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1To everyone who posts about "learning more math"--- (self.math)
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3submitted 7 years ago * by hbetx9Algebra
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5I've seen so many of these posts that I'm just baffled. Here is the skinny. First of all, most important, GO LEARN ALGEBRA. Seriously, I know you think its bullshit but its the most basic skill in some ways that any mathematician should know. Second learn Calculus: Single and Multivariable. If you are still interested here are some things to go onto next:
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7(1) Discrete mathematics: This includes equivalence relations (probably one of the most important things for you understand ever), propositional calculus (logic) proof techniques (induction) and some basic combinatorics (Pigeonhole principle). You can literally find any text book and start reading. The theory is kinda a hodge podge, but those are the major themes.
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9(2) Linear Algebra: Again, one of the most important subjects you will ever study. Once you understand this, you are really on your way, and this stuff comes up everywhere. Many mathematicians have said many of the biggest proofs in the world come down to "just some linear algebra". The major point here is to understand that there is only one vector space for each dimension over a field and understand how a linear transformation becomes a matrix only after a choice of basis. Here equivalence relations come up again!
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11(3) Differential equations: Unless you're focused on engr math or serious applied stuff, don't worry too much about this. Seriously, its not that integral (haha get it!).
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13(4) Complex Analysis: Yes, mathematicians and engr. actually do study "imaginary" numbers, but there is nothing imaginary here. This is serious stuff, do it.
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15Okay, so now you're about at a sophomore/junior level place in mathematics. How to finish it off? Its not that unclear:
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17(1) Abstract Algebra -- Grab any book read about groups, rings, fields, vector spaces and modules. Proofs will be difficult here but work through it. There are so many books here, avoid Lang (good book but not for starting out), Dummit/Foote is okay. As a ugrad I had a good time with Rotman's An introduction to abstract algebra.
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19(2) Analysis -- Grab Baby Rudin. No seriously, Grab this book, sit in a room for a semester and just fuckn' read it. You will basically be "redoing" calculus. This is a trial by fire, go!
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21(3) Topology -- Grab Introduction to Topology by J. Munkries. Its so well written it might as well be a coffee table book.
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23There now, you basically have done everything a math major would. Yes there are lots of things that are missing, arguably the most important things depending on what your goals are. Typically one studies Num. Theory along with Abstract Algebra, or studies Analysis and Differential Equations together or Analysis and Topology. Seeing the links across different topics is important, but I'm just giving the overview here.
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25Not every mathematician studies logic deeply and there are LOT of fringe topics that I'm omitting (including some of my favs: Projective Geometry, Varieties, Lattice/Order theory, Combinatorics, Elliptic Curves, Coding theory, Harmonic Analysis, etc). However, none of these are required courses at more than a 1% of programs.
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27Stop asking for a "good book on blah" or "I'm a novice and want to learn more" because these questions are either (1) easy/clear to answer from literally 10 seconds of google/reading older posts or (2) is too vague to be of use. in order for the community to help you, its important for you to state why you want to learn what you want to learn. Stop trying to learn a topic about some buzzword you just found out about. Its probably not that important. Go to wiki, read the basic pages and get an idea. Then pick one thing and study it deeply for a while. Typically finding a book is easy, finding a study partner is hard. The latter is what the community should be for, not the former. There is no reason anyone in the world "has to learn measure theory" -- period. Or Galois theory, or anything in mathematics, unless you are becoming a mathematician or a professional in a mathematical field (abstract theoretical academic computer science for example, NOT programming/web developing).
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29If you're just learning to learn great! Lovely! Pick up a book and start going through it! Don't skip the basics and don't pretend like this is the most important thing ever, it just what you find interesting. I would be more reactive to someone saying "So I'm reading measure theory and I don't quite get why this part of the definition of this is stated this way" or "What do they really mean by almost"? I hate answering questions like "I want to learn measure theory" because that whole statement is just crap. If you do, start learning and ask a more meaningful question.
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31TL;DR: I'm trying to address all posts like this at once.
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33EDIT: Thanks to all who have upvoted to get this post to the top and to Shimei for addressing the concerns. Hopefully this is a small step towards more meaningful discussions on the front page (of /r/math).
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39[–]kingkarlit0s 21 points 7 years ago 
40Just thought I'd mention there is an entire subreddit for these questions too -- /r/learnmath
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44[–]hbetx9Algebra[S] 5 points 7 years ago 
45indeed.
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49[–]thehotelambush 29 points 7 years ago 
50Thank you. This subreddit needs more content and less r/learnmath + r/cheatatmathhomework.
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54[–]AtomHeartMother1970 16 points 7 years ago 
55I don't think it's nice to, and would not want to discourage people who are excited about something from asking questions about it or getting advice.
