# How to Write Proofs with Functions with the Math Sorcerer

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

This is a course on PROOF WRITING with Functions:)

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.

Course Content

• Introductory Videos –> 6 lectures • 33min.
• Two More Full Introductions with Sample Proofs –> 2 lectures • 30min.
• Proofs with Injections, Surjections, and Bijections –> 10 lectures • 49min.
• Proofs of Key Properties of Surjective and Injective Functions –> 4 lectures • 13min.
• Direct Image and Inverse Image Proofs –> 5 lectures • 27min.

Requirements

• How to Write Proofs in Set Theory.
• Understand Mathematical Logic.

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:)

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