Self-studying math

Have any of you successfully studied math by yourself from a high school level to higher maths such as linear algebra, trig, calc? Right now I'm currently sitting at what feels like zero knowledge of maths. I know your basic arithmetic but I'm not particularly amazing at it. I don't know algebra at all. But being a programmer, I want to learn more math. I want to be able to study computer science and its related math. But right now it's a brick wall, how do I get over it? What study plan do I follow? Khan academy? Books? I feel so lost with it all.

if you're a good programmer you probably have the pathways for basic proofs in your head already. Book of Proof and How to Prove It are excellent introductions to mathematical proof and they don't require much more than a sharp mind and arithmetic knowledge.

I'm in a similar situation but I am missing even basic high school math. I use Khan academy and I like it, but I'd like something more based on history/philosophy and stuff like that. I wouldn't mind learning formal logic before learning how to count. Hope you understand what I mean. Is there any book that teaches math this way? Preferably something that goes from early math to higher math, I'd like to avoid switching books too often Does something like that exist?

https://m.youtube.com/user/njwildberger It's possible. NJ wildberger's channel actually has a good video on studying linear algebra if that's what you want, no book required. He also has a math foundations series you can go through to get an idea of mathematics from the "bottom" as he sees it, up. I think that basic math serge lang book might be useful for you to learn algebra too. It's basically an entire high level high school education in one book. Shows you how much time we really waste in high school. Also take that image with a grain of salt, do some research for what books would suit your purposes on your own time.

>>11753 >I wouldn't mind learning formal logic before learning how to count. The Greeks learned how to count, and then learned geometry before they even entered schools of philosophy.

>>11755 Yes of course, I was just giving an example on how I would like to learn math. It's not like I strictly want a historical chronology of math, but I would definitely be ok with learning some basic stuff later on The innovation of numbers is actually super interesting in my opinion. There was a 2 hour lecture on YouTube about it but I can't seem to find it right now.

Me all the time btw we learn that 7-9 grade

Does anyone know a book to learn conic section in depth? My searches on Duckduckgo weren"t very successful, websites are often too superficial and don't demonstrate.

>>11790 >conic sections "Conics and Cubics" has a pretty extensive discussion of conics in the context of algebraic geometry.

>>11753 You might like "Mathematics for the Nonmathematician" by Morris Kline.

What are some good starting points for a retard who can't do basic high school geometry and algebra?

>>16876 Khan academy.

>>11748 I got my degree in Mathematics and Computer Science so I never really "Self studied" I always had a professor to ask questions to, but I'm sure if you put in the effort you'll be able to do it.

your infographic is good except it has Dummit & Foote as the first introduction to algebra. Don't get me wrong, it's a fantastic book, but you could easily spend an entire year reading it and doing no other math. A more quick & dirty introduction for someone not wanting to specialize in algebra would be Herstein's "Abstract Algebra". Anyway, the math in CS is not that closely related to the math in math programs. You will want a very solid understanding of real analysis, linear algebra, and the basics of proof. From there you will be well prepared for statistics, machine learning, optimization, control theory(you also need differential equations for this one, I recommend Arnol'd), and the theory of computation/complexity. Donald Knuth's "Concrete Mathematics" is a must-read for people interested in the math involved with CS. Anyway, if you don't want a really structured path of study, or don't know what math in particular you want to study, I recommend a wonderful little trio of books called A Mathematical Gift. It's sort of an intro to the fun parts of math for people who know calculus.

Elementary mathematics for self-study, arithmetic, algebra, and geometry.

Elementary mathematics for self-study, trigonometry and calculus. Incidentally, that's the calculus book Feynman learned from.

>>11748 My dude, I am going through the EXACT same problem as you right now! Glad to know I'm not the only one in this situation!

After Thompson's elementary math books, study this and you'll be ready to do some basic science.

My partner is trying to study up on foundational maths sonshe can get into computer science, programming, power electronics, etc. Gonna bump this thread and come back later if she has any links or ideas to contribute.

>>18500 >>18501 thank you very much for these

Im following this book, I think its worth to upload in this thread, the author did a very nice explanation construction the numeric sets. Im just in chapter 3 at the moment and the construction of the set of Integers from the natural numbers is one of the coolest things i ever have seen Im my self study of math. I have a list of other books I wans to read/solve following this one, the author give very nice references in the ending of chapters and at hard exercises as well.