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59[–]hbetx9Algebra[S] 23 points 7 years ago 
60This isn't about discouragement, this is about getting people to think about the questions their asking before they post so that they ask something that can be answered. If you read through the language on the comments here, no one is saying that we don't want to help people. However, personally I get sick of answering the same vague question 20,000 times. Furthermore, if you aren't serious enough about studying something to do a bit of research, then you probably shouldn't be posting at all.
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64[–]Paul-ish 9 points 7 years ago 
65Agreed. People asking simple questions in here is analogous to a high school student showing up at a math conference looking for help with his calculus homework. "ಠ_ಠ" is all they would get.
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69[–]GrishaPerelman 1 point 7 years ago 
70dude how did you do that eye thing? really cool!
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74[–]Paul-ish 2 points 7 years ago 
75It is really quite simple, you just ಠ_ಠ.
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79[–]hbetx9Algebra[S] 0 points 7 years ago 
80So why not make some effort to change it? You think it impossible?
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84[–]Lanza21 6 points 7 years ago 
85Meh. It isn't like this place is flowing with legit topics. You can come to this subreddit once a week and read all the articles in a short time. Discouraging less then quality posts isn't exactly the highest priority.
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88[–][deleted] 7 years ago 
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92[–]hbetx9Algebra[S] 1 point 7 years ago 
93Simple typo.
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97[–][deleted] 1 point 7 years ago 
98No problem. I prefer when people respectfully correct my comments, just trying to pay it forward. :)
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102[–]thehotelambush 10 points 7 years ago 
103I actually don't care if people post things like that, I just want to see more interesting math in r/math.
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107[–]hbetx9Algebra[S] 1 point 7 years ago 
108Getting questions like this to not fill up the front page is one good step.....
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115[–]hbetx9Algebra[S] 3 points 7 years ago 
116I teach for a living, you are far from alone!
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120[–]rantrantrant2 -2 points 7 years ago 
121Aren't you the guy who fucked over the kidney donator?
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125[–]Pwrong 3 points 7 years ago 
126Maybe there should be r/mathcontent, r/mathopenproblems, or r/mathematicians
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130[–]hbetx9Algebra[S] 1 point 7 years ago 
131I would change the last one to r/mathematics
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135[–]sensical 2 points 7 years ago 
136I think it's futile to try and get rid of the newbie posts in this subreddit. Absolutely hopeless.
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140[–]qpla 1 point 6 years ago 
141I used to be the guy (on a different account) who would, every time exam season rolled around, would make the post reminding people to keep /r/math clean and use /r/learnmath and /r/cheatatmathhomework (which is actually (or at least once was) a pretty helpful community.). Since I've stopped, I've noticed a great increase in those sorts of posts going unchecked.
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145[–]tdyo 12 points 7 years ago 
146I don't want to "learn more about x," but I do have a quick question about what I should focus on if I want to use mathematics for a particular application. I only ask now because I don't think it justifies its own independent post and you demonstrated a comprehensive understanding of mathematical fields.
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148I've been learning R to do statistical analysis, and I feel that I can perform certain operations, but I don't really understand what is going on mathematically, or behind the scenes, if you will. I want to develop and test mathematical models for ecological (and other) purposes in grad school, which seems to implement matrices extensively. I just finished a linear algebra course this past quarter, and I am scheduled to continue the linear algebra sequence next quarter. I am beginning to see how building linear models using statistical data works from the mathematical perspective (instead of just plug and chug with an algorithm). Should I keep focusing on linear algebra? What about non-linear models, etc? Or are there some applied statistics topics I should be considering?
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150My main problem isn't with how to learn some topic, but which topics I should be learning to accomplish what I want (that is, creating and testing mathematical models, based on given statistical data). I appreciate any insight you may be able to provide.
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154[–]hbetx9Algebra[S] 3 points 7 years ago 
155This is a much more focused question than the ones I was directing at, and I encourage you to post this to bring it to more light. I'm far from a stats guy, however you could someone out answering your question if you say what it is you're trying to do in ecology. What are the particular linear models are you considering? Why do you think they aren't sufficient (and hence the question about whether or not you should look into non-linear stuff)?
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159[–]tdyo 1 point 7 years ago 
160I have no specific model in mind. I'm more interested in the "meta" sense (as Reddit likes to say it) of creating and testing models at this point, and in this case, when to know a particular linear model is, in fact, insufficient. To be honest, I'm not even sure if this is an appropriate question for r/math, since r/math tends to be on the pure math end of the spectrum. I'll take your advice though, and post a thread. Would this be relevant for r/math, or should I try r/statistics (I just checked if that existed after typing it). Thanks for your feedback.
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164[–]hbetx9Algebra[S] 6 points 7 years ago 
165I'd bet /r/stats would be better, but try one and if you don't get a good response, try the other.
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169[–]oddthink 2 points 7 years ago 
170I'm a physicist who's pretending to be a statistician, so both my math and statistics are a little weak. My take is that it's okay to be a generalist; there's just too much out there to follow all the rabbit holes.
