Welcome to Discrete Mathematics 2, a course introducting Inclusion-Exclusion, Probability, Generating Functions, Recurrence Relations, and Graph Theory. Below, you will find the videos of each topic presented. If you have any suggestions or would like more practice on a certain topic, please send your suggestions to contact@trevtutor.com

### Lectures

##### Counting and Probability

Permutations and Combinations Review

Catalan Numbers

Discrete Probability

Axioms of Probability

Conditional Probability

Inclusion-Exclusion Principle

Inclusion-Exclusion Practice Problems

Inclusion-Exclusion “At Least/Exactly”

Derangements

##### Generating Functions and Recurrence Relations

Generating Functions

Coefficient Extraction and Extended Binomial Theorem

Partial Fraction Decomposition

Integer Partitions

Combinatorial Families

Recurrence Relations

Homogeneous Recurrence Relations

Non-Homogeneous Recurrence Relations

Generating Functions and Recurrence Relations

##### Graph Theory

Introduction to Graph Theory – Basics and Terminology

Subgraphs, Complements, and Complete Graphs

Isomorphisms and Bipartite Graphs

Vertex Degree and Regular Graphs

Euler Circuits and Euler Trails

Planar Graphs

Euler’s Theorem

Hamilton Cycles

Graph Coloring and Chromatic Polynomials

Trees

Tree Directories and Traversals

Dijkstra’s Algorithm

##### Exam Solution Videos

Midterm 1 Video Solutions

Midterm 2 Video Solutions

### Exercises

##### Generating Functions and Recurrence Relations

Coefficient Extraction

Homogeneous Recurrence Relations

Homogeneous Recurrence Relations 2

Nonhomogeneous Recurrence Relations

### Exams and Worksheets

Discrete Math 2 – Midterm 1

Discrete Math 2 – Midterm 1 Solutions

Discrete Math 2 – Midterm 2

Discrete Math 2 – Midterm 2 Solutions

Discrete Math 2 – Final

Discrete Math 2 – Final Solutions

Hi, Are there any videos about recurrence and relations? Your tutorials have helped me on my previous tests and my upcoming exam topic includes recurrence and relations.

Thank you so much for these tutorials. I have told all my friends to check out your website I am certain that they will find it useful as well.

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Recurrence Relation videos will be uploaded over the next 4-5 days.

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When will the trees video come out? Or do you have it referenced in another video?

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One suggestion: Chinese remainder theorem 😀 Thanks alot for all the good work 🙂

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The tutoring video is great. It’s taught in a way fun and easy to understand, with clear reasoning. Thank you very much for creating such great tutoring.

Do you have brief notes of the key points discussed in the video? That will help on review.

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Thanks! Unfortunately I have no such notes for each video. If anything, they’d just be near-exact copies of what was written in the video, which in that case I’d rather just recommend a textbook than notes for a written guide.

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Hello thanks for your tutorials. As you said you don’t have any notes for each video. Which text book will be better for written guide that will help me to better understand of Discrete mathematics?

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Grimaldi’s Discrete Math and Its Applications, as well as the Book of Proof which is available online for free.

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your videos are simply awesome.

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hi sir,

I would strongly recommend if you can make videos on number sequence, sum of sequences and its applications. These are also one of the toughest topics for me and I hope that from your videos these topics will be easily understandable for me. Thanks and Regards.

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Trev,

i cannot explain how useful the videos are!

There are very few teachers who can bridge that theoritical and textual knowledge to the real world applications/problems.

i find your videos help me solve some of the problems im dealing with.

thanks a ton

sai

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Thank you so much for posting these videos! They’re extremely clear and well done!

I had a question about the last example in the Discrete Math: Coefficient Extraction and Extended Binomial Theorem video.

In the second step, when x^6 was factored out of the series, why isn’t the remaining geometric series to the power of 6?

i.e. why did the equation become:

[x^50] x^36 (1 + x + x^2 + …)

As opposed to:

[x^50] x^36 (1 + x + x^2 + …)^6

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Hi, do you have videos that cover Warshall’s algorithm and lattices?

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