** "He took topics that appeared to be complex and simplified them with the use of great analogies and tossing the jargon out the window."** – Oneika Valere

4.4/5 Instructor Rating:
★ ★ ★ ★
★

Fattah has B.S. in Mathematics and Geophysics from theUniversity of Oklahoma in Oklahoma, USA. He has taught and tutored many college students both in the United States and Iraq. His love for teaching made him one of four students in Iraq to receive a full scholarship to pursue a B.S. degree in the States so to return back to his home country and teach.

He is passionate about Math & Science and loves to share his passion with others. To him, Mathematics and Sciences are crucial for everyone to learn no matter how little. He is a BIG believer in visual learning, and his aim is to deliver the concepts in an easy and direct way so as to make the learning process fast for everyone.

**Important Details**

- Length of time users can access this course: lifetime
- Access options: desktop & mobile
- Certificate of completion included
- Redemption deadline: redeem your code within 30 days of purchase
- Updates included
- Experience level required: all levels

**Requirements**

- Knowledge of basic operations like addition and multiplication

**Terms**

- Unredeemed licenses can be returned for store credit within 30 days of purchase. Once your license is redeemed, all sales are final.

- Your First Program
- Sets
- Sets intro - 0:19
- Defenition of a Set - 8:41
- Number Sets - 10:10
- Set Equality - 9:16
- Set-Builder Notation - 9:56
- Types of Sets - 11:49
- Subsets - 10:27
- Power Set - 5:06
- Ordered Pairs - 4:59
- Cartesian Products - 14:08
- Cartesian Plane - 3:38
- Venn Diagrams - 3:13
- Set Operations (Union, Intersection) - 14:35
- Properties of Union and Intersectio - 10:16
- Set Operations (Difference, Complement) - 11:57
- Properties of Difference and Complement - 7:29
- De Morgan’s Law - 8:17
- Partition of Sets - 15:49

- Logic
- Logic Intro - 0:22
- Statments - 7:13
- Compound Statements - 13:10
- Truth Tables - 9:20
- Examples - 13:03
- Logical Equivalence - 6:39
- Tautologies and Contradictions - 6:15
- De Morgan’s Laws in Logic - 11:34
- Logical Equivalence Laws - 3:23
- Conditional Statements - 12:58
- Negation of Conditional Statements - 9:31
- Converse and Inverse - 7:25
- Biconditional Statements - 8:46
- Examples - 11:50
- Digital Logic Circuits - 12:54
- Black Boxes and Gates - 15:18
- Boolean Expressions - 6:23
- Truth Tables and Circuits - 9:24
- Equivalent Circuits - 6:37
- NAND and NOR Gates - 7:12
- Quantified Statements-ALL - 7:36
- Quantified Statements-ANY - 6:39
- Negations of Quantified Statements - 8:28

- Number Theory
- Introduction - 0:35
- Parity - 12:43
- Divisibility - 10:45
- 44-Prime Numbers - 8:03
- 45-Prime Factorization - 8:33
- GCD, LCM - 17:23

- Proofs
- Proofs - 5:40
- Terminologies - 7:37
- Direct Proofs - 8:45
- Proof by Contraposition - 11:26
- Proofs by Contradiction - 17:16
- Proofs by Exhaustion - 13:36
- Existence & Uniqueness Proofs - 15:57
- Proofs by Induction - 11:41
- Induction Examples - 18:46

- Functions
- Introduction - 0:24
- Functions - 15:05
- Evaluating a Function - 12:29
- Domain - 15:56
- Range - 5:29
- Function Composition - 9:43
- Function Combination - 9:00
- Even and Odd function - 8:19
- One-to-One Function - 8:18
- Inverse Functinos - 10:10

- Relations
- Introduction - 0:25
- The Language of Relations - 10:26
- Relations on Sets - 12:44
- The Inverse of a Relation - 6:05
- Reflexivity, Symmetry, and Transitivity - 13:07
- Examples - 7:31
- Properties of Equality & Less Than - 7:48
- Equivalence Relation - 6:42
- Equivalence Class - 6:30

- Graph Theory
- Introduction - 0:28
- Graphs - 11:25
- Subgraphs - 8:32
- Degree - 9:52
- Sum of Degrees of Vertices Theorem - 23:22
- Adjacency and Incidence - 9:15
- Adjacency Matrix - 16:16
- Incidence Matrix - 8:04
- Isomorphisms - 8:23
- Walks, Trails, Paths, and Circuits - 12:41
- Examples - 10:18
- Eccentricity, Diameter, and Radius - 6:47
- Connectedness - 20:03
- Euler Trails and Circuits - 17:36
- Fleury’s Algorithm - 10:15
- Hamiltonian Paths and Circuits - 5:46
- Ore's Theorem - 14:08
- The Shortest Path Problem - 12:58

- Statistics
- Introduction - 0:19
- Terminologies - 3:05
- Mean - 3:31
- Median - 3:11
- Mode - 3:01
- Range - 8:00
- Outlier - 4:18
- Variance - 9:25
- Standard Deviation - 4:14

- Combinatorics
- Combinatorics - 3:29
- Factorials! - 7:46
- The Fundamental Counting Principle - 13:24
- Permutations - 12:50
- Combinations - 12:01
- Pigeonhole Principle - 6:10
- Pascal's Triangle - 8:20

- Sequence and Series
- Introduction - 0:19
- Sequnces - 6:37
- Arithmatic Sequance - 12:19
- Geometric Sequances - 8:57
- Partial Sums of Arithamtics Sequance - 11:56
- Partial Sum of Geometric Sequance - 6:31
- Series - 12:32

access

Lifetime

content

17.0 Hours

enrolled

234