>>19519 Enjoy :3

>>I wouldn't mind learning formal logic before learning how to count. >The Greeks learned how to count, and then learned geometry before they even entered schools of philosophy. So? That doesn't mean we have to. I know I'll be teaching my children how to think well, well before I teach anything about counting. It's the natural order of things. Sure, they might become acquainted with counting before mastering thought, but that shall be subservient to thought. A person who thinks well, if he needs it, will soon enough teach himself to count well. A world so edified will be more effective: efficient, robust, interesting.

>>19560 That's right, and you should teach your children to read Shakespeare before they learn the alphabet, too! Makes so much sense.

>>19560 without well-understood examples, it is unnecessarily difficult to acquire new knowledge. Knowledge naturally grows out of curiosity and generalization, not top-down Bourbaki style rigor.

and those above in the false hierarchy are prime examples of failure for all the earth to witness for all time

>>19560 if you don't know what it means for two numbers to be equal, how can you understand what the difference between 'true' and 'false' is in mathematics?

i feel statistics is the only really useful one for cs because you really need it for machine learning and data science. Cant think of anything else i would have ever frequently used. If you do 3d graphics you might need quaternions but its something you do once and forget about again.

>>19560 Not bad. You can teach your 6 year old propositional logic, and by the age of 10 he will find out, from Russell and Whitehead, that 1+1=2.

>>21395 what is linear algebra?

>>21395 What is discrete mathematics?

>>21424 >>21425 Name one thing you didnt get in high school and needed for coding.

Mit opencourseware is a great resource for watching lectures and doing practice problems with answers. It's good for any subject but I liked the discrete math course (Mathematics for computer science)

>>21426 The other day I was messing around with the godot game engine and I needed to rotate an object around an arbitrary vector that could be set by the user in the editor. There wasn't an existing function that could do this, and every post or github issue I found while searching said basically "you can't and it's impossible, you have to rotate around the local origin". Luckily I know linear algebra, so I just used conjugation by the pivot axis's transform and a rotation matrix to accomplish it quite efficiently. I would not have been able to do this in high school, although maybe some people can. A couple weeks ago I had to write a gradient noise function for some graphics work because the one that came in the standard library didn't do what I wanted it to. I just read a paper on the subject and put it together using my knowledge of numerical analysis. I probably could have copied the algorithm with just high school calc, but coming up with a modified version that does what I needed it to do required a deeper understanding that you only get with higher level math. You don't need the same level of math for every kind of programming of course. Certainly you don't need the same kind of math for everything. My brother is a compiler dev and he never uses linear algebra, but he's got a good handle on graph theory. That being said, you can absolutely get by without math. It's just harder and you'll often do really stupid things without realizing it. You see it all the time with 3d graphics and game programming. Someone will want to, say, make one object move towards another. So they'll rotate the first object towards the second, and have it walk forward by some delta every frame. But oh no, he target object is moving! So they re-do the expensive rotation every frame. A linear algebra student would realize that a simple interpolation between the two nodes can accomplish the same thing with just element-wise scaling and addition. Plus they would be able to easily add effects like rubber-banding and spring-like bouncing, while the other person would be basically SOL if those weren't part of the engine already. The first person in this hypothetical would probably say they don't need math, and they're right in some sense; they got the job done. But they also don't realize the benefit that learning math would give them.

>>21426 >Name one thing you didnt get in high school and needed for coding. Linear algebra stuff, just like >>21434 And I'm about to start project related to stuff from "Concrete Mathematics" textbook.

>>21434 Vector math is something i had in high school. Covered calculating sections between planes and other objects too. Only thing i learned new in university was the mentioned quarternions to solve gimbal lock for 3d rotations. noise functions is something i also never had in high school though personally it doesn't feel like learning math. Its just shopping for a nice looking pattern. Side node blender is really comfortable for this kind of visual work. You can test custom functions quick in phyton and mix them in the node editor for some post-processing. Its really comfortable for experimenting.

>>21437 There is also proving algorithms, stochastic calculus, semi-math formal language and automata theory, numerical methods, first order logic and set theory, topology, finite element method and other stuff taught on univs. And yes quiet some part of cs crowd is using such stuff daily.

