How to Write Proofs with Functions with the Math Sorcerer
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
Course content
- Preview04:47
- 06:21The Image of a Set Under a Function
- 06:51The Inverse Image of a Set Under a Function
- 05:08Definition of a Surjective(Onto) Function
- 05:04Defnition of an Injective(one to one) Function
- 04:55Intuitive Explanation for Injective, Surjective, and Bijective Functions
Instructor
![The Math Sorcerer](data:image/svg+xml,%3Csvg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 64 64"%3E%3C/svg%3E){kind=avatar}
- 4.7 Instructor Rating
- 618 Reviews
- 2,895 Students
- 13 Courses
I was born on a small unnamed Island in the Pacific Ocean inhabited mostly by natives who practiced mathematics on a daily basis.
My mother was a witch who specialized in Calculus and my father was a warlock who was well versed in the dark arts of Algebra.
As I grew older so did my thirst for knowledge, and so I set out on a long voyage to improve my mathematical skills. I traveled the world for years and learned a great deal of mathematics, but it wasn't until I met that raging Hobbit that my true powers started to show.
I am here today to share my magical powers with you.
Come join on me on this journey as we explore the world of mathematics together.