Math Proofs 101: Mathematical Structures, Sets And Logic
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Math Proofs 101: Mathematical Structures, Sets And Logic

Learn How To Deductively Prove Any Mathematical Fact! Realize The True Nature Of Mathematics From A New Perspective!
4.4 (12 ratings)
Instead of using a simple lifetime average, Udemy calculates a course's star rating by considering a number of different factors such as the number of ratings, the age of ratings, and the likelihood of fraudulent ratings.
586 students enrolled
Created by Kody D'Amours
Last updated 7/2015
Current price: $10 Original price: $20 Discount: 50% off
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  • 5.5 hours on-demand video
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  • Certificate of Completion
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What Will I Learn?
Prove ANY Mathematical Fact
Understand Truth And Validity
Approach Mathematics With A Great New Perspective
View Curriculum
  • You should purchase "How To Prove It"

When we grow up and take math courses, we tend to ask: "Why is that true?" Most of the time, the teacher tells you something like "because that's the way it is." In this course, we reintroduce all of mathematics in the perspective that we should have. We answer and PROVE the "why" in our lives. The greatest part is that we are dealing with truth - something that science or any other subject can talk about. Everything proven in this course is absolute truth and cannot be denied.

Many students get their first exposure to mathematical proofs in a high school course on geometry. Unfortunately, students in high school geometry are usually taught to think of a proof as a numbered list of statements and reasons, a view of a proof that is too restrictive to be very useful.

Learn How To Prove It Today!

In this course, we learn how to prove amazing mathematical facts:

  • The square root of 2 is irrational
  • An even number plus an even number is an odd number
  • Prove that certain functions are continuous
  • Prove that there are infinitely many prime numbers
  • Understand infinity!
  • What is equality and inequality?

The proofs in this course may sound extremely simple, but if I were to ask you to prove 1+1=2, could you do it? It takes 362 pages to prove this fact! Well, there are better methods today, but the process of proving things is more fun than you can imagine!

What Are You Waiting For? Sign Up Today!

Who is the target audience?
  • ANYONE Can Take This Course! NO PREREQUISITES!!!
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Curriculum For This Course
Expand All 30 Lectures Collapse All 30 Lectures 05:15:42
What Is Logic?
5 Lectures 46:25

Welcome to my course! I am excited to show you a new perspective on deduction and logic.

Preview 04:43

Deductive Reasoning and Logical Connectives

See how to compare two logical systems and determine equivalences.

Truth Tables

See an example of how we can prove basic equivalences in logic theory.

Truth Table Example

Though we know how to prove these statements, learn how we can simplify more intricate logical sytems using a few easy rules.

Laws of Logic
Set Theory
5 Lectures 51:25

Learn about the first and only object needed in all of logic and mathematics.

What is a Set?

Watch and see how these sets can act a lot like logical systems.

Operations on Sets

Realize the misunderstandings of the implication and how unicorns are in fact purple!

Implication - See Why Unicorns Are All Purple!

Sometimes we want to say (p->q)^(q->p), but the biconditional takes care of this common logical relation.


In this lecture, we prove basic facts about set theory without using truth tables.

Proofs Involving Sets
Quantificational Logic
5 Lectures 54:23

Understand existence and universal quantification.

Introduction to Quantifiers

Understand everything about the empty set!

Everything is True About Nothing

How can you take an English statement and determine the opposite of that statement?


Test your knowledge of quantifiers and the ability to negate.

Negation of a Quote From Abraham Lincoln

Thought we were done with sets? In this lecture, we learn more about operations on sets.

More Operations on Sets
How To Prove It
4 Lectures 43:19

Welcome to the first lecture where we get into mathematical proofs!

Preview 10:46

Sometimes, it's not possible to prove a mathematical fact, so we need more proof techniques.

Proof by Contrapositive

This is one of the most common proof techniques. Prove an implication by assuming the implication fails and that this implies a crazy contradiction such as 1+1=fish!

Preview 13:28

Mathematical induction is a very different and uncommon approach but sometimes is very necessary!

Mathematical Induction
6 Lectures 01:13:21

Forget everything you learned about the x-y plane in Algebra class. In this course, we reinvent this idea in a more concrete way.

Preview 10:01

What does it mean for two things to be equal? Sometimes this definition can change, but there are some rules about when two things are equal that have to be satisfied.

Equivalence Relation

Forget everything you learned about functions. We approach this idea very much algebraically, however we give a new perspective.

Mathematical Functions Part 1

Mathematical Functions Part 2

There are some properties of functions that may seem useless but end up being used all over mathematics in very unique ways.

Properties of Functions

There is yet another way to compare things. Sometimes we want to say certain things are "bigger" or "better" than other objects. In this lecture, we state the rules needed to make this possible.

Ordering Relation
The Countable Infinity And The Uncountable Infinity
4 Lectures 43:29

There are two infinities!

Countable Sets and Uncountable Sets: What Is Infinity?

Let's start proving some weird things about infinity...

Properties of Countable and Uncountable Sets

It turns out that this giant infinite set is tiny compared to other sets.

Rational Numbers Are Countable!

Learn about one of the biggest sets in set theory. We prove that the set of real numbers is, in fact, uncountable.

The Real Numbers Are Uncountable!!!
1 Lecture 03:20

Congrats on finishing this course!

About the Instructor
Kody D'Amours
4.5 Average rating
193 Reviews
4,372 Students
8 Courses
56 Graduate Credits, B.S. Mathematics, Crypto Certificate

Math Should be Fun!  It Should Be Enjoyable And Taught Dynamically!

I love what I teach. I feel like math has a negative connotation to it, and that it is the teacher's job to build enthusiasm and interest through their own passion for the subject. Right now, most students take their math classes just to get the degree requirements - and I respect that - but I also want the student to enjoy what they are learning. This can be hard to do, but I am willing to try my best. When students hit a wall in their mathematics career, then they need someone to help them back up. My goal is to be that person. I have seen how many professors teach, and there are many styles that I like to incorporate. I like to show math in a different and interesting perspective that hopefully is also applicable.