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do u have in mind a pde book which will be suitable for me, im only 14 but i know ODE's, calc 1,2,3, linear algebra, and proof writing, so im somewhat good at reading books but are there any u think would be specifically good ; ps i still want it to include things like fourier transformations

Really wonderful video, thank you for sharing. Agree on all points. 1. I’m curious, do you want to do grad school? Or are you self-studying for fun? It seems like you’ve studied and mastered much harder books than the courses you listed! 2. You said you did a math minor - what was your major? Super curious! Thanks for the great videos! Enjoying binging them

YES. I wish someone told me to use note cards in undergrad! This is great advice, you’re basically talking about deliberate practice and spaced repetition

Loved this video! Especially loved the “math is suffering, that’s why we like it” bit 😂 Copping that phrase for my own students! Question: as you said, a lot of this advice sounds like it’s geared to self-study (e.g. a grad student or hobbyist). Do you have any analogous tips for toxic mindsets during undergrad studies? Like, you don’t get to pick the book you want to use, or the exercises. And I don’t know if you have the time to solve extra problems from other books… Cheers and thanks again!

Thanks! This review turned me on to his book on soap films and minimal surfaces! I have Spivak's vol 2-4 on the subject and am currently having some fun with Needham's "Visual Differential Geometry and Forms" I did a quick skim of reviews on Oprea's Intro to DG and saw that he stays with the Frenet-Serret frames and does not introduce Forms. I'm loving your channel! Thank you for these reviews!

The look really good BUT .... hard to find in the USA ... also, there should be good money in "rebinding" books with spiral format! Thanks for the heads up ... I'll keep an eye out for these texts!

You have very unique videos on TH-cam. Good job ! 👍👍

EXCELLENT ... content and video! As always, thank you! I studied from (among others) a text by David Williams entitled WEIGHING THE ODDS ... Cambridge Press, 2001, so expensive

Check out 'Partial Differential Equations - An Introduction' by David Colton (Dover) - an execellent short introduction to modern pde's + solutions ...

Stanley J. Farlow Partial Differential Equations for Scientists and Engineers (Dover Books on Mathematics) highly recommended, undergraduate level.

Thanks for the video! 🎉🎉🎉 I have the book by Zill (extended version with PDE) and it's as good as it gets for ODE at the engineering/physics level, but also as a brief introduction to PDE. For PDE proper, i have the books by Asmar and Haberman, but still haven't studied them ... i skimmed them and read little chuncks and they look great! I also have the book by Pivato to dwelve deeper into the theory...

9:10 damn, i hoped you showed the Pivato book 😅

This might be the type of situation where people should think before they type.

I am surprised that no one is talking about Applied Partial Differential Equations with Fourier Series and Boundary Value Problems by Haberman, This is a good book for starters.

How well can that student do proofs and what is his background in real analysis?

Evans' book is for math graduate students specializing in pde.

Strauss' book is for beginner students in mathematics.

You continue to do an incredibly nice job of reviewing these texts ... very consistent, very balanced ... I really enjoy viewing your videos even though it cost me a bit of money as I often discover books that I wish to investigate more thoroughly! Thank you! I almost forgot to mention your careful attention to PRICE ... most students are on a budget and I am sure they appreciate your well-founded comments!

I believe that E-books are in general superior to physical copies primarily for two reasons. One, index search is easier. Two, notes can be directly added to where they are relevant.

Amazing review.

The uni Im transferring to in the fall uses Applied Partial Differential Equations w/ Fourier Series and Boundary Value Problems - Richard Haberman. I own a copy of the 4th ed, but I haven't gotten too deep into it as Im still taking ODE's. That said, it starts out fairly readable and I was able to understand it having just Calc 3 under my belt. I would imagine as the book gets further along Ill need some linear algebra. The preface of the 4th edition doesn't mention needing to know analysis, and explicitly states that it keeps proofs to a minimum which I would assume precludes needing analysis as a pre-requisite.

A personal issue for me is: I don't like s as a variable. Especially when hand written, s can be confused for a 5. Nice to see a new exercise series here.

Mathematics can be frustrating. Sometimes we need a mental break. I know I've been to the point of quitting math a couple of times. One of the undergrad advisors has said that when you are working on your Ph.D. in math, your love for math needs to be just a little greater than your tolerance for the frustration of the work. That's a paraphrase. It was an important idea. Perspective is important in anything. Why do we do the things we do? Psychology suggests: we don't always know. We need to seek to understand what is really important to us in life.

