I found the Real Analysis course to the really really hard back in university. I thought it was like the CS information analysis when looking at the course title. It was nothing like that at all. It didn't help that the professor teaching it was pretty bad. I remember he used to jog into the class carrying a tennis racket and in tennis sporty dress with headband, seemingly just coming back from a tennis practice and acting to be cool. People just rolled their eyes. The teaching was just reading off the book. Darn, it was one of the top schools. How did this clown get in?
Mathematics for the Adventurous Self-Learner
31–40 of 216 posts
Re: Mathematics for the Adventurous Self-Learner
#32Earlier quoted context omitted.
Ha, I came here to shamelessly self-promote, but I see my book has already been mentioned! Here is a direct link to the preview: https://minireference.com/static/excerpts/noBSguide_v5_previ... I won't claim that Chapter 1 is complete and detailed review of all of high school math, but I did my best to cover all the essential topics needed for mechanics and calculus so that the book will be self-contained.
The book looks lovely. Did you write it using latex? What is your tooling to author a book like this?
Yep, standard LaTeX with the book class.
The preview linked is a little outdated so it shows the old figures, but the latest version has all the figures done in TikZ (a vector drawing package using LaTeX syntax, see https://www.overleaf.com/learn/latex/TikZ_package for examples).
There is no "tooling" per se for the book production (just run pdflatex to get the PDF, then upload to lulu.com and amazon.com, and they take care of the printing). I do have some scripts to enforce naming and notation conventions though, and there is some advanced git-rebase kung fu going on that allows me to reuse the high school prerequisites from Chapter 1 of the MATH & PHYS book for the LINEAR ALGEBRA book as well (basically when I fix typo in the master branch, I have to rebase the LA branch).
One thing that has been tremendously useful and I highly recommend for any authoring task, is using text-to-speech for proofreading: https://docs.google.com/document/d/1mApa60zJA8rgEm6T6GF0yIem...
Re: Mathematics for the Adventurous Self-Learner
#33I think it's great that people are posting book links like this, however, what I've found most helpful is actually having someone to help guide you.
I realize how lucky I was that I found a Discord server ran by a math PhD graduate who is willing to help us guide our learning. From this, I've started learning Algebra and Analysis (just starting with the latter). It's nice to have someone to discuss problems with when you get stuck and to guide you. Likewise, he can suggest exactly which problems I should do for a give chapter, that way I don't spend my time doing ones that just repeat the same simple things over and over and can focus on nice, conceptual ones. So, if you can, please try to find someone to help guide you, or be that guide for someone else! Having it has made me seriously consider going back for a mathematics masters (and maybe PhD), switching from my physics background.
Re: Mathematics for the Adventurous Self-Learner
#34I am going to suggest something that might go against this idea of self-studying math. Do not do it alone. I mean, it is okay to self-learn mathematics as much as possible but don't let that be the only way to learn. Find a self-study group where you can discuss what you are learning with others. I think the social-effect can be profound in learning. I realized this when I used to learn calculus on my own. My progres…
Ha - I actually suggested the exact same thing before seeing your post. It's definitely much better to have a group. Since I've found this group I'm currently in, I've also been much more motivated, but also able to get feedback from more advanced people, and pare the problem numbers down to only the ones that are useful and will help me build concepts, limiting how many "calculation" problems I have to repeat.
Re: Mathematics for the Adventurous Self-Learner
#35Earlier quoted context omitted.
Our site (brilliant.org) is designed for your use-case, among others.
Yep, brilliant.org + the first book from minireference.com are what OP needs.
I found that the community on brilliant.org can be quite toxic. I was a member for awhile, but quit due to the people on the site.
Re: Mathematics for the Adventurous Self-Learner
#36I pretty much followed the same route as OP re-studying mathematics seriously after 10 years in industry after initially doing a CS degree and doing mostly software engineering but transitioning into Data Science the last 3 years. When I saw Book of Proof then Spivak then Apostol on his list I chuckled because that’s exactly the route I ended up following as well. Studying from 04:30 to 06:30 in the week and about 8 hours split up over the weekend, Spivak took 8 months to complete (excluding some of the appendix chapters) but if you can force yourself to truly master the exercises - and Spivak’s value is the exercises - then you’re close to having that weird state called “mathematical maturity” or at least an intuition as to what that means. You can forget about doing the starred exercises, unless you’re gifted. Spend a lot of time on the first few chapters (again, the exercises), it will pay off later in the book. It was a very frustrating experience and I had so much self doubt working through it, it’s an absolutely brutal book. Some exercises will take you literally hours to try and figure out.
If you do Book of Proof first you will find Spivak much easier, since Spivak is very light on using set theoretic definitions of things. Even the way he defines a function pretty much avoids using set terminology. Book of Proof on the other hand slowly builds up everything through set theory. It was like learning assembly language, then going to a high level language (Spivak) and I could reason about what’s going on “under the hood”. Book of Proof is such a beautiful book, I wish I had something like it in high school, mathematics would have just made sense if I had that one book.
I read a quote somewhere, think it was Von Neumann that said, you never really understand mathematics, you just get used to it. Keep that in mind.
Re: Mathematics for the Adventurous Self-Learner
#37I think it's great that people are posting book links like this, however, what I've found most helpful is actually having someone to help guide you. I realize how lucky I was that I found a Discord server ran by a math PhD graduate who is willing to help us guide our learning. From this, I've started learning Algebra and Analysis (just starting with the latter). It's nice to have someone to discuss problems with when…
Could you share the discord server? Thank you.
Re: Mathematics for the Adventurous Self-Learner
#38http://www.goodtheorist.science/ this is a step by step for theoretical physics.
Re: Mathematics for the Adventurous Self-Learner
#39I know this is going to be the case for likely nobody, but I have browsed most of the self-study math threads that pop up here as a forever-on-my-todo-list thing and I have a remark to make: I have yet to find a guide that does not start with the assumption that you graduated highschool. That is a very reasonable assumption to make. We are in a community of technology and engineering, it would be a bit ridiculous to…
I'm also in a similar situation. I graduated highschool and passed mathematics, barely.
I didn't absorb any knowledge and switched classes halfway through my last year.
I'm studying CS in University now and will have to do a math-related subject and I'm quite nervous about it, because my mathematics skill is extremely low, and has been my entire life.
I've also been bookmarking guides like this but haven't gotten to looking into them (pure haziness) other than reading the introduction, which usually says "this guide assumes highschool level mathematics".
Re: Mathematics for the Adventurous Self-Learner
#40I pretty much followed the same route as OP re-studying mathematics seriously after 10 years in industry after initially doing a CS degree and doing mostly software engineering but transitioning into Data Science the last 3 years. When I saw Book of Proof then Spivak then Apostol on his list I chuckled because that’s exactly the route I ended up following as well. Studying from 04:30 to 06:30 in the week and about 8…
Heh, nice to find someone who walked a similar path! :-)
Ah Spivak...yes, I absolutely agree it's one of the best books to build up that mathematical maturity everyone talks about.
For me Spivak took about 6 months and I managed to do almost all of the starred exercises - Gifted? No. Brutally determined: yes. And I was quite fortunate to be in a place in life where I could put serious hours in to it at the time.
After that, I learned to relax a bit more as I realised I had pushed myself way too hard and was close to burning out. I still love looking back at that damn book though. There's just something that's so special about it...the way the exercises build upon each other and connect together. It's really unique.