>>21437 >Only thing i learned new in university was the mentioned quarternions to solve gimbal lock for 3d rotations. Ironically I think the stuff you learn in your first linear algebra class tends to be less useful than the stuff you learn later. Row reduction and all that is good to know about but it doesn't come up that often. On the other hand, the theory of vector spaces and transforms is incredibly useful, especially for CS. Mainly because it lets you turn sequences of spatial operations into matrix products, and if you know what you're doing you can precompute certain parts of it for better performance, but doing so requires you to be able to do algebra with matrices. >Its just shopping for a nice looking pattern I'm talking about writing your own implementation of something like this https://en.m.wikipedia.org/wiki/Simplex_noise not just using a noise library. To be fair, it's not hard to find a noise library, but there are plenty of situations where you'd want to write it yourself. >Side node blender is really comfortable for this kind of visual work. I love blender for that kind of thing, although I wish you could write regular glsl scripts that run on the GPU and integrate them with the node editor thing. The nodes can quickly turn into a rat's nest of wires if you're trying to do something especially complicated, and when you're done the results are only useful in blender. Nice for prototyping but if you're writing graphics software you're going to have to rewrite everything in actual shader code.

BTW I proposed creation of /math/ board. Anyone agrees it would be nice? >>>/q/9201

I'm not a programmer,should I learn mathematics? And if yes - why?

>>22542 >I'm not a programmer irrelevant >should I learn mathematics? if you want to >if yes, why? Because you want to

>>21446 It will be awesome, but it will need to allow tex using mathjs or something related, so people can just write proofs or help in a readable way.

>>22550 > but it will need to allow tex using mathjs it can be done server side

If anyone looks for books on First Order Logic and Topology look for books of Kuratowski. They were translated to English from Polish.

Howard Eves' Foundations and Fundamental Concepts of Mathematics is a great introductory text into mathematics, focusing on the, well, Foundations, and the Fundamentals, but what's interesting to note, about this book, is that it takes a historical approach, starting with what could be called ```pre-hellenic mathematics''' proto-mathematics---those empirically derived techniques for counting sheep---well, cattle---or measuring land---but soon progresses into ```hellenic''' that more intellectually rigorous style, that Mathematics has come to be infamous for. The book is a survey, for sure, and perhaps covers ideas you've already studied, but the historical order, makes it interesting, if not for the Math, but for the History of Math, which can help one grasp intuitions that one might have been unaware of missing. I read the first chapter, and excepts from other chapters, and it does seem to be, an excellent resource for beginners, intermediates, and experts, in their own special ways. My interest is in foundations, and philosophies---yes, I know---of Mathematics. I'd be interested to see what philosophical differences, different ages, with their different knowledges of Mathematics, might have conceived as the Mathematics. There definitely seems to be some interest in Mathematics on LAINCHAN, but it seems a bit scattered. I hope, perhaps, we can strengthen the local Mathematical culture, by going though this fun little book, of 9 chapters, of 5 sections each---solving the ```exercises''' puzzles as we progress.

>>23339 Greek mathematics started well before the hellenic period. Pythagooras lived ca. 600BC. Sure, Euclid did his work in Alexandria, but the tradition he built on stretches way back.

>>22544 and ProofWiki's definition pages are based and eternal-pilled

Try to prove the general equation for quadratic polynomials, completing squares. Its a bit more abstract, but yoou only have to add and substract the same quantity (add a zero) and work with simple algebra.

I got my college degree in Math, and studied math in graduate school before dropping out due to depression. I sort of want to get back into Math. Does anyone want to form a discord study group? I am mostly interested in applied topics, like Optimization, Numerical Analysis, Statistics, and Algorithms. I would not mind fundamental stuff once in awhile.

>>23865 By the way, if there is interest, message me on discord: Mouse#7577.

I failed 9th grade math and eventually dropped out. Are the books in the OP out of reach for someone like me?

>>24103 I haven't read most of those books, but the first row seems to cover the subjects you would expect to find in a Highschool Maths curriculum, if you want to know what you missed by dropping out they would probably give you a solid foundation for moving forward.

>>11748 to be very honest i don't think you can really learn math by yourself. of course there are books and lectures out there but math is twice more practice than lessons. you need to pick up the intuition and the little tips you can't really get outside of practice with a teacher. your knowledge of math is really incomplete if you don't work things out with your hand and an experienced person on your shoulder. coming from a physics undergraduate

>>24653 i don't agree with this. it is very helpful to have a teacher to help you build mathematical intuition and learn little tricks, but it is not required. i am finishing a math/cs degree right now, and i have done most of it learning on my own time. i go to a decent university but it is nothing special, and i have had some very poor professors.

