 # UdemyAdvanced Calculus/Real Analysis with the Math Sorcerer Selected Topics in Advanced Calculus/Real Analysis with tons of Beautiful Proofs What you'll learn
• 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
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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 Who this course is for:
• Math Majors
• Anyone with a strong desire to learn higher level mathematics
• • • CleaningCode, wendox, deacanfrost and 41 others
Author
TUTProfessor