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/sci/ - Science & Math

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9862618 No.9862618 [Reply] [Original]

Go on libgen.io or otherwise obtain the following exercise books:
>Advanced Problems in Mathematics - S.T.C. Siklos (University level problems for highschool math)
>Solving Mathematical Problems: A Personal Perspective - Terence Tao
>Yet Another Introduction to Analysis - V. Bryant (assumes only basic Calculus familiarity)

Obtain the following brainlet reference material which you will use to directly research things:
>Better Explained - Math
>Better Explained - Calculus
>An Infinite Descent into Pure Mathematics (free pdf) - https://infinitedescent.xyz/
>Anything else from the sticky guide

Your learning algorithm:
Start with any exercise book and attempt the first excercise, don't read the chapter.
If successful continue until you finish all the exercises, every single one, no exceptions.
Failure? Research directly the problem in your brainlet guides. Keep notes about everything you learn.
Still failure? Research the relevant chapter of said exercise book.
Still failure? Go on math.stackexchange and search for an answer similar to your problem, then go solve your problem.
>Critical: Do not look at the solutions manual in the appendix of w/e exercise book you're doing
Attempt to prove your answer is correct, research how to do this in the Tao book, the Pure Math book, or math.stackexchange, or Wikipedia
Only when you are absolutely sure you have the correct answer, look it up in the solutions guide.

This is not a meme, it's evidence based teaching: https://infinitedescent.xyz/20180214-exercises-ibl/
This won't take that long either, because like every other skill you'll get better at it with practice

How to fail
>Skipping problems
>Looking up the answers without at least thinking/attempting how you would prove it correct yourself
>Passively reading instead of directly researching the problem you want to solve
>Not keeping notes

>> No.9862644

your post is too long i cant include it in a single screencap

>> No.9862667

>>9862618
>Advanced Problems in Mathematics
Took a peek into this book out of interest. This is definitely not a brainlet book. It literally poses a problem and then works out a solution on the next page. This is not how a brainlet learns. Brainlets need at least 10 pages of formalities before they can even do a problem in the topic, and then they want a couple of pretty pictures here and there. In this book, the first problem is one of the most boring types of diophantine equation (solve by bounding values) and the solution is a wall of text.

That said, the problems were interesting. I would like to know if there is anything similar to this book but that works with more advanced content.

>> No.9862682

>>9862667
The 2003 booklet Advanced Problems in Core Mathematics is based on a less advanced syllabus, the pretty pictures and things a brainlet would look up in the Better explained guide, they can also just start with Tao's book and progress to the advanced exercise book. Probability and Statistics by M.R. Spiegel is another book where it's entirely exercises.

Advanced content, I can only think of Richard Bass' Real Analysis for Graduate Students (free) http://bass.math.uconn.edu/real.html as it's a crash course in all the math you would need to pass a pretest for grad school, so probability basics, topology basics, ect.

>> No.9862687

>>9862682
>Tao's book
Dude, Tao's book is for mathematical olympiads. When do you see a brainlet going to the IMO my dude?

>>9862682
>Richard Bass' Real Analysis for Graduate Students
Appreciate the recommendation. Gave it a quick look and I think I'll pass. Measure theory is actually too advanced for what I need. To be clear, I'm looking for more material to train for university level math olympiads as I'll be taking several this year. The contents of these types of Olympiad are actually limited by freshman/sophomore tier mathematics. I would love to study the Lebesgue integral but really I am not in a position where I can waste time learning something that I know will not appear in the competition. At least for this year.

>> No.9862693

>>9862687
Paul Zeitz' Art and Craft of Problem Solving is olympiad type stuff, harder than Tao I found.
I'm a brainlet and I managed to do Tao's book, and pass the Sixth Term Examination Paper for Mathematics admissions (UK), as in my grades in HS were profoundly shite until I started doing this algorithm of solving problems by myself.

