Mô tả

MASTER DISCRETE MATH 2020 IS SET UP TO MAKE DISCRETE MATH EASY:

This 461-lesson course includes video and text explanations of everything from Discrete Math, and it includes 150 quizzes (with solutions!) after each lecture to check your understanding and an additional 30 workbooks with 500+ extra practice problems (also with solutions to every problem!), to help you test your understanding along the way.

This is the most comprehensive, yet straight-forward, course for Discrete Mathematics on Udemy! Whether you have never been great at mathematics, or you want to learn about the advanced features of Discrete Math, this course is for you! In this course we will teach you Discrete Mathematics.

Master Discrete Math 2020 is organized into the following 24 sections:

  • Mathematical Statements

  • Set Theory

  • Functions And Function Notation

  • Relations

  • Additive And Multiplicative Principles

  • Binomial Coefficients

  • Combinations And Permutations

  • Combinatorial Proofs

  • Advanced Counting Using The Principle Of Inclusion And Exclusion

  • Describing Sequences

  • Arithmetic And Geometric Sequences

  • Polynomial Fitting

  • Solving Recurrence Relations

  • Mathematical Induction

  • Propositional Logic

  • Proofs And Proving Techniques

  • Graph Theory Definitions

  • Trees

  • Planar Graphs

  • Coloring Graphs

  • Euler Paths And Circuits

  • Matching In Bipartite Graphs

  • Generating Functions

  • Number Theory

AND HERE'S WHAT YOU GET INSIDE OF EVERY SECTION:

Videos: Watch engaging content involving interactive whiteboard lectures as I solve problems for every single math issue you’ll encounter in discrete math. We start from the beginning... I explain the problem setup and why I set it up that way, the steps I take and why I take them, how to work through the yucky, fuzzy middle parts, and how to simplify the answer when you get it.

Notes: The notes section of each lesson is where you find the most important things to remember. It’s like Cliff Notes for books, but for Discrete Math. Everything you need to know to pass your class and nothing you don’t.

Quizzes: When you think you’ve got a good grasp on a topic within a lecture, test your understanding with a quiz. If you pass, great! If not, you can review the videos and notes again or ask for help in the Q&A section.

Workbooks: Want even more practice? When you've finished the section, you can review everything you've learned by working through the bonus workbooks. These workbooks include 500+ extra practice problems (all with detailed solutions and explanations for how to get to those solutions), so they're a great way to solidify what you just learned in that section.

YOU'LL ALSO GET:

  • Lifetime access to a free online Discrete Math textbook

  • Lifetime access to Master Discrete Math 2020

  • Friendly support in the Q&A section

  • Udemy Certificate of Completion available for download

So what are you waiting for? Learn Discrete Math in a way that will advance your career and increase your knowledge, all in a fun and practical way!


HERE'S WHAT SOME STUDENTS OF MASTER DISCRETE MATH 2020 HAVE TOLD ME:

  • “The course covers a lot of Discrete Math topics helping someone like me who knew nothing about discrete mathematics. The course structure is well-arranged and the explanation for every topic is given in a very simple manner. It helped me a lot. I really want to thank the instructor for helping me to explore this amazing world of Discrete Math." - Shibbu J.

  • "This course is great. Discrete Math is difficult, but Amour's explanations are very clear. I have bought other math courses by Kody Amour and all of them are great, well-explained and easy to follow." - Susan M.

  • "Very comprehensive course and exceptionally articulated." - Faisal Abbas

  • "Best course for Discrete Maths on Udemy." - Vatsal P.


Will this course give you core discrete math skills?

Yes it will. There are a range of exciting opportunities for students who take Discrete Math. All of them require a solid understanding of Discrete Math, and that’s what you will learn in this course.

Why should you take this course?

