Advice for Learning Mathematics

In this video we discuss learning mathematics, forgetting mathematics, how to remember math, and what is the most important math. We also discuss some books for learning algebra, calculus, and real analysis. Do you have advice for people? If so, please leave a comment below.
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[@enigmatico6209]

Math is so overly complicated that just memorizing formulas won't do, you'll just forget them very quickly. I feel like it's easier to try to understand the logic about it, and then replicate it whenever you are working on a problem that requires a specific formula. Like, instead of memorizing that when integrating a volume in cylindrical coordinates the formula is the double integral of the region times dz r dr d theta, memorize the setup of the integral (the polar coordinates at the xy plane and z being the height of the cylinder) and then figure out how a slice of that cylinder would look like and figure out what the volume of that slice is (indeed the arc of the slice will be r dr). That way even if you forget a formula, you can figure it out and if you forget how something work, it will be easier to refresh your memory when reviewing it. Naturally this also requires you to be able to prove stuff on your own, which is not always easy. Specially at the beginning. It's hard...

[@RKP689]

When I was pursuing my Masters in System Engineering in my 2nd semester I stuck with a PDE and I didn't know how to solve it. The exact PDE later appeared in assignment and I have decided that I should approach to my Professor and quite to my surprise he told me that even I don't know the exact solution. So, let's solve together and together after banging our heads for one or two weeks finally my Prof solved it and that was an amazing experience.

[@madhavpr]

Great advice, especially this one: "The most important math you can do is the math you want to do". I understand that this video talks about basic math but I'd like to share a story. I was/am fascinated by shapes, curves and surfaces, "rotating objects" and wanted to understand them rigorously. The materials and the books I referred used the language of Lie groups, smooth manifolds and related topics. I'm not a math student, I don't have a math degree, my day job isn't related to geometry but I study mathematics for pure fun. Having fun with math and putting in the hours is my motivation. Also, a few years from now, I want to explain shapes and geometry to my daughter (she's just 1.5 years old now). I realized that my analysis and topology background were relatively okay, but my abstract algebra was next to horrible. I picked up Gallian and Fraleigh and attempted a lot of problems in group theory. Fast forward to now, I am studying matrix groups and basic Lie theory (books- Matrix groups for undergraduates and Naive Lie Theory). I started this journey a week ago and it has been a joyride so far. Thanks a lot for this amazing video.

[@AndreTJones]

I’m back in college after 20 years and I have forgotten almost everything math related 😢.

[@jackwatt8988]

There is a quote by Knuth I really like: "In high school, our math program wasn't much, and I had never heard of calculus until I got to college. But the calculus book that we had was (in college) was great, and in the back of the book there were supplementary problems that weren't assigned by the teacher. So this was a famous calculus text by a man named George Thomas (second edition). Our teacher would assign, say, the even numbered problems, or something like that (from the book). I would also do the odd numbered problems. In the back of Thomas's book he had supplementary problems, the teacher didn't assign the supplementary problems; I worked the supplementary problems. I was scared I wouldn't learn calculus, so I worked hard on it, and it turned out that of course it took me longer to solve all these problems than the kids who were only working on what was assigned, at first. But after a year, I could do all of those problems in the same time as my classmates were doing the assigned problems, and after that I could just coast in mathematics, because I'd learned how to solve problems" (Don Knuth )

[@zamplify]

Thing is, he didn't need to solve a partial differential equation for 30 years so forgetting it was correct. You only have so much bandwidth and the ability to learn and forget quickly is extremely valuable.

[@hypergraphic]

That's good advice! I'm finally getting off my butt and I'm starting community college this fall. Will definitely apply this piece of wisdom.

[@highviewbarbell]

I bought a very large, hard cover dotted notebook (A5+ from Leuksturm if you wondered) this summer before starting my first math class in the first year of my degree, with the goal of at the end of each math class, taking my notebooks and re-writing the entire thing in a day, with nicer handwriting, better examples, and none of the scratch work or class work, just all the important stuff I would ever need from it to use again in the future. With this I accomplish the multiple goals of committing all the ideas to memory, using critical thinking to boil the class down to all the essential knowledge, and having beautiful books to reference later in life where I can just pull out my notes from college to refer to again later

[@SwinkMediaHouse]

Today’s my first day in Discrete Math and I’m trying to remain calm and go through all the layers to understanding it. When you said it’s known as a weed out class I started really playing attention bc I’m a CompSci major and your pep talk was real & honest… thanks for the advice.

[@Br4nd0nS4n7os1995]

Yo tengo todos los libros 📚 de matemáticas de Baldor. Es muy famoso. ❤

[@katanawusi]

Could you make a video about the best order to learn math. Example start with addition subtraction and so on all the way to say calculus.I've always heard that math has to be learned in the proper order as one builds upon the last. thank you.

[@jelielenriquez7847]

fun fact about Baldor: A few years ago a newspaper decided to sell that math book in parts. So every week you bought the newspaper and it came with a part of the Baldor.