>> No.9862713

>>9862693
>Paul Zeitz' Art and Craft of Problem Solving is olympiad type stuff
I already have my man Paul Zeitz. Amazing book. I really just wish it was longer. I feel like the calculus section could be expanded by a lot, and there is no linear algebra section which is tragic because linear algebra always appears in some way or another in competitions.

>I'm a brainlet and I managed to do Tao's book
Well you must be a high-end brainlet. One must keep in mind that this book was not written by old guy Tao. It was literally written by 15 year old Tao, a kid that was balls deep into IMO tier problem solving, just retired after getting his gold medal.

>> No.9862719

>>9862687
>university level olympiads
Po-Shen Loh, math professor at Carnegie Mellon University and coach of the US International Math Olympiad team runs this site which is all problems: https://v1.expii.com/grandmaster

Crux Mathematicorum also has undergrad level olympiad problems

>> No.9862725

>>9862618
How do I go about 'keeping notes'?

>> No.9862749

>>9862719
I am aware of Crux, but not of the other source so thank you for that. That said, I am mainly looking for problem-oriented textbooks, not just problems. This is because I consider my strengths to be in number theory and calculus, but when it comes to combinatorics, geometry and linear algebra I still prefer having problems divided by topic/technique and having a reference of the main theorems and proofs for that topic/technique.

>> No.9862763

>>9862687
>Tao
I am nowhere near olympiad ability or anything but I could finish Tao's book by taking forever trying the questions, some I couldn't solve, but just the process of at least reading and trying to understand the question was enormously helpful for solving future problems in undergrad.

>>9862725
Make a bunch of text files per subject, add to it whenever you learn something, look up cornell style notes

>> No.9862775

>>9862749
>Combinatorics
Knuth's Concrete Math or TAOCP Combinatorial Algorthims volume is all I can think of, though CMath is filled with silly tricks at times. There is a ridiculous amount of exercises in TAOCP (Art of Computer Programming) most of them are math. Aluffi's Algebra Chapter 0 is where I really learned Linear Algebra. Geometry I have no idea, my only experience is 'Analytical Geometry' out of Simmons Calculus text. Good luck with the olympiad I thought they hired coachs for these things or had olympiad groups at schools that met weekly with old tests to go through them

>> No.9862779

>>9862775
Thanks for the recommendations. I'll be checking them out. By the way, I have a coach and we have a reading list but I'm just saw this thread and thought I could ask for some extra material.

>> No.9862798

>>9862618
lucid dreaming

>> No.9862894
File: 49 KB, 333x205, feelsbadman.png [View same] [iqdb] [saucenao] [google]
9862894

i hesitate to read these kinds of books by Tao. He is a literal genius bred to do math. I'm just a brainlet. how can we possibly relate?

>> No.9862897

>>9862894
Well, smart people are just brainletlets.

>> No.9862930

>>9862897
that made me feel a lot better. thanks anon.

>> No.9863149

>>9862644
buy a bigger screen

>> No.9863226

>>9862719
>Po Shen Loh
That site expii.com is a better idea than khan academy, go directly to exercises that automatically determine if you need more practice at something and then keep feeding you concepts until you understand.

>> No.9863294
File: 176 KB, 957x485, Screenshot_2018-07-12 sci - Brainlet Guide to Learning Basic Math - Science Math - 4chan.png [View same] [iqdb] [saucenao] [google]
9863294

>>9862644

>> No.9863300
File: 199 KB, 260x370, Screenshot_2018-07-12 Bijective Combinatorics (Discrete Mathematics and Its Applications) Nicholas Loehr 9781439848845 Amaz[...].png [View same] [iqdb] [saucenao] [google]
9863300

>>9862779
I have looked into various books and I really liked this one.
It's rigorous yet easy.

>> No.9863301

>>9862798
Can you elaborate?
How do lucid dreams affect your problem solving abilities?

>> No.9863767

>>9863294
Thanks for screencaping this legendary thread. How do I give gold?

>> No.9865106

>>9862618
Im an extreme fucking brainlet with what book should start?

>> No.9865186

>>9862618
or you could just read the wiki books and avoid exercise books like a normal non autist