Discrete Mathematics is the branch of mathematics dealing with objects that can assume only distinct, separated values. Discrete means individual, separate, distinguishable implying discontinuous or not continuous, so integers are discrete in this sense even though they are countable in the sense that you can use them to count. The term “Discrete Mathematics” is therefore used in contrast with “Continuous Mathematics,” which is the branch of mathematics dealing with objects that can vary smoothly (and which includes, for example, calculus). Whereas discrete objects can often be characterized by integers, continuous objects require real numbers.

Almost all middle or junior high schools and high schools across the country closely follow a standard mathematics curriculum with a focus on “Continuous Mathematics.” The typical sequence includes:

Pre-Algebra -> Algebra 1 -> Geometry -> Algebra 2/Trigonometry -> Precalculus -> Calculus Multivariable Calculus/Differential Equations

Discrete mathematics has not yet been considered a separate strand in middle and high school mathematics curricula. Discrete mathematics has never been included in middle and high school high-stakes standardized tests in the USA. The two major standardized college entrance tests: the SAT and ACT, do not cover discrete mathematics topics.

Discrete mathematics grew out of the mathematical sciences’ response to the need for a better understanding of the combinatorial bases of the mathematics used in the real world. It has become increasingly emphasized in the current educational climate due to following reasons:

Many problems in middle and high school math competitions focus on discrete math

Approximately 30-40% of questions in premier national middle and high school mathematics competitions, such as the AMC (American Mathematics Competitions), focus on discrete mathematics. More than half of the problems in the high level math contests, such as the AIME (American Invitational Mathematics Examination), are associated with discrete mathematics. Students not having enough knowledge and skills in discrete mathematics can’t do well on these competitions. Our AMC prep course curriculum always includes at least one-third of the studies in discrete mathematics, such as number theory, combinatorics, and graph theory, due to the significance of these topics in the AMC contests

Discrete Mathematics is the backbone of Computer Science

Discrete mathematics has become popular in recent decades because of its applications to computer science. Discrete mathematics is the mathematical language of computer science. Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in all branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations are tremendously significant in applying ideas from discrete mathematics to real-world applications, such as in operations research.

The set of objects studied in discrete mathematics can be finite or infinite. In real-world applications, the set of objects of interest are mainly finite, the study of which is often called finite mathematics. In some mathematics curricula, the term “finite mathematics” refers to courses that cover discrete mathematical concepts for business, while “discrete mathematics” courses emphasize discrete mathematical concepts for computer science majors.

Discrete math plays the significant role in big data analytics.

The Big Data era poses a critically difficult challenge and striking development opportunities: how to efficiently turn massively large data into valuable information and meaningful knowledge. Discrete mathematics produces a significant collection of powerful methods, including mathematical tools for understanding and managing very high-dimensional data, inference systems for drawing sound conclusions from large and noisy data sets, and algorithms for scaling computations up to very large sizes. Discrete mathematics is the mathematical language of data science, and as such, its importance has increased dramatically in recent decades.

IN SUMMARY, discrete mathematics is an exciting and appropriate vehicle for working toward and achieving the goal of educating informed citizens who are better able to function in our increasingly technological society; have better reasoning power and problem-solving skills; are aware of the importance of mathematics in our society; and are prepared for future careers which will require new and more sophisticated analytical and technical tools. It is an excellent tool for improving reasoning and problem-solving abilities.

Starting from the 6th grade, students should some effort into studying fundamental discrete math, especially combinatorics, graph theory, discrete geometry, number theory, and discrete probability. Students, even possessing very little knowledge and skills in elementary arithmetic and algebra, can join our competitive mathematics classes to begin learning and studying discrete mathematics.

Does the course get updated?

It’s no secret how discrete math curriculum is advancing at a rapid rate. New, more complex content and topics are changing Discrete Math courses across the world every day, meaning it’s crucial to stay on top with the latest knowledge.

A lot of other courses on Udemy get released once, and never get updated. Learning from an outdated course and/or an outdated version of Discrete Math can be counter productive and even worse - it could teach you the wrong way to do things.

There's no risk either!

This course comes with a full 30 day money-back guarantee. Meaning if you are not completely satisfied with the course or your progress, simply let Kody know and he will refund you 100%, every last penny no questions asked.

