How to Write Proofs with Functions with the Math Sorcerer

Higher Level Proof Writing Course with Injective and Surjective Functions. TONS of beautiful Proofs:)

What you'll learn

Understand the Definition of a Function
Understand the Notions of Domain and Codomain
Understand the Function Notation that is Used in Higher Level Mathematics
Under the Definition of the Direct Image of a Set Under a Function
Understand the Definition of the Inverse Image of a Set Under a Function
Understand the Definition of Injective(one to one), Surjective(onto), and Bijective
How to Write Proofs with Functions
How to Prove Functions are Injective(One to One)
How to Prove Functions are Surjective(Onto)
How to Prove a Function is a Bijection
How to Write Proofs involving the Direct Image of a Set
How to Write Proofs involving the Inverse Image of a Set
How to Prove Functions are Not Injective
How to Prove Functions are Not Surjective
How to Prove Several Key Results Surrounding Injective and Surjective Functions
How to Prove Several Key Results Surrounding the Direct and Inverse Image of a Set

Requirements

How to Write Proofs in Set Theory
Understand Mathematical Logic

Description

This is a course on PROOF WRITING with Functions:)

It is extremely helpful to know How to Write Proofs in Set Theory before jumping into this material or at least know some mathematical logic.

Because this material is more advanced and this is a PROOF WRITING course, this course includes multiple introduction videos.

The first section has various introductory videos.

The second section has TWO videos which are both considered roughly full introductions.

The best way to learn to write proofs is to watch someone else give careful proofs and then try to do it on your own.

This is the MANTRA behind this course which is full of beautiful 100% correct well written proofs!!!

Basically just,

1) Watch the introduction videos if you need to. Even if you don't need to, watch them anyways, it's worth it!!!! These cover the very basic things that you should know regarding functions.
2) Watch the PROOF videos in ANY order. Take notes, try to understand them.
3) Try to do the proofs on your own! If you can't, watch the video and cheat and try again.

It takes A LOT of effort to learn to write proofs like the ones you see in these videos, so don't feel discouraged if you find it difficult, it is supposed to be tough.

This is an EXCELLENT course for anyone who wants to jump into proof writing and has some knowledge of basic proofs. I hope you enjoy watching these videos and working through these problems as much as I have:)

Who this course is for:

Anyone Currently Taking a Course Involving Proof Writing with Functions
Anyone who wants to learn about proper function notation and how to write proofs with functions