Udemy just started a ten-day sale. To get the best prices, now is the time! To make us extra happy, please use one of our referral links. Either the current monthly code TPOT_MAY25 or click a link from our “Coupons” page.
Recent Posts
Recent Comments
- Hania Uscka-Wehlou on Discrete Mathematics part 1 is out!
- Altin on Discrete Mathematics part 1 is out!
- Martin on Discrete Mathematics part 1 is out!
- Henry on Discrete Mathematics part 1 is out!
- Hania Uscka-Wehlou on Discrete Mathematics part 1 is out!
Hi, Dear Hania!
I am one of your students on Udemy. I would like to thank you for your Calculus and Linear Algebra courses on Udemy, they helped me a lot. Actually I am a Computer Science undergraduate student. I didn’t take math seriously until I learned Artificial Intelligence which contains a lot of Math material (where they try to model the problems into Math problems, solve the math problems and turn the solution into code) After watching your videos, I find my self loving Math ( Thanks again )
I would like to ask you 3 questions about math.
First of all, I find that you will post your discrete math on Udemy in the future. Can you tell me the approximate date? ( Yeah, because I think I need to learn that LOL ) By the way, would you consider teaching Probability or Statistics?
Secondly, I think problems are interesting but hard. Could you please give me some advice on how to improve mathematical problem solving skills in general?
Finally, I think I am confused by the vast branches of mathematics. For example, I learned a little bit about Graph Theory, and it’s very different than Calculus. I don’t think I can use Calculus techniques to solve Graph theory problem ( maybe I can, but I don’t know how? ) You know there are a lot of subjects under Mathematics. If I am interested in combinatorics or Graph Theory or Optimization, What do I need to learn next? I think I am lost in the Math maze.
Thank you very much!
Hi, Dear Honglin!
Thank you for this lovely message! I’m really happy to hear that our courses helped you to love Math.
Now, your questions:
1. Discrete Mathematics 1 (the one we are working on now) will be released around September 2025; Discrete Mathematics 2 around six months later, I think.
(Sorry, no plans for Probability or Statistics… Definitely not my cups of tea…)
2. You develop problem-solving skills by (a) reading solutions to problems and by this learning various methods and tricks, OR (b) watching other people solve problems and trying to understand their reasoning. Later: try to solve a lot of problems yourself. But it will be hard if you don’t have any example, so, if you didn’t get it at school, I recommend (a) and/or (b) before you start solving problems by yourself, otherwise it can be very frustrating. If the problems in my courses are hard, try the books that I recommend to each course, they have often also easier problems. You get the list of books here:
https://www.wehlou.com/hania/files/uu/Practice_and_books.pdf
3. Indeed, Calculus will not prepare you for Graph Theory. An introduction to Graph Theory is often given in Discrete Mathematics courses (in my courses: in the second one, DM2). If you can’t wait for my course, I can recommend the following book that has a very good chapter on Graph Theory (an introduction, because it is “only” a DM book, and Graph Theory is a huge branch of Math on its own…):
https://discrete.openmathbooks.org/dmoi4.html
Combinatorics is also covered there, and it will be covered in our DM1, so the first one (expected Sep 2025).
If you have a lot of time on your hands, our courses can lead you through the Math maze. Here is some advice about the optimal order of studying them:
https://www.wehlou.com/hania/files/uu/Optimal_order_of_studying_our_courses_Plus_all_the_OUTLINES.pdf
And a link with more information:
https://www.thepoweroftwo.courses/practical-information-about-our-courses-on-udemy/
I wish you all the best! Don’t get lost in the Math maze 🙂
Kind regards,
Hania
Thank you very much for your reply and the information!
I am very much looking forward to your Discrete Mathematics course in September.
Hi, Hania,
My name is Rutvik. I’m from India. I have purchased all of your courses. Because, after completing my undergraduate studies in mechanical engineering, I became interested in mathematics. So I was wondering about where to begin when I came across your courses. And I started to learn on a regular basis.
This year, I was admitted to a second master’s degree in mathematics. My first master’s degree was in a transport-related field, but it focused on statistics and probability.
I seek to acquire further knowledge in pure and advanced mathematics. I would like to inquire which book is most suitable for me to commence studying Ordinary Differential Equations, Partial Differential Equations, topology, and complex analysis, ranging from beginner to expert level.
Could you recommend any books? I am exclusively referring to academically focused texts pertaining to rigorous mathematics.
Hi Rutvik,
Thank you for this message. Congratulations on your admission to your (second!) master’s degree in mathematics! It is an impressive achievement.
I’m very happy that you are aiming for pure and advanced mathematics. Sadly, I cannot recommend any books in English on the topics you need. The reason for this is that I studied these subjects in Poland, using books and notes in Polish… and I have’t (yet) taught them in Sweden (or on Udemy, in English).
If I come across some good book on these subjects, I will let you know. In the meantime I suggest that you pose your question on Stackexchange or on any other thematic forum. People there can give you really good advice.
Also, if you find a really good book on ODE, please, let me know, as I’m planning a course on this subject in one or two years from now.
I wish you a lot of success in your studies!
Kind regards,
Hania
PS. Thank you for purchasing all our courses. We appreciate your support!
Hello, ma’am.
I apologize for the late response.
Thank you for developing these types of courses in this manner. I have never learned math this way.
I could not find the book myself.
So I type into ChatGPT what type of book I want, and it responds with this.
”
For a rigorous and academically focused study of Partial Differential Equations (PDEs), especially suitable for advanced undergraduates, graduate students, or researchers in mathematics, here are the top recommendations, categorized by style and depth:
—
🥇 Most Recommended for Rigorous Academic Study
1. “Partial Differential Equations” by Lawrence C. Evans
Level: Graduate
Why it’s best:
The gold standard for mathematical rigor in PDEs.
