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Mathematics for the Adventurous Self-Learner

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Re: Mathematics for the Adventurous Self-Learner

#111

Post by mathgenius »

dorchadas wrote: post #33

I 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…

I would say that learning mathematics is virtually impossible without a teacher. Like, would you try learning Karate without a teacher? How about if you get with a bunch of friends and you all try to learn it together? No way.

Even the professionals try to find someone to learn a new concept from. There's something about mathematical writing that is too fragile/brittle for wetware.

One other strategy: I've noticed the really smart (arrogant?) people just don't bother reading new mathematics, they re-invent it themselves. It's actually worth trying if you can stomach it.

Re: Mathematics for the Adventurous Self-Learner

#112

Post by goto11 »

gavinray wrote: post #6

I 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 went to the local library and borrowed high-school level textbooks. Just start from the level where you absolutely understand everything, however low you need to go. Solve all the exercises. You will blaze through the easy stuff, but the exercises will make it clear to you when you need to begin paying attention.

Re: Mathematics for the Adventurous Self-Learner

#113

Post by dotancohen »

sn9 wrote: post #64
gavinray wrote: post #6

I 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 would use Khan Academy. Start at a level that feels too easy, even if it's elementary school math. The key to learning anything is to start at a level that feels too easy and gradually increase difficulty. As you finish a subject, see if there's a corresponding book in the Art of Problem Solving store [0]; you can revisit the subject at a deeper level that will strengthen your foundation. The AoPS books will also e…

++Anki

Myself and my daughters use Anki every day. It has been the defining factor in turning my mediocre job into a career. And Ankidroid on Android is open source.

Re: Mathematics for the Adventurous Self-Learner

#114

Post by alenmilk »

gavinray wrote: post #6

I 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…

https://schoolyourself.org/learn/algebra is great. You start from addition subtraction and go through your list for the most part. Khan academy is great too, but with schoolyourself you can walk through it a bit faster.

Re: Mathematics for the Adventurous Self-Learner

#115

Post by mikorym »

I would recommend Conceptual Mathematics: A First Introduction to Categories by Lawvere.

It is written by a true pioneer. And also, you will impress your friends by your hipster foray into category theory.

However, this book is far from being hipster. Also, I would not be surprised if a high school student would be able to follow this book over the course of a year or two.

If you titled the book: Sarcastic introduction to how simple set theory is then I would actually be fooled that it were the correct title.

Re: Mathematics for the Adventurous Self-Learner

#116

Post by sampo »

There is 3 books listed that essentially cover the freshman (first year) courses in Calculus. And 4 for Linear Algebra. If you work your way through even 2 different books for one topic, you are going to have a broader foundation in the topic than a normal math student in a normal university after completing the corresponding course. And you will have spent much more time, too. University courses don't usually cover everything that is in a textbook. And students don't usually read books through. In fact, students usually try to skim the course notes just enough so that they can solve the weekly problem sets.

There is maybe nothing wrong with being thorough with the elementary topics if you're studying for fun. But if you're studying for applications, I think you should cover the basics only adequately, and then quickly move on to more advanced topics. Basic Calculus is only the foundation, stuff that is actually useful in applications comes later. Basic Linear Algebra can be useful in its own right, but the advanced stuff is even more useful.

I suggest building an adequate foundation, not a comprehensively thorough foundation, and then moving on to the more powerful stuff. Which varies depending on what you actually want to use math for.

Re: Mathematics for the Adventurous Self-Learner

#117

Post by TheTrotters »

chobytes wrote: post #20
hackernews7643 wrote: post #2

One thing I don’t think is discussed enough is the process of how self-learners in math get critical feedback. Most advanced level math textbooks do not have solutions to check their work against nor do they have a way to get feedback by an expert and this is essential for learning. Least with programming, you can get immediate feedback and know whether what you did is correct or not.

Learn proofs well and you get pretty good and knowing when you’re right. Enough for almost any problem you’ll be likely to encounter in a math textbook anyway.

I strongly disagree.

It's a little like saying "learn programming well enough and you'll know if some piece of code works as expected without running it."

Re: Mathematics for the Adventurous Self-Learner

#118

Post by russfink »

ivansavz wrote: post #16
look_lookatme wrote: post #12

Earlier quoted context omitted.

The No Bullshit Guide To Math And Physics https://minireference.com/ I bought the Math and Physics copy because it has an ebook option and the first chapter is the Math guide. I’m going through a few pages a day and it’s crisp and straightforward. There is a sample of the first chapter on the site, I suggest you check it out to see if this is what you are looking for. Found via an HN thread from last year on this top…

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.

Is it still in progress, or does the sample omit some information on purpose? E.g the logarithmic operations. Good book, good idea!

Re: Mathematics for the Adventurous Self-Learner

#119

Post by learner1215 »

strls wrote: post #99
polyphonicist wrote: post #85

Earlier quoted context omitted.

Which university, if you don't mind me asking? Can you share the names of the textbooks?

The books are called "Essential Mathematics" 1 and 2. They correspond to these modules. http://www.openuniversity.edu/courses/modules/mst124 http://www.openuniversity.edu/courses/modules/mst125 Second-hand OU books are usually bought from https://www.universitybooksearch.co.uk/

Could you provide the direct links for the books used in: MST123, MST124, MST125? I could not find them in your links.

Re: Mathematics for the Adventurous Self-Learner

#120

Post by graycat »

dougabug wrote: post #95
gavinray wrote: post #6

I 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…

Precalculus in a Nutshell is a beautiful little book by George F Simmons, which pretty much captures everything you need to know to undertake the study of calculus. https://www.maa.org/press/maa-reviews/precalculus-mathematic... Linear algebra is quite a beautiful, approachable subject; and a certain amount of it is necessary to make the leap from single variable to multi-variable calculus. Without a good grip on cal…

Simmons? WOW! He's a serious mathematician, e.g., as in his

George F. Simmons, Introduction to Topology and Modern Analysis.

I studied it one summer in an NSF program at Vanderbilt. Then I concluded that he is one heck of a good math writer.

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