Did you know that a meta study from 2023 that looked at tens of others studies on worked examples in the field of math education has been determined to be MORE beneficial than hard core problem solving itself for students learning mathematics? The reason is simple. Any problem that is truly fully solved in detail will identify your gaps in understanding. Pure problem solving will take longer and there will exist WAY more frustration and you will never truly have insight if there are small nuances you have not mastered on some math building blocks that are prerequisite to your topic of study. You can then LATER add problem solving but only after you have basic mastery of the concepts that are new to you. Books on any undergraduate math and graduate math that will be structured in the style of fully worked examples will be a goldmine. Sadly I doubt many will take the lead to make those kind of books even though there is right now actual hard core evidence that for students learning new math topics or new math areas, worked examples done right will ALWAYS be significantly better than you having to be subjected to enormous cognitive load that is typical of standard problem solving, aka MATH PHOBIA. Math phobia exists only when cognitive load is high(typical problem solving) and specially in middle school and high school when you never get proper explanations of the concepts and mechanisms of WHY every formula works as it does, that you are forced to just accept. If you find some pioneer educators out there who tried really hard to make formal logic and proofs accessible(without over simplification) to students in high school and even maybe at the end of middle school please let me know. I'll probably buy every one of those books because I'm interested in the pedagogical tools and examples they use to make proofs and logic digestible to way younger people than what's currently done today where mostly only once you get to college/university you start learning how to read , understand and write proofs.

Today we are gonna be solving some calculus of variations problems using the Euler-Lagrange equation. I've tried to make this as simple as possible, but let me know if there's anything that can be improved upon. If you're interested in exclusive content be sure to check out our TH-cam memberships or our Patreon. Also consider using our affiliate links if you want to help support what we do! Video on the Komzsik book: th-cam.com/video/0pp4BUF7-hs/w-d-xo.htmlsi=iqCVeeXlTctHLgeK

Awesome MT! interested to know ALL the books you read in 2024..

Thanks for the video!!! 🙏🙏🙏 hope the new year is going great 🎉🎉🎉 By the way I have a suggestion for you: I'm reading a book on differential forms by Fortney (Springer edition), and it's wonderful!! Should you ever wanna learn df, it's the best introductory book, with a lot of pictures and intuition! PS: i found a used copy of the Oprea book on differential geometry and will couple it with the book by Tapp when the time comes

at 2.19 what do you mean by the example of R as an R-vector space being too much for someone who has learned Linear Algebra? Isn't that the whole point of a first course in Linear Algebra?

A note on the review of the first book: In Europe, as I understand it, calculus is synonymous with what is called real analysis in the US

Great reviews. A very nice and friendly book on functional analysis is "An Introduction to Functional Analysis" by James C. Robinson (2020) - solutions to all exercises in back! ...

I think I would also enjoy the book by Malik. But I just finished Calc I so I don't think I'll be picking it up any time soon. I think I'm ready to dive into Real Analysis, do you recommend the book by Tao? Its hilarious that you hate discrete probability lol.

Do u solve all the exercises?

Today I show my most read books of 2024. If you want to buy any of these books be sure to check out our affiliate links! Also check out our Patreon or our TH-cam Memberships! As of the upload of this video, I am still in the process of importing content from Patreon. I ask for your patience. Thank you for supporting us! Shoutout to @CrazyShores for encouraging me to do this video! I also apologize for the echo present in the video.

I notice you didn't select Baby Rudin ... smart! That's a very concise text and the one used in my first analysis course ... this one looks to be a better jumping off point!

Your reviews are always so solid ... insightful, balanced, informative! Thank you for taking the time to prepare all these data!

I have several Fourier Analysis ... looks to be a welcome addition with some real-world applications ... thanks for pointing it out! After searching, I found nothing about a second edition ... that means AMAZON!

This could be the most valuable review you have ever presented. I have used this text and I agree! Thank You!

Nice Lecture ... quick but I can always stop the video and follow the steps! Thank you!

You find (and review) some unique texts and your reviews are very helpful! Thank you!

Very Nice Set

10:38 IIUC basically no-one in UK universities has tenure anymore, but "senior lecturer" in the UK is equivalent to a tenured US "assistant professor" title. Only actual, full professors are titled "professor" in the UK (and Ireland). OTOH Alcock's position is in mathematics education and it seems that her research is all or almost all in that area.

7:02 How would this compare to Pugh’s _Real Mathematical Analysis_ ? Is this actually more in-depth than Pugh?

Sir indian authors are good

What is the need to learn PDEs?

Have you heard of Partial Differential Equations: A First Course by Rustum Choksi? It's supposed to require just real analysis, basic familiarity with multivariable calculus, and linear algebra.

Where are the links for parts 1 and 2?

Oh thank God, it's not just me. I bought a PDE book, and I struggled to get through the first few pages. It assumed too much prior physics knowledge for me.

Excellent ... again! Thank you!

How you find such great books at spectacular prices, I don't know ... but I take my hat off to you! Great Job!