Welcome to the main Discrete Mathematics page. To go to a specific course, please click on the one of the links under the Discrete Mathematics tab above. No calculators required for this course! Here’s a description of course topics.

### Discrete Math 1

**Set Theory **– We begin by introducing sets. We discuss Cartesian Products, Power Sets, Operations, Subsets, and the Well Ordering Principle. This is the foundation of all of Discrete Mathematics.

**Logic** – This is a hyper-introduction to Propositional and Predicate Logic. Proofs are done by truth tables and basic rules of inference. We quickly touch on Predicate Logic and define the quantifiers a little more intuitively than most textbooks.

**Counting **– Although basic counting is simple, we look at the many ways that we can arrange people at tables, how many ways we can distribute books to children, and how many integer solutions there are to specific equations. We also look at the Binomial Distribution, which is incredibly important for fast expansion of polynomials.

**Proof Techniques **– Without proof techniques, you would never learn *real* mathematics. Although only simple proofs are done in the course, we introduce methods so in later courses you’re able to jump right into proofs without much difficulty.

**Relations and Functions **– We briefly touch on relations and functions. What is a function? What does it mean to be one-to-one, onto, bijective, or have inverse functions? What is symmetry, reflexivity, transitivity?

**Number Theory **– After introducing the pigeonhole principle, we discuss divisibility, prime numbers, greatest common divisors, and the Euclidian Algorithm. This is probably the most computational component in the course.

**Formal Languages** – We touch on formal languages and finite state machines. This introduction is very brief, but gives a basic overview of what’s to come in future courses. If demand is high to continue, I will probably do an entire separate course on this topic. Formal Languages are very involved and are very fun.

### Discrete Math 2

**Probability** – We look at finite probability and conditional probability. This is nothing too difficult, and is no more involved than an introductory statistics course.

**Inclusion-Exclusion Principle **– This is an important topic that covers derangements as well. What is a derangement? Well, consider 20 students take a test. How many ways can we have the tests marked so that no student is marking his own test? What is the probability that this can happen?

**Generating Functions** – Suppose our conditions on counting are a little bit stricter, and our questions are a little bit more challenging. How can we find the number of ways to do something that sounds so complicated? We introduce generating functions that produce power series, where each coefficient is the number of ways to complete some item of length *n*.

**Recurrence Relations **– We look at relationships between numbers. In a recurrence relation, the *n-th *number depends on some combination of previous numbers in the sequence. We look at solutions of recurrence relations, both homogeneous and non-homogeneous, as well as some word problems. We also take a look at how we can solve recurrence relations with Generating Functions.

**Graph Theory** – We cover a huge variety of basic topics and terminology in graph theory. We take a look at walks, trails, paths, circuits, cycles, Eulerian trails, Hamilton paths, subgraphs, isomorphisms, planar graphs, and relevant proofs.

**Optimization and Matching** – Another topic in Graph Theory, but we move into a very specific type of graphs – trees. We introduce trees, their properties, and then move into shortest path algorithms. Specifically, we look at Dijkstra’s algorithm.

**Extra Content** – Upon request, I added videos on flow networks and minimal cuts.

Just saw your discrete math videos yesterday and I’ve learned more watching 5 of your videos than 6 weeks worth of college. Thank you for your work and keep it up!

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One of the best tutors available online .. THANKS 🙂

I passed my midterm with highest scores just by watching your Discrete Mathematics tutorials thank you so much keep up the good work 🙂

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Excellent videos I have ever found. Really awesome. Can I have any text script of those videos? They will help me to understand more and more about discrete mathematics or any slide of those lectures? Thanks 🙂

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I do not have scripts for any of these videos, and unfortunately I cannot export the files I use to pdfs or slides since the program doesn’t export backgrounds that aren’t white.

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Your videos have helped EXTREMELY, more than my professor to be honest!

My exams next week if I passed you are all I have to thanks!

much appreciation Trevor!

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Just wanted to say thanks, your lessons have been a big help.

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Hey trev,

Is it possible you to share the slides that you’ve used in the videos, It will help us a lot to revise after watching your videos. I am preparing for some exam and I can’t make clean notes of everything. I tried and took proper notes in Generating functions and recurrence relations. But it took one entire week. So share the slides, If you could,

PLEASE ……

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Just wanted to say thanks, your lessons have been a big help.again thank u teacher

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Hi, Tev, I am taking MAD1100 at FIU, for summer semester I had done exam 1, and two, I do not know the results, but my filling is that I failed both, I have a chance to get a C if I get the right help, I am not young but my reasons to be an student at my age, is to be an inspiration to my family and others young students that age doesn’t mater to get an education. What can you recommend me, what I should emphasizes to get my goals?

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By far the best discrete math videos that I’ve come about, they’ve tought me more that I learned during the entire semester.. I am most greatful. Keep up the good work, you are making a world of difference.

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I’ve been a software developer for 42 years so I felt it was time to refresh my discrete maths knowledge your excellent course combined with some free Harvard machine learning courses have filled my lockdown hours nicely. Thank you!

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Hi I just had a question about surjective functions. Would it be possible for a function with a horizontal asymptote to be bijective when mapped from the domain of real numbers to codomain of real numbers?

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