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172Linear algebra is very useful; you should be able to understand the "projection" arguments for why linear regression works, know what a matrix rank is, and know at least SVD and QR decompositions.
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174If you go nonlinear, it more looks like just straight optimization, so theory won't help you too much.
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176I'd focus on the applied statistics, if I were you. Learn (at least once) what all the R2 metrics, and F-statistics, and p-values, and the like really mean, for linear regression. Then, if you start using more complicated models (like GLMs, etc.), I'd just trust that they were done right.
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178Understanding the 5-minute elevator version of many techniques is better than knowing all the odd back corners of one.
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182[–]tdyo 1 point 7 years ago 
183My take is that it's okay to be a generalist; there's just too much out there to follow all the rabbit holes.
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185Yeah, exactly. That's more or less why I've started asking around.
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187Understanding the 5-minute elevator version of many techniques is better than knowing all the odd back corners of one.
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189This is basically what I'm after. I just want to know what I'm doing, in the hopes of being able to apply it on my own later ("Wait, I could try THIS technique, and...blah blah") without it violating some cardinal assumption of the underlying mathematics.
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191I'll focus on how the applied stats relates to linear algebra and vice versa, and go from there. Thanks for the feedback.
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195[–]oddthink 1 point 7 years ago 
196I'd say learn linear regression well, its assumptions and its failure modes, then use that as your measure when looking at other techniques. Learn PCA (principal components) as a prototype for shrinkage methods, etc.
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198GLM is then just OLS under a mapping, with appropriate loss functions. Things like GAMs are linear regression, where the model automatically looks for the right way to spline out the response. And so on.
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200Mixture models (multilevel/hierarchical regression, etc.) are a different beast, though. It's worth trying to track down a class that will teach you that, preferrably from the Bayesian point of view. I may be a bear of little brain, but it took me a while to understand what was going on there.
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204[–]tavernkeeper 1 point 7 years ago 
205I would be interested in responses to this question too. I'm just starting undergrad and have been in love with ecology and statistics since high school (which actually was a few years ago despite just now starting undergrad). Strangely, I didn't really care for statistics while taking the class, but it has remained stubbornly useful and relevant since then.
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209[–][deleted] 10 points 7 years ago 
210Can we sticky stuff on reddit? Please?
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214[–]PSquid 2 points 7 years ago 
215You could always push to have it linked from the subreddit sidebar - I'd guess that'd serve the same purpose as a sticky.
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219[–]hbetx9Algebra[S] 1 point 7 years ago 
220Amen.
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224[–][deleted] 22 points 7 years ago 
225d/dt{ Number of posts about "learning more math" before this post } == d/dt{ Number of posts about "learning more math" after this post }
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229[–]hbetx9Algebra[S] 5 points 7 years ago 
230poss abou mah" his pos ? Just kidding. Yeah I know but this is the best I can think to do, and at least it gives a break down, hopefully people will find it useful.
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234[–]willis77 23 points 7 years ago 
235People who ask this question don't want a breakdown of advanced math. They are bored people. They are people who want to start a project they wont finish. They read something neat about math, or felt guilty for letting their old skills erode, and now they come here seeking a cure that doesn't involve years of hard work and (often boring) practice. Sure, maybe one out of a hundred is serious about learning for the long haul, but they tend to be the ones who have already done some due diligence to focus their questions.
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237In conclusion, you are fighting a battle that is too often won by nobody. For every time we suggest khan academy on here, some internet soul goes off for a few hours and gets bored. Math was never meant to be easy; it requires a certain amount of pain before you can do fun things with it. It's not their fault and it's not yours.
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241[–]hbetx9Algebra[S] 0 points 7 years ago 
242Indeed about the battle not being won by anyone, however the more the community comes together and sets standards for what we will or will not positively respond to, and the more clear those standards are explained, the better the community gets. BTW, where do you get off putting blame on me? You're saying its my fault they are board? You're saying its my fault they post?
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246[–]dolgar 7 points 7 years ago 
247It's not their fault and it's not yours.
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251[–]hbetx9Algebra[S] 1 point 7 years ago 
252Ah, thanks, didn't read carefully enough.
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256[–]hbetx9Algebra[S] 3 points 7 years ago 
257It reminds me of someone going on to /r/programming and saying, "So I've never had a programming course in my life, but I really think I should learn objective-C, is there a good reference?"
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261[–]acetv 7 points 7 years ago 
262That's how I learned Java.
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266[–]hbetx9Algebra[S] -4 points 7 years ago 
267Java is not objective-C. How about object databases? Maybe we should teach someone to be a web-programmer instead of teaching them a bit of programming, HTML and CSS first, we'll just sit them in front of a django project and look at them odd when they don't understand even how to do a DNS override because they don't understand what an IP is or how