Welcome to Discrete Mathematics 1, a course introducing Set Theory, Logic, Functions, Relations, Counting, and Proofs. 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

##### Set Theory

Cartesian Products

Subsets and Power Sets

Set Operations

Indexed Sets and Well Ordering Principle

##### Logic

Truth Tables

Truth Table Proofs

Logic Laws

Conditionals, Converses, Inverses, Contrapositives

Rules of Inference

Quantificational Logic

##### Counting

Factorials and Permutations

Permutation Practice

Combinations

Binomial Theorem, Pascal’s Triangle

Combinations with Repetition

Permutations and Combinations Practice

##### Proof Techniques

##### Relations and Functions

Partial Orders

Introduction to Functions

Injections, Surjections, Bijections, Inverses

##### Number Theory and Formal Language

Divisibility

Modular Arithmetic

Primes and GCD

Euclidian Algorithm

Formal Languages

Finite State Machines

### Additional Exercise Videos

##### Set Theory

Cartesian Products

Set Operations

Sets and Subsets

Subsets and Power Sets

Symmetric Difference

##### Logic

Conditionals

Exclusive Or

Logic Laws

Logic Laws 2

Negating Quantifiers and Translation

Quantifiers and Unique Quantifiers

Sheffer Stroke

Statement Identification and Translation

Truth Tables

##### Counting

Combinations with Repetition

Permutations

Permutations and Combinations

Rule of Sum and Rule of Product

##### Proof Techniques

Direct Proofs

Mathematical Induction

Mathematical Induction 2 (Derivatives and Matrices)

Pigeonhole Principle

Proof by Cases

##### Relations and Functions

Functions

Inverse Functions

Inverse Functions 2

Relations

Surjective Functions

##### Number Theory and Formal Languages

Congruency Proofs

Divisibility

Euclidean Algorithm and GCDs

Finite State Automata

Floor and Ceiling

Formal Languages

### Exams and Worksheets

Discrete Math 1 – Midterm 1

Discrete Math 1 – Midterm 1 Solutions

Discrete Math 1 – Midterm 1 Video Solutions

Discrete Math 1 – Midterm 2

Discrete Math 1 – Midterm 2 Solutions

Discrete Math 1 – Midterm 2 Video Solutions

Discrete Math 1 – Final

Discrete Math 1 – Final Solutions

Very useful website, Now i know where to study discrete maths from 🙂

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Thanks for your support.

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thanks. you really helped me

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Hey I just finished 2nd lecture of Discrete Mathematics Part 1 … I would say great work. You have pretty great teaching talent ! Keep it up !

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Can you please update some tree’s problem to the final practice exam?

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Indeed, you have done a great job.

Suggestion: Please write about the prerequisites below the course content.

Otherwise what are the prerequisites for discrete mathematics 1 and Linear Algebra.

Thanks a tan for your tireless effort.

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The first course in each list requires no pre-reqs. Just need some basic high-school math.

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This is going to be great help to learn a lot of this stuff before I take Discrete in the fall semester in college. Discrete will be the hardest math class in the fall so these videos are a great help before I learn it,cause most of my time will be spent understanding Discrete cause I have many other classes to worry about that will be on the easier side like Calc and physics. Thanks for you help your videos make sense and you are a great tutor.

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Your videos are literally what I go to after every DM lecture. You are getting me through this class!! My prof is a mathematician and all, but teaching is not his strong point. Soooo cheers!!! 😀

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you are better than my dumb tutor.

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You are awesome! Very useful materials.

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you’ve make this course easy 4 me. Thanks 4 all your Time and Effort God bless.

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Hi i have a question can you give me a solution for that i didnot understand.

here is the question:

If a function is bijective then it is both injective and surjective explain why we need both definitions of injective and surjective with examples of your own(you can have more than one).

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