You either end up with Discrete Math skills, go on to succeed in college level discrete math courses and potentially make an awesome career for yourself, or you try the course and simply get all your money back if you don’t like it…

You literally can’t lose. Ready to get started?

Enroll now using the “Add to Cart” button on the right, and get started on your way to becoming a master of Discrete Mathematics. Or, take this course for a free spin using the preview feature, so you know you’re 100% certain this course is for you.

See you on the inside (hurry, your Discrete Math class is waiting!)

Some content was used from Creative Commons, and attribution is provided within the curriculum of this course.

Bạn sẽ học được gì

Analyze and interpret the truth value of statements by identifying logical connectives, quantification and the truth value of each atomic component

Distinguish between various set theory notations and apply set theory concepts to construct new sets from old ones

Interpret functions from the perspective of set theory and differentiate between injective, surjective and bijective functions

Construct new relations, including equivalence relations and partial orderings

Apply the additive and multiplicative principles to count disorganized sets effectively and efficiently

Synthesize counting techniques developed from counting bit strings, lattice paths and binomial coefficients

Formulate counting techniques to approach complex counting problems using both permutations and combinations

Prove certain formulas are true using special combinatorial proofs and complex counting techniques involving stars and bars

Connect between complex counting problems and counting functions with certain properties

Develop recurrence relations and closed formulas for various sequences

Explain various relationships and properties involving arithmetic and geometric sequences

Solve many recurrence relations using polynomial fitting

Utilize the characteristic polynomial to solve challenging recurrence relations

Master mathematical induction and strong induction to prove sophisticated statements involving natural numbers by working through dozens of examples

Use truth tables and Boolean Algebra to determine the truth value of complex molecular statements

Apply various proving techniques, including direct proofs, proof by contrapositive and proof by contradiction to prove various mathematical statements

Analyze various graphs using new definitions from graph theory

Discover many various properties and algorithms involving trees in graph theory

Determine various properties of planar graphs using Euler's Formula

Categorize different types of graphs based on various coloring schemes

Create various properties of Euler paths and circuits and Hamiltonian paths and cycles

Apply concepts from graph theory, including properties of bipartite graphs and matching problems

Use generating functions to easily solve extremely sophisticated recurrence relations

Develop a deep understanding of number theory which involve patterns in the natural numbers

Yêu cầu

  • You should be comfortable with high school algebra
  • Be ready to learn an insane amount of awesome stuff
  • Prepare to succeed in any college level Discrete Math course
  • Brace yourself for tons of content

Nội dung khoá học

30 sections

Introduction

5 lectures
Welcome To Discrete Mathematics!
02:38
What Is Discrete Mathematics?
05:31
Why Study Discrete Mathematics?
01:49
Who Should You Take Discrete Mathematics?
02:47
How To Obtain Your Free Textbook
00:58

PART 1.1 (FOUNDATIONS): MATHEMATICAL STATEMENTS - Analyze Truth In Statements

23 lectures
Mathematical Statements In Discrete Math
02:13
Mathematical Statements Quiz
1 question
Atomic And Molecular Statements - How To Break Apart Complex Statements
09:27
Atomic And Molecular Statements Quiz
1 question
An Overview Of Implications
09:22
Implications Quiz
1 question
Direct Proofs Of Implications
05:36
Direct Proofs Of Implications Quiz
1 question
What Is The Converse And The Contrapositive Of A Statement?
07:43
Converse And Contrapositive Quiz
1 question
The Dreaded If And Only If Connective
02:57
Biconditional Quiz
1 question
What Does It Mean To Be Necessary And Sufficient?
03:57
Necessary And Sufficient Quiz
1 question
What Exactly Are Free Variables and Predicates?
03:06
Free Variables and Predicates Quiz
1 question
What Are Universal Quantifiers And Existential Quantifiers?
05:15
Universal And Existential Quantifiers Quiz
1 question
How To Properly Negate Quantifiers
01:22
Negating Quantifiers Quiz
1 question
How To Unravel Implicit Quantifiers (Or Hidden Quantifiers)
03:32
Implicit Quantifiers Quiz
1 question
Mathematical Statements Assignment With Solutions
15 questions

