Discrete Math 2

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

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13 thoughts on “Discrete Math 2

  1. 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.

    Like

  2. 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.

    Like

    • 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.

      Like

      • 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?

        Like

  3. 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.

    Like

  4. 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

    Like

  5. 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

    Like

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