>>18506 Thanks for the Instructors solutions I didn't know about that

>>21397 No need to ignore 100 years of progress on foundations. If you want to go the foundational route, you can use the Calculus of Inductive Constructions or a variant to define "1", "+", "=", and "2" very naturally, at which point the proof of 1+1=2 is trivial. (Even 100 years ago, you could just assume the Peano axioms, so the myth you needed hundreds of pages to demonstrate 1+1=2 formally was wrong even back then.) Of course this is still very silly and any sane person would first teach what natural numbers are and how to write recursive algorithms and inductive proofs on natural numbers, and then after that is mastered generalize those ideas to arbitrary inductive types. That said, there's nothing wrong with teaching logic at an early age. You don't start with formal symbolic stuff. It should be more like having them figure out what's wrong with "Monkeys like bananas. [Child's name] likes bananas. Therefore, [Child's name] is a monkey!"

>>19519 >>18500 Second attempt at making this post. Since Sep 2020 I'd went over the arithmetic book effectively to check whether I need to go through it whole or not. Decided to move on to algebra and started from Chapter 1. Life happened during winter 2020 and once I had my focus back, I continued going through it. Made some progress then had another secondary obligation during early summer 2021 and am now finally back on track. These books are a very enjoyable and structured read; had a friend (holds a Math degree) check them out - they confirm books as very well structured for self learning. This is nothing new to anyone doing some research and looking at book's reviews. This time around though I'd decided that my progress is way too slow so starting from scratch again, going back to Arithmetic first, will help develop a steady habit, a "groove".

>>24674 I promise with a teacher you can learn 2-3x faster

What are the pros and cons of learning math through khan academy instead of a proper math book? Is there a superior option? Should I use both?

>>27480 pro: you might have an easier time paying attention con: kahn academy and similar services tend to be good for basics (meaning anything you would need for an engineering degree) but bad for advanced material. I think that to really grok advanced math you need to spend serious time going through a textbook.

Lainons, what ways of studying math is effective, besides reading books and solving problems from them? Maybe some of you can give tips on organizing info / etc.

>>28082 Once you've gotten to the point with a subject where reading books rarely imparts new information, something I like to do is write up my own well-formatted notes with an emphasis on things that I find confusing. Just writing these notes is a very good way of organizing knowledge, and then you can refer to them later instead of looking for a book or reading your soykafty lecture notes.

>>28085 note: this is how a lot of textbooks start their life

>>28085 >>28086 Thanks

>>27482 Kahn is too superficial for an engineering degree, it wasn't even enough for my 10 credits worth of mathematics in my CS degree.

>>28082 Began learning programming languages bottom-up by gradually implementing mathematics found in the literature. I am >>27094 and am very very slowly going over the books one by one. I found that this works for me, combining multiple interests into one activity so that the tougher segments aren't as much of a slowdown.

Any book recs for someone who has a bachelor's in engineering but is still interested in math? Maybe something directed towards controls, as I'd be interested in going to graduate school for autonomous controls (e.g., cars, uavs, maybe even industrial applications, etc.)

For German lainons, I highly suggest Höhere Mathematik in Rezepten - Christian Karpfinger Höhere Mathematik 2 Springer Verlag (mit Wirbel als Bild)

do not self study. school exists for a reason

>>29177 Horrible advice. School is a trap You can learn on your own or from a tutor if you must.

>>29178 Depends on the person, I can't concentrate in school but I can study well by myself or from a good tutor.

>>29177 Nowadays schools exist to pass exams or get qualifications, all with the end goal of getting a job, not an education. I think >>29178 saying use a tutor might be more valid because if you explain to the tutor you want understanding, not to pass a test, they can teach you for that purpose. They're also more personal than a teacher.

>>18319 imo this book is a gem.

>>11748 my friend got into category theory. https://smile.amazon.com/gp/product/1108711820 it's the set of things that underly things. I tried it out a bit. It seems fun but not super practical for day to day work.

I found an youtube math channel where one guy just solved examples and tried to apply teached stuff to real-life situations. He omitted all unnecessary theory and proofs. I've prepared with this on my IT university math exam in 5 days. Not enough to get A, but enough for passing. >>29177 Unfortunately in my country math teachers aren't very good and online courses are much better option.

Math tutorials and notes: https://tutorial.math.lamar.edu/ An interesting article: https://danluu.com/math-bias/ Good YT channel: https://www.youtube.com/c/3blue1brown/videos >>11748 Is Calculus: An Intuitive and Physical Approach by Morris Kline a good book?

>>30750 Link? we are all short and empty

>>30780 It's called Isibalo, but it's in Czech language, not English, sorry. But I'm sure that there are more good math channels in different languages on Youtube.

>>30751 The "standard" Calculus textbook for self-studying is Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra by Apostol, which is mentioned in the second link you posted. For a more rigorous approach, read Introduction to Calculus and Analysis, Volume I by Courant and John.