PART 1.2 (FOUNDATIONS): SET THEORY - Construct New Sets From Old Sets

22 lectures
Introduction To Sets In Discrete Math
01:41
Introduction To Sets Quiz
1 question
An Overview Of Set Notation
06:29
Set Notation Quiz
1 question
What Is Set Builder Notation?
06:00
Set Builder Notation Quiz
1 question
A Complete Review Of Set Theory Notation
04:59
Set Theory Notation Quiz
1 question
Interpreting Relationships Between Sets
02:51
Relationships Between Sets Quiz
1 question
What Is The Power Set?
04:39
Power Set Quiz
1 question
Cardinality - How To Count Elements Of Sets
04:53
Cardinality Quiz
1 question
Operations On Sets - Making New Sets From Old Sets
06:06
Operations On Sets Quiz
1 question
How To Combine Sets With The Cartesian Product
05:08
The Cartesian Product Quiz
1 question
Venn Diagrams - A Complete Introduction
02:41
Venn Diagrams Quiz
1 question
Sets Assignment Part One With Solutions
24 questions
Sets Assignment Part Two With Solutions
5 questions

PART 1.3 (FOUNDATIONS): FUNCTIONS AND FUNCTION NOTATION - Apply Set Theory

17 lectures
What Are Functions In Discrete Math?
04:29
Functions Quiz
1 question
How To Interpret Functions With Set Theory - Part One
04:38
Interpreting Functions With Set Theory - Part One Quiz
1 question
How To Interpret Functions With Set Theory - Part Two
02:38
Interpreting Functions With Set Theory - Part Two Quiz
1 question
What Are Recursively Defined Functions?
05:55
Recursively Defined Functions Quiz
1 question
Introduction To Surjective, Injective And Bijective Functions
12:37
Surjective, Injective And Bijective Functions Quiz
1 question
The Difference Between Injective And Surjective Functions
04:17
Injective And Surjective Functions Quiz
1 question
Image And Inverse Image - A Closer Look Into The Codomain
13:20
Image And Inverse Image Quiz
1 question
A Complete List Of Function Definitions
05:58
Function Definitions Quiz
1 question
Functions Assignment With Solutions
10 questions

PART 1.4 (FOUNDATIONS): RELATIONS - Construct Relationships Within Sets

6 lectures
What Is A Relation Between Sets?
05:25
Relations Between Sets Quiz
1 question
Equivalence Relations - Reflexive, Symmetric And Transitive
13:07
Equivalence Relations Quiz
1 question
Partially Ordered Sets (Posets) - Asymmetry And Totally Ordered Sets
11:02
Posets Quiz
1 question

PART 2.1: ADDITIVE AND MULTIPLICATIVE PRINCIPLES - Count Disorganized Sets Well

15 lectures
What Is The Additive Principle?
04:35
Additive Principle Quiz
1 question
What Is The Multiplicative Principle?
05:35
Multiplicative Principle Quiz
1 question
How To Count Sets In Discrete Math
01:37
Counting Sets Quiz
1 question
Revisiting The Additive Principle With Sets
01:24
Additive Principle Quiz 2.0
1 question
Using The Cartesian Product To Interpret The Multiplicative Principle With Sets
08:43
Multiplicative Principle Quiz 2.0
1 question
What Is The Principle Of Inclusion And Exclusion - Cardinality Of A Set Union
05:40
The Principle Of Inclusion And Exclusion Quiz
1 question
Computing The Cardinality Of A Union Between Three Sets
04:54
PIE Application Quiz
1 question
Additive And Multiplicative Principles Assignment With Solutions
9 questions