Covers weak solutions, Sobolev spaces, distribution theory.
Extensive theoretical exercises.
Use in universities: Standard textbook for graduate PDE courses (e.g., Stanford, Berkeley).
Prerequisites: Real analysis, functional analysis (ideally).
📘 Publisher: AMS Graduate Studies in Mathematics
—
🧠 Supplemental for Theory and Deeper Insight
2. “Partial Differential Equations in Action” by Sandro Salsa
Level: Advanced undergraduate to graduate
Strength: Clear examples and motivation; good balance between applications and theory.
Use case: Complement Evans to build intuition.
—
3. “Elliptic Partial Differential Equations of Second Order” by Gilbarg & Trudinger
Level: Advanced graduate
Focus: Elliptic PDEs in great theoretical depth.
Style: Classic, rigorous, geometric intuition.
Ideal for: Those pursuing research in analysis, differential geometry, or elliptic theory.
—
📐 For Functional Analysis and PDEs Together
4. “Partial Differential Equations: An Introduction” by Walter A. Strauss
Level: Upper undergrad to early graduate
Style: Less abstract than Evans, but mathematically solid.
Use case: Great as a precursor before Evans.
—
🛠 For Applied Mathematicians (still rigorous)
5. “Introduction to Partial Differential Equations” by Gerald B. Folland
Level: Graduate
Style: Rigor + analysis-based approach.
Focus: Fourier methods, distribution theory, Sobolev spaces.
”
I hope this information is helpful to you.
Thank you, Rutvik, for sharing this list with me and all my students reading this blog! I appreciate it.
Kind regards,
Hania
Hi, Dear Hania!
I am one of your students on Udemy. Thank you for your advice about how to improve mathematical problem solving skills last time. I now have two more questions about problem solving which makes me very confused.
The first problem, in my opinion, is very abstract or silly? The question comes from when I look through some historical mathematicians. It’s all about Galois’s story. I didn’t learn Group theory, I just looked at his life experience. There are two things that shocked me. The first is that he was able to solve an open question when he was a teenager. The 2nd thing is he created the Group Theory, and solve the problem by his new theory. Well, the 2nd one shocked me even more. Because, How come one is able to come up with his new theory? Is that legal? I never create theory. If I created a theory, how other people agrees with me? And Is that necessary to solve problems by creating new theory? Some mathematical problems have not been solved for many years. Is it because we have not created new theories? Because I never solved problems like that. I solve problems by learning some formulas and applying the formulas.
The 2nd problem is about a statement from a mathematician YiTang Zhang. Well, you may not know him, but he is very popular in China ( actually I’m from China ) He said several times “Pure mathematics is basically useless for industry”. I don’t know what exactly is Pure mathematics, but it sounds like very abstract theory in mathematics (like you said the difference between Calculus and Real Analysis in lecture)? Well, do you agree with him… or do you think learning some abstract theory can help to solve problems in real world?
Thank you!!!
Hi, Dear HongLin,
These are very big questions and I’m not really able to answer them…
Pure mathematics is an abstract topic; one uses this term to make a distinction between theoretical work and the so called “applied mathematics” when you apply maths for solving practical problems (like approximating stuff, computing various values that you later use in your engineering work, for example). Your remark about “Real Analysis versus Calculus” is indeed one example of “pure versus applied mathematics”.
I have found this thread that contains some answer that contradict YiTang Zhang’s statement:
https://www.reddit.com/r/math/comments/2o8dqz/how_does_pure_mathematical_research_benefit/
How one develops mathematical theories and if problem-solving exercises help:
I think it will be different from person to person. Galois was indeed a fantastic genius, but you have this type of people in other domains too, like Mozart in music. Hard to say what made them achieve so much that early in their lives. As I don’t belong to this group, I cannot say 😉
Kind regards,
Hania
Hello ma’am,
This is Rutvik. I am currently on section 11 of precalculus course 1. However, I am encountering significant challenges in comprehending the proof.
I can comprehend your preceding action. What makes this a pivotal step? What is the reason for not incorporating another theorem? That is the origin of my issue. Instead of logically deriving the proposition or theorem, I began to memorize proofs in order to resolve the issue, which is not a wise approach.
Therefore, what necessary modifications must I make to ensure that I can follow logical steps instinctively rather than relying on the brute force of memorization?
Would you be able to provide me with some assistance?
Hello Rutvik,
There is no simple answer to this question. Conducting proofs is one of the most challenging tasks in mathematics, and you are by far not alone with your struggle.
Actually, you need to put yourself through many, many proofs in order to gain experience in this field. If there is some particular proof that you find challenging, you can always ask me a question about it (but, please, use the QA under the video that the question refers to; answering mathematical questions outside Udemy’s QA is a highly inefficient way of working for me…), and I will do my best to clarify.
I am working now on “Discrete Mathematics 1”, and this course will contain a much larger section about proofs (than Prec1). I hope to release it by the end of the Summer.
In the meanwhile I can recommend the following books:
https://richardhammack.github.io/BookOfProof/Main.pdf
https://eng.libretexts.org/Bookshelves/Computer_Science/Programming_and_Computation_Fundamentals/Mathematics_for_Computer_Science_(Lehman_Leighton_and_Meyer)
https://agorism.dev/book/math/intro/How%20to%20Read%20and%20Do%20Proofs%3A%20An%20Introduction%20to%20Mathematical%20Thought%20Processes%20by%20Daniel%20Solow.pdf
I hope that this helps.
You are welcome to ask me questions about specific proofs on the QA for Prec1!
Kind regards,
Hania