Advanced Calculus/Real Analysis with the Math Sorcerer
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
- Calculus 1, 2, 3, Differential equations + some proof writing experience is the typical recommendation for this material
- A strong desire to learn higher level mathematics
This is a University Level course on Selected Topics in Advanced Calculus/Real Analysis with a major focus on WRITING PROOFS:)
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.
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.
If you finish even 50% of this course you will know A LOT 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 I have:)
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. I hope you enjoy this course and learn lots of mathematics.
Who this course is for:
- Math Majors
- Anyone with a strong desire to learn higher level mathematics
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.