Discrete Math 1

Welcome to Discrete Mathematics 1, a course introducting 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

Set Operations
Indexed Sets and Well Ordering Principle

Logic

Logic Laws
Conditionals, Converses, Inverses, Contrapositives
Quantificational Logic

Counting

Binomial Theorem, Pascal’s Triangle
Combinations with Repetition
Permutations and Combinations Practice

Proof Techniques

Proof by Contradiction
Mathematical Induction

Relations and Functions

Introduction to Functions
Injections, Surjections, Bijections, Inverses

Number Theory and Formal Language

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

9 thoughts on “Discrete Math 1

  1. 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.

    Like

  2. 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.

    Like

  3. 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!!! 😀

    Like

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