[@tmann986]

I remember I did pretty well in multi variable calculus and a friend was taking it and asked for help, I looked at it and said the same thing “I have no idea 😅” though after about 10 minutes reviewing what he was doing I was able to pick it up and sorta help him. I felt revisiting old classes I could learn so much faster

[@fcuantico]

Thanks for this video, and for your advice. One advice that I will give is that believe in your self, trust your gut feeling but always check (prove if possible) and be careful to confuse the fact that you can logically follow a mathematical argument, with is "evident". By this I mean, find the path that make you see the why and how the mathematical argument follows.

[@thiagogregory1]

The takeaway I personally got from this video is that it's totally ok not to be the outstanding in your math classes. It's ok to be good, it's ok to learn just enough to progress successfully (emphasis on successfully). We will forget and as long as we are humble and recognize that we forgot and relearn what we forgot, it will all be ok

[@yanlicui3683]

I totally agree with you! We're using Stewart books in my AP Calculus and Calculus III classes. We love this book.

[@John_Smith__]

Totally agree with the message. And for those who "left Math behind" due to professional reasons do Math Again and you will find it is as fun as when you first learned it, if not more.

[@satyavivekanandbattula1091]

thank you so much sir really useful video

[@chronixgamingferret6960]

thx so much for the great advice!

[@soupypunk-pk5ys]

Thank you. I need to practice and learn more trig today but I haven’t been wanting to because I’m stressed about time. Just gotta get the grade for now!

[@nadercs2669]

Isn't it funny how even as professors, we can forget things? And it's not just the little stuff, but even big concepts like solving partial differential equations. It’s a bit unnerving, but it’s also strangely comforting, don't you think? It goes to show that it's okay to forget. We're all human, after all. And your point about the way we approach education? Spot on. The constant pressure, the race against time, it’s all too much sometimes. Your talk made me realize that it’s okay to take things slow, to absorb information at our own pace. I also really liked your advice about focusing on the math that interests us. It’s a game-changer, not just for math, but for everything in life. Doing things we love helps us retain knowledge better, and it makes the process so much more enjoyable.

[@jamesjohn2537]

Sir you made my day a count and why I should always divers and familiarise myself with a lot of subjects in mathematics, then looking forward engineering mathematics only. Yes, is better to prepare ahead because we don't know when we face such challenges like that professor...

[@AFSmashMan]

Hi! I noticed the almighty KZbin algorithm hasn't sent me any of your videos for a while, and thought to come to this one and like it. Hope you're doing well. Thanks for making vids!

[@Pabloparsil]

Hi Math Sorcerer, I wonder if you could make a video explaining if the differential inside an integral has meaning by itself or not, and why engineers move around the dx and dy in equations freely and it turns out to be okay

[@philosophyoftrucking]

Extremely profound.

[@nictibbetts]

By the way when he says “basic math” he is referring to calculus, trigonometry, and college level algebra.

[@Nightking605]

Amazing video, as always.. you are my inspiring mentor in studying... pls keep it up👍🏽😎👍🏽

[@hemrajue3434]

Obviously we feel nervous when we are introduced to new areas of maths. Practice maths daily may ease our journey a lot. Of course I am a learner,I make mistakes I know that perfection is far away and keep learning until it make sense I don't worry about my mistakes I am sure that i correct those one day.

[@ronaldjorgensen6839]

thank you own stewart been through each before will buy albor one day

[@successorof68]

I dont really enjoy real analysis, but I really love number theory, linear algebra, and cryptography. Do you think I (as a math major) should always keep up with real analysis even after I m done with the class or I can move on and study number theory and stay towards number theory field?

[@neilbryanclosa462]

amazing inspiration

[@douglasstrother6584]

I'd be curious about this PDE that you couldn't solve. Separation of variables into orthogonal coordinates is a routine method to decompose a PDE in to a number of ODEs. Physical requirements on the solutions constrain the separation varibles to certain values. Was this not a valid approach? Satisfying boundary conditions on a PDE (and ODE) can be the difficult part of the problem. Was that the hard part?

[@jannikolaidovic]

Im very eager to learn more about Linear Algebra, so i was thinking of buying a book on that subject that mainly focuses on the practical part. Im currently finishing up with my Data Science MSc and i want to strengthen my knowledge. Any recommendations on books?

[@jecodedoncjesuis875]

thank

[@gdog0622]

I’m looking for some advice Would it make sense to simply study whatever I feel interested in? I feel like I should learn a course from start to finish to learn it as best as I possibly can but I have a hard time keeping focus on it for that long. I more often just pick up a book and study whatever I’m interested in at the time. Is studying whatever an effective use of my time?

[@cherry1leii]

Maybe you could choose about 3 topics you're interested in and when you're bored with the one just switch to the other one and then after a while you would achieve something without losing your motivation

[@eisbar2polar246]

😃

[@user-so3pg4ob8t]

This channel is a tresure