How to Write Proofs in Set Theory with the Math Sorcerer
What you'll learn
- How to Write Mathematical Proofs with Sets
- The Mathematical Notation Surrounding Sets
- The Definition of a Set and Subset
- The Definition of Union, Intersection, Relative Complement(Set Minus), and Absolute Complement
- How to Show one Set is a Subset of Another
- How to Show Two Sets are Equal
- How to Use Various Proof Techniques in Set Theory Proofs
- How to use the Method of Double Inclusion
- How to Prove Sets are Equal without the Method of Double Inclusion
- How to Do a Proof by Contradiction
- Understand the Common Sets found in Mathematics including the Natural Numbers, Integers, Rational Numbers, Real Numbers, and Complex Numbers
- Understand what Empty Set actually is
- Understand Venn Diagrams
- Understand the Powerset and How to Find it
- Understand Cardinality(Bonus Section, More Advanced)
- How to Prove Two Sets have the Same Cardinality(Bonus Section, More Advanced)
- Be Highly Motivated:)
This is a course on PROOF WRITING with Sets:)
This course starts with some VERY BASIC definitions regarding the theory of sets. Some simple examples are given at the beginning, but soon after, the PROOFS begin!!
Important Note: A formal prerequisite for this material is an understanding of mathematical logic. However I have tried to explain the ideas from logic as they come up in the proofs.
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!!!
1) Watch the introduction videos if you need to. These cover the very basic things that you should know regarding sets.
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. I hope you enjoy watching these videos and working through these problems as much as I have:)
Who this course is for:
- Anyone who Wants to Learn How to Write Basic Proofs with Sets
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.