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: 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

**Who this course is for:**

- Math Majors
- Anyone with a strong desire to learn higher level mathematics