What you'll learn:
- Understand Advanced Mathematical Notation
- How to Write Proofs in Advanced Calculus
- How to Prove the Triangle, Reverse Triangle, and Bernoulli's Inequality
- How to Prove Various Important Results Regarding Sequences
- How to Prove the Squeeze Theorem
- How to Prove a Sequence Converges
- How to Prove a Sequence Diverges
- How to Prove Results Regarding Cauchy Sequences
- How to Prove a Sequence is Cauchy
- How to Write a Delta Epsilon Proof
- How to Prove a Function is Continuous
- How to Prove a Function is Uniformly Continuous
- How to Prove Pointwise Convergence
- How to Prove Uniform Convergence
- How to Prove a Function is Differentiable
- How to Prove a Function is Not Differentiable
- Understand the Convergence of Infinite Series
- How to Use Dirichlet's Test
- How to Find a Pointwise Limit
- How to Prove Various Key Results in Advanced Calculus
This is a University Level course on Selected Topics in Advanced Calculus/Real Analysis with a major focus on WRITINGPROOFS:)
Note: Advanced Calculus(aka Real Analysis) is typically considered the HARDEST course a mathematics major will take.
This course is a step above a general mathematics course. Students should have familiarity with writing proofs and mathematical notation.
Basically just,
1) Watch the videos, and try to follow along with a pencil and paper, take notes!
2) Try to learn to write the proofs as I do. If you understand the proofs then you have learned a great deal. If you can write the proofs on your own then you have really graduated to the next level.
3) Repeat!
If you finish even 50% of this course you will know ALOT of Advanced Calculus and more importantly your level of mathematical maturity will go up tremendously!
Advanced Calculus is a beautiful yet notoriously difficult subject to learn and teach. 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.