PART 2.2: BINOMIAL COEFFICIENTS - Count Bit Strings, Lattice Paths And Much More

15 lectures
Subsets - Revisiting Set Theory
09:11
Subsets Quiz
1 question
What Are Bit Strings?
12:08
Bit Strings Quiz
1 question
What Are Lattice Paths?
08:43
Lattice Paths Quiz
1 question
An Introduction To Binomial Coefficients
15:07
Binomial Coefficients Quiz
1 question
A Complete List Of Interpretations Of Binomial Coefficients
01:50
Binomial Coefficient Interpretations Quiz
1 question
What Is The Recurrence Relation For The Binomial Coefficient?
01:35
Recurrence Relation For The Binomial Coefficient Quiz
1 question
A Deep Explanation Of Pascal's Triangle
03:07
Pascal's Triangle Quiz
1 question
Binomial Coefficients Assignment With Solutions
11 questions

PART 2.3: COMBINATIONS AND PERMUTATIONS - Formulate Complex Counting Techniques

7 lectures
An Introduction To Permutations In Discrete Math
02:18
Permutations Quiz
1 question
A Closer Look Into k-Permutations Of n Elements
06:32
k-Permutations Quiz
1 question
The Closed Formula For The Binomial Coefficient
03:14
Binomial Coefficient Formula Quiz
1 question
Combinations And Permutations Assignment With Solutions
10 questions

PART 2.4: COMBINATORIAL PROOFS - Apply Special Combinations

10 lectures
What Are The Patterns In Pascal's Triangle & Binomial Identities
09:21
Pascal's Triangle Patterns Quiz
1 question
An Introduction To Combinatorial Proofs
20:01
Combinatorial Proofs Quiz
1 question
Introduction To Stars And Bars - Part One
11:26
Stars And Bars Quiz
1 question
Introduction To Stars And Bars - Part Two
10:50
Stars And Bars Quiz 2.0
1 question
Combinatorial Proofs Assignment With Solutions
3 questions
Stars And Bars Assignment With Solutions
10 questions

PART 2.5: ADVANCED PRINCIPLE OF INCLUSION AND EXCLUSION - Avoid Double Counting

11 lectures
Advanced Counting Using The Principle Of Inclusion And Exclusion
10:58
Advanced Counting Quiz
1 question
How Do You Count Derangements?
09:02
Derangements Quiz
1 question
An Introduction To Counting Functions With Unique Properties
06:30
Counting Functions With Unique Properties Quiz
1 question
How To Count Surjective Functions Using The Principle Of Inclusion Exclusion
05:57
Counting Surjective Functions
1 question
How To Count Functions To Solve Problems From Different Contexts
05:56
Counting Functions Quiz
1 question
Advanced Counting Using The PIE Assignment With Solutions
10 questions

PART 2.6: COUNTING REVIEW WITH DETAILED SOLUTIONS

2 lectures
Counting Review Assignment Part One
10 questions
Counting Review Assignment Part Two
9 questions

PART 3.1: DESCRIBING SEQUENCES - Recurrence Relations And Closed Formulas

9 lectures
How To Interpret Sequences
03:51
Interpreting Sequences Quiz
1 question
Closed Formulas For Sequences Versus Recursive Definitions
07:31
Closed Formulas Versus Recursive Definitions Quiz
1 question
Examples Of Sequences With Closed Formulas And Recursive Definitions
11:52
Examples of Sequences Quiz
1 question
How To Construct Sequences Using Partial Sums
04:19
Partial Sums Quiz
1 question
Describing Sequences Assignment With Solutions
8 questions

PART 3.2: ARITHMETIC AND GEOMETRIC SEQUENCES - Explain Various Relationships

11 lectures
Introduction To Arithmetic Sequences
05:01
Arithmetic Sequences Quiz
1 question
Introduction To Geometric Sequences
04:34
Geometric Sequences Quiz
1 question
Computing Sums Of Arithmetic And Geometric Sequences
05:16
Sums of Arithmetic And Geometric Sequences Quiz
1 question
Summing Arithmetic Sequences: Reverse And Add
02:30
Sums of Arithmetic And Geometric Sequences 2.0 Quiz
1 question
Summing Geometric Sequences: Multiply, Shift And Subtract
03:20
Summing Geometric Sequences Quiz
1 question
Arithmetic And Geometric Sequences Assignment With Solutions
9 questions

