Discrete Mathematics Course

241 Enrolled
17 Hours
\$15.99\$199.00
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116 Lessons (17h)

• Your First Program
• Sets
Sets intro0:19
Defenition of a Set8:41
Number Sets10:10
Set Equality9:16
Set-Builder Notation9:56
Types of Sets11:49
Subsets10:27
Power Set5:06
Ordered Pairs4:59
Cartesian Products14:08
Cartesian Plane3:38
Venn Diagrams3:13
Set Operations (Union, Intersection)14:35
Properties of Union and Intersectio10:16
Set Operations (Difference, Complement)11:57
Properties of Difference and Complement7:29
De Morgan’s Law8:17
Partition of Sets15:49
• Logic
Logic Intro0:22
Statments7:13
Compound Statements13:10
Truth Tables9:20
Examples13:03
Logical Equivalence6:39
De Morgan’s Laws in Logic11:34
Logical Equivalence Laws3:23
Conditional Statements12:58
Negation of Conditional Statements9:31
Converse and Inverse7:25
Biconditional Statements8:46
Examples11:50
Digital Logic Circuits12:54
Black Boxes and Gates15:18
Boolean Expressions6:23
Truth Tables and Circuits9:24
Equivalent Circuits6:37
NAND and NOR Gates7:12
Quantified Statements-ALL7:36
Quantified Statements-ANY6:39
Negations of Quantified Statements8:28
• Number Theory
Introduction0:35
Parity12:43
Divisibility10:45
44-Prime Numbers8:03
45-Prime Factorization8:33
GCD, LCM17:23
• Proofs
Proofs5:40
Terminologies7:37
Direct Proofs8:45
Proof by Contraposition11:26
Proofs by Exhaustion13:36
Existence & Uniqueness Proofs15:57
Proofs by Induction11:41
Induction Examples18:46
• Functions
Introduction0:24
Functions15:05
Evaluating a Function12:29
Domain15:56
Range5:29
Function Composition9:43
Function Combination9:00
Even and Odd function8:19
One-to-One Function8:18
Inverse Functinos10:10
• Relations
Introduction0:25
The Language of Relations10:26
Relations on Sets12:44
The Inverse of a Relation6:05
Reflexivity, Symmetry, and Transitivity13:07
Examples7:31
Properties of Equality & Less Than7:48
Equivalence Relation6:42
Equivalence Class6:30
• Graph Theory
Introduction0:28
Graphs11:25
Subgraphs8:32
Degree9:52
Sum of Degrees of Vertices Theorem23:22
Incidence Matrix8:04
Isomorphisms8:23
Walks, Trails, Paths, and Circuits12:41
Examples10:18
Eccentricity, Diameter, and Radius6:47
Connectedness20:03
Euler Trails and Circuits17:36
Fleury’s Algorithm10:15
Hamiltonian Paths and Circuits5:46
Ore's Theorem14:08
The Shortest Path Problem12:58
• Statistics
Introduction0:19
Terminologies3:05
Mean3:31
Median3:11
Mode3:01
Range8:00
Outlier4:18
Variance9:25
Standard Deviation4:14
• Combinatorics
Combinatorics3:29
Factorials!7:46
The Fundamental Counting Principle13:24
Permutations12:50
Combinations12:01
Pigeonhole Principle6:10
Pascal's Triangle8:20
• Sequence and Series
Introduction0:19
Sequnces6:37
Arithmatic Sequance12:19
Geometric Sequances8:57
Partial Sums of Arithamtics Sequance11:56
Partial Sum of Geometric Sequance6:31
Series12:32

Master the Backbone of Mathematics and Computer Science with 17 Hours of Content

MF
Miran Fattah

Miran Fattah | BS in Mathematics & Geophysics

4.4/5 Instructor Rating: ★ ★ ★ ★
Fattah has B.S. in Mathematics and Geophysics from the University 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 as 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.

15,431 Total Students
2,076 Reviews

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.

4.5/5 stars based on 4,414 students enrolled ★ ★ ★ ★

• 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

Specs

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