Advanced Calculus/real Analysis With The Math Sorcerer

Last updated 5/2023

MP4 | Video: h264, 1920x1080 | Audio: AAC, 44.1 KHz

Language: English | Size: 3.67 GB | Duration: 7h 32m

Selected Topics in Advanced Calculus/Real Analysis with tons of Beautiful Proofs:)

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

Requirements

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

Description

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.

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 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

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