PART 3.3: POLYNOMIAL FITTING - Solve Many Recurrence Relations With Polynomials

5 lectures
What Is Polynomial Fitting?
05:43
Polynomial Fitting Quiz
1 question
What Are Finite Differences?
06:11
Finite Differences Quiz
1 question
Polynomial Fitting Assignment With Solutions
10 questions

PART 3.4: SOLVING RECURRENCE RELATIONS - Apply Characteristic Polynomials

13 lectures
How To Solve Recurrence Relations
04:49
Recurrence Relations Quiz
1 question
What Are Telescoping Sequences?
07:34
Telescoping Sequences Quiz
1 question
Utilizing Iterations To Interpret Recurrence Relations
07:31
Iterations Quiz
1 question
An Overview Of The Characteristic Root Technique
05:40
Characteristic Root Technique Quiz
1 question
What Is The Characteristic Polynomial And The Characteristic Equation?
06:58
Characteristic Polynomial Quiz
1 question
How To Use The Characteristic Root Technique For Repeated Roots
09:16
Repeated Roots Quiz
1 question
Solving Recurrence Relations Assignment With Solutions
8 questions

PART 3.5: MATHEMATICAL INDUCTION - Prove Statements With Natural Numbers

23 lectures
An Introduction To Induction - An Advanced Proving Technique
07:21
Induction Quiz
1 question
How To Interpret The Base Case And The Inductive Case In Induction
22:25
Base Case And Inductive Step Quiz
1 question
How To Formalize Proofs In Discrete Math
02:19
Formal Induction Quiz
1 question
An Overview Of The Induction Proof Structure
05:58
Induction Proof Structure Quiz
1 question
Our First Example Of Using Mathematical Induction
08:29
Example Of Using Mathematical Induction Quiz
1 question
Our Second Example Of Using Mathematical Induction
05:49
Example Of Using Mathematical Induction Quiz 2.0
1 question
Our Third Example Of Using Mathematical Induction
07:24
Example Of Using Mathematical Induction Quiz 3.0
1 question
A Warning About Mathematical Induction
05:33
A Warning About Mathematical Induction Quiz
1 question
Strong Induction - An Introduction With Chocolate Bars
06:49
Strong Induction Quiz
1 question
Using Strong Induction To Prove Statements About Chocolate Bars
03:53
Using Strong Induction Quiz
1 question
Using Strong Induction To Prove: Natural Numbers Factor Into Products Of Primes
03:30
Using Strong Induction Quiz 2.0
1 question
Induction Assignment With Solutions
11 questions

PART 3.6: SEQUENCES REVIEW WITH DETAILED SOLUTIONS

1 lectures
Sequences Review Assignment With Solutions
10 questions

PART 4.1: PROPOSITIONAL LOGIC - Determine Truth Values Of Molecular Statements

19 lectures
An Introduction To Arguments and Propositions In Mathematics
08:31
Arguments Quiz
1 question
What Are Truth Tables - Interpreting Complex Statements With Truth Values
11:09
Truth Tables Quiz
1 question
What Is Logical Equivalence?
07:19
Logical Equivalence Quiz
1 question
What Are De Morgan's Laws?
01:42
De Morgan's Law Quiz
1 question
Using Truth Tables To Show How Implications Are Disjunctions
01:10
Implications Are Disjunctions Quiz
1 question
The Negation Of The Negation Is Logically Equivalent To The Original
01:47
Double Negation Quiz
1 question
What Does It Mean To Negate An Implication?
03:01
Negating An Implication Quiz
1 question
Deductions - How To Deduce Within A Proof
08:19
Deductions Quiz
1 question
Let's Go Beyond Propositions
03:03
Propositional Logic Quiz
1 question
Propositional Logic Assignment With Solutions
5 questions

