Advanced Calculus/Real Analysis with the Math Sorcerer (Udemy.com)
Selected Topics in Advanced Calculus/Real Analysis with tons of Beautiful Proofs:)
Created by: The Math Sorcerer
Last updated May 2026
What you will 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
Course 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.
Instructor Details
- 4.7 Rating
449 Reviews
The Math Sorcerer
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.
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Reviews
By Iuri Bachnivsky on 9/16/2026
This was a great course. I took advanced calculus and some real analysis over 20 years ago and wanted a refresher as continuing education. Your breakdowns for problems, including the recommendation of using scratchwork before a proof, was so helpful. And your visual insight into helping me understand things like uniform continuity, as well as pointwise and uniform convergence, I simply cannot overstate how insightful it was. I wish my professors years ago did this. Excellent material and I look forward to more of your courses for my self-study.
By David Chen on 10/30/2025
I'm trying to dive deeper in advanced mathematics and after reading a whole textbook on real analysis, revisiting the content through this format definitely is helping my understanding of the materials better!
By Alexander T Kellough on 8/20/2025
Seem to be missing some definition secitons, where it could be helpful to intuit about the definitions. I don't think it's necessary, as all the definitions are given that are relevent to the given problem, but may help tranition over to a textbook to be able to transalte from first order logic to intuition.
By Thabang Makhofola on 7/20/2024
I took this course back in third year and never entered the exam. I learnt mathematics is a collection of rules that are justifiable throughs proofs. First assume and then a series, of implications, follows that assumption (direct proof). The triangle inequality, as a rule, is justified through a direct proof.
By Rob Gale on 10/1/2023
Lots of great examples but doesn’t cover a full first semester course in RA at a typical university. The content is great but could go further. More homework problems would help the course as well.
By Anonymized User on 7/24/2023
Really appreciate the facilitator going through the thought process involved in every solution. This is perhaps one of the best courses I have come across so far on Udemy. Facilitator is at times humorous, but very concise and clear with every explanations. Even the toughest problems are explained very clearly. Will definitely recommend
By Anders Bremberg on 2/8/2023
some steps could have been written and not just spoken; like the square root of both sides of the triangle equation. But good match regardless with my previous knowledge.
By Jason Abramovitz on 8/11/2022
By the power of Archimedes, I declare this course most excellent! The Math Sorcerer works through dozens of real analysis problems, some of them quite challenging. The problems are solved from start to finish with explanations along the way so you can really learn how to work through these exercises.
By Jennifer Tucker on 1/25/2022
I FAILED this course last semester, so I'm taking it this semester over. Let me tell you, I got a 92% on my first assignment courtesy of you breaking everything down for me into digestible bites. I absolutely adore your videos, so I also purchased Modern Algebra. Thank you so much!!!!
By Fernando Boessenkool on 7/13/2020
I really enjoyed this course. The way the teacher does the proofs helps in understanding the content. I really recommend it. I suggest to the teacher that, when presenting new examples, use the whiteboard, as it is much better than seeing the computer screen.
Quality Score
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Overall Score : 94 / 100










