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Mathematics for the Adventurous Self-Learner

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Re: Mathematics for the Adventurous Self-Learner

#121

Post by ivansavz »

russfink wrote: post #118
ivansavz wrote: post #16

Earlier 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.

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

The preview is a "special build" of the book that removes most of the content and leaves only the section formulas and headings --- this way to ensure the internal navigation works, but it's confusing since it looks like chunks are missing. Previously I would cut only selected pages but then the links didn't work. Sorry for the confusion. You can check the preview on amazon for the real page numbers: https://www.amazon.com/dp/0992001005/noBSmathphys

Re: Mathematics for the Adventurous Self-Learner

#122

Post by abvr »

TheTrotters wrote: post #117
chobytes wrote: post #20

Earlier quoted context omitted.

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."

That's what seperates them both, it's not about immediate formal checking from a compiler here, but rather if our proof is being justified adequately according with the rules of deduction and reasoning, it's a more intuitive approach in math, although you do end up knowing whether something is right or wrong, akin to programs.

Re: Mathematics for the Adventurous Self-Learner

#123

Post by tinyhouse »

It was a great read. I bookmark this post hoping one day to buy a couple of the recommended books. It's just too hard for me right now to find the time. Life is too busy with a family, a full time job, and all the distractions around. Self learning is one of the most enjoyable things.

Re: Mathematics for the Adventurous Self-Learner

#125

Post by dhimes »

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 hope I'm not too late here, but if you are in the US I would highly, highly recommend signing up for developmental classes at your local community college. You are exactly whom those classes are for. If you've tried on your own before and struggled to stay motivated, doing it in a structured way, in 15 week "sprints", may be just the kickstart to your self-study program you need.

Disclaimer: I was a full-time community college professor for a decade. I had no idea what a resource they were. It's small money compared to either the alternative of a university or not succeeding. If you use them you will succeed. It's what they do, and they've been doing it for a very long time.

Re: Mathematics for the Adventurous Self-Learner

#126

Post by zuzuleinen »

dotancohen wrote: post #113
sn9 wrote: post #64

Earlier quoted context omitted.

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.

Can you tell me what type of cards did you use for your career? I'm thinking to start using Anki, but not sure how to structure the cards. Thanks!

Re: Mathematics for the Adventurous Self-Learner

#127

Post by appleflaxen »

dotancohen wrote: post #113
sn9 wrote: post #64

Earlier quoted context omitted.

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.

Can you elaborate in how it's been that transformative? I get why it's a useful tool, but you seem particularly enthusiastic. How are you using it?

Re: Mathematics for the Adventurous Self-Learner

#128

Post by greymalik »

bemmu wrote: post #98
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 solved this by just buying all the high school math textbooks and going through those on my own. I preferred this way, because it lets you have the same background as everyone else. In attempt #1 I was jumping ahead to read the interesting stuff (calculus), and while I could make some progress, it was needlessly difficult because I didn't start from the basics. It attempt #2 I started from the very beginning (cours…

Can you clarify how step 3 was different for you from step 2? (I’ve had similar unsuccessful steps 1 and 2, wondering what they keys were for you to turn the corner)

Re: Mathematics for the Adventurous Self-Learner

#129

Post by jostylr »

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…

A few ideas:

* Guesstimation:Solving the World's Problems on the Back of a Cocktail Napkin. Math is a tool. Start using it with some simple arithmetic and scientific notation. Once it becomes something you can use and play in that context, everything else becomes a lot easier. This is water cooler talk and is something actually usable immediately.

* Speed Mathematics Simplified. From the 1960s. Wonderful book about doing arithmetic from left to right. Also has some good stuff about decimals/fractions/percents as well as checksums. Being quick with arithmetic and getting that number sense makes everything else easier.

* Burn Math Class. Gives an appropriate viewpoint for a lot of math. Gets a little whacky as it goes on, but the core ideas should help you take ownership of math.

* ... gap not sure what to put in ... Maybe Precalculus in a Nutshell... But play around with GeoGebra. Exploring geometry, trigonometry, and precalculus visually is key to getting an intuition about. Get to know the behaviors of the functions, but don't get lost in trig identities or solving random algebraic equations. Things like Newton's method (or the Secant Method) are more important for learning about than lots of arbitrary algebraic simplifications (they can be important too)

* Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach. At some point, if you mastered K-12 math and want to get a good mix of theory and application and efficiency, this book by John and Barbara Hubbard is really quite nice. It puts linear algebra in one of its primary contexts of being the main foundation for solving nonlinear systems.

Re: Mathematics for the Adventurous Self-Learner

#130

Post by throwlaplace »

ColinWright wrote: post #97
throwlaplace wrote: post #45

Earlier quoted context omitted.

this is excellent execellt advice. seriously anyone interested in learning math, chancing on this comment, should write it down. i wish i could upvote many more times. i have a bachelors in pure math and am 10 years out. i have time and again revisited things and didn't make good substantive progress until i came to these same exact conclusions. especially the part about skipping the exercises. if you're not trying t…

> this is excellent execellt advice ... especially the part about skipping the exercises. if you're not trying to write a dissertation or pass a qual (and you're just interested in learning and being exposed) then you don't need to do them I think this is deeply mistaken. In a well-chosen book, such as the ones in the submitted article, doing the exercises is not to test your memorisation, it's to develop your unders…

>Ignore the exercises if you want, but you almost certainly will end up knowing about the math, but not able to do it.

Isn't that literally exactly what I said?

> if you're not trying to write a dissertation or pass a qual (and you're just interested in learning and being exposed) then you don't need to do them

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