PART 4.2: PROOFS AND PROVING TECHNIQUES - Overview Of Common Proving Techniques

15 lectures
What Is A Proof In Discrete Math?
01:30
What Is A Proof?
1 question
The Proof That There Are Infinitely Many Primes
11:05
The Fundamental Theorem Of Arithmetic Quiz
1 question
How To Create A Direct Proof - Proving If n Is Even, Then n^2 Is Even
03:21
Direct Proof Quiz
1 question
Creating A Proof By Contrapositive With An Example
05:18
Contrapositive Proof Quiz
1 question
Creating A Proof By Contradiction - Proving The Negative Of A Statement Is False
08:51
Contradiction Proof Quiz
1 question
Proof By Counterexample - How To Proving A Statement Is NOT True
07:18
Counterexample Proof Quiz
1 question
How To Use Cases To Prove Statements
06:56
Cases Proof Quiz
1 question
Proofs Assignment With Solutions
4 questions

PART 4.3: SYMBOLIC LOGIC AND PROOFS REVIEW WITH DETAILED SOLUTIONS

1 lectures
Symbolic Logic And Proofs Review Assignment With Solutions
8 questions

PART 5.1: GRAPH THEORY DEFINITIONS - An Introduction To Graph Theory

19 lectures
Introduction To Graphs And Graph Theory
05:57
Introduction To Graphs Quiz
1 question
What Is A Graph?
05:52
What Is A Graph Quiz
1 question
What Are Isomorphic Graphs? What Does It Mean To Be Isomorphic In This Context?
08:01
Isomorphic Graphs Quiz
1 question
The Definition Of A Subgraph And An Induced Subgraph
04:27
Subgraphs Quiz
1 question
An Overview Of Simple Graphs, Multigraphs And Connected Graphs
02:23
Types Of Graphs Quiz
1 question
An Overview Of Complete Graphs And The Degree Of A Vertex
05:15
Complete Graphs And Degrees Quiz
1 question
The Handshaking Lemma With Examples
10:09
The Handshake Lemma Quiz
1 question
Advanced Graphs: Bipartite Graphs And Complete Bipartite Graphs
03:05
Bipartite Graphs Quiz
1 question
A Complete List Of Important Definitions In Graph Theory
06:28
Important Graph Theory Definitions Quiz
1 question
Graph Theory Definitions Assignment With Solutions
3 questions

PART 5.1: TREES - Discover Many Various Properties And Algorithms Involving Tree

15 lectures
What Are Trees And Why Are They Important?
04:11
Trees Quiz
1 question
Properties Of Trees - Part One
11:02
Properties Of Trees Quiz
1 question
Properties Of Trees - Part Two
05:00
Properties Of Trees Quiz 2.0
1 question
Properties Of Trees - Part Three
07:19
Properties Of Trees Quiz 3.0
1 question
Breadth First Searches And Depth First Searches With Rooted Trees
05:33
Algorithms With Rooted Trees Quiz
1 question
An Overview Of Rooted Trees
06:12
Rooted Trees Quiz
1 question
What Are Spanning Trees?
09:17
Spanning Trees Quiz
1 question
Trees Assignment With Solutions
4 questions

PART 5.2: PLANAR GRAPHS - Determine various properties using Euler's Formula

9 lectures
An Introduction To Planar Graphs - Graphs That Don't Intersect Themselves
01:55
Planar Graphs Quiz
1 question
What Is Euler's Formula For Planar Graphs
04:52
Euler's Formula Quiz
1 question
The Complex Nature Of Non-planar Graphs
07:52
Non Planar Graphs Quiz
1 question
Interpreting Polyhedra With Graph Theory
03:13
Polyhedra Quiz
1 question
Planar Graphs Assignment With Solutions
5 questions

PART 5.3: COLORING GRAPHS - Apply Various Coloring Schemes To Color Graphs

13 lectures
A Look Into Coloring Graphs In General
06:06
Coloring Graphs Quiz
1 question
What Is The Four Color Theorem?
02:39
Four Color Theorem Quiz
1 question
Cliques And The Clique Number In Graph Theory
06:54
Cliques Quiz
1 question
An Introduction To Coloring Graphs - Brooks' Theorem
04:44
Brooks' Theorem Quiz
1 question
Coloring Edges Of Graphs, Instead Of Vertices
06:43
Chromatic Index Quiz
1 question
An Introduction To Ramsey Theory
01:48
Ramsey Theory Quiz
1 question
Coloring Assignment With Solutions
3 questions

PART 5.4: EULER PATHS AND CIRCUITS - Understanding Special Paths And Cycles

7 lectures
Euler Paths And Circuits In Graph Theory - Part One
04:05
Euler Paths And Circuits Quiz
1 question
Euler Paths And Circuits In Graph Theory - Part Two
02:07
Euler Paths And Circuits Quiz 2.0
1 question
Hamiltonian Paths - A Look Into Very Special Paths On Graphs
03:46
Hamiltonian Paths Quiz
1 question
Euler Paths And Circuits Assignment With Solutions
1 question

PART 5.5: MATCHING IN BIPARTITE GRAPHS - Apply Concepts From Graph Theory

4 lectures
An Introduction To Matching In Bipartite Graphs
07:47
Bipartite Matching Quiz
1 question
Understanding Hall's Marriage Theorem
08:03
Hall's Marriage Theorem Quiz
1 question

PART 5.6: GRAPH THEORY REVIEW WITH DETAILED SOLUTIONS

2 lectures
Graph Theory Review Assignment Part One With Solutions
12 questions
Graph Theory Review Assignment Part Two With Solutions
6 questions

PART 6 (EXTRA): GENERATING FUNCTIONS - Easily Solve Complex Recurrence Relations

13 lectures
An Introduction To Generating Functions
07:25
Generating Functions Quiz
1 question
How To Create A Generating Function - Part One
07:06
Creating Generating Functions Quiz
1 question
How To Create A Generating Function - Part Two
08:50
Creating Generating Functions Quiz 2.0
1 question
What Is Differencing With Generating Functions?
09:31
Differencing With Generating Functions Quiz
1 question
Multiplication And Partial Sums
10:31
Multiplication And Partial Sums Quiz
1 question
How To Solve Recurrence Relations With Generating Functions
07:29
Solving Recurrence Relations With Generating Functions Quiz
1 question
Generating Functions Assignment With Solutions
11 questions

PART 7 (EXTRA): NUMBER THEORY - Study Patterns And Secrets Of Natural Numbers

23 lectures
Introduction To Number Theory - My Favorite Math Topic!
03:08
Number Theory Quiz
1 question
What Is Divisibility - Dividing versus Dividable
13:06
Divisibility Quiz
1 question
A Formal Representation Of The Division Algorithm
02:31
The Division Algorithm Quiz
1 question
An Overview Of The Remainder Classes
05:49
Remainder Classes Quiz
1 question
Introduction To The Congruence Modulo (mod n)
09:19
Mod n Quiz
1 question
What Are Properties Of Congruences In Number Theory?
08:31
Properties Of Congruences Quiz
1 question
How To Properly Divide While Working With Congruences (mod n)
07:06
Dividing Mod n Quiz
1 question
How To Solve For Variables In Congruences
09:56
Solving For Variables In Congruences Quiz
1 question
Which Congruences Have No Solutions?
03:17
No Solutions In Congruence Quiz
1 question
A Complete Guide To Solving Linear Diophantine Equations Part One
09:58
Linear Diophantine Equations Quiz
1 question
A Complete Guide To Solving Linear Diophantine Equations Part Two
09:23
Linear Diophantine Equations Quiz 2.0
1 question
Introduction To Number Theory Assignment With Solutions
9 questions

PART 8: CONCLUSION - HOW TO KEEP LEARNING

2 lectures
Conclusion Lecture
02:47
Bonus Lecture (Coupon Codes For Other Courses - Updated 6/30/20)
00:40

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