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)
This is a course on PROOF WRITING with Sets:)
This course starts with some VERYBASICdefinitions 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!!!
Basically just,
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 ALOT 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 Ihave:)
Note this course has lots of very short videos. If you are trying to learn math then this format can be good because you don't have to spend tons of time on the course every day. Even if you can only spend time doing 1 video a day, that is honestly better than not doing any mathematics. You can learn a lot and because there are so many videos you could do 1 video a day for a very long time. Remember that math can be challenging and time consuming, so if you just do a little bit every day it can make your journey much more enjoyable. Ihope you enjoy this course and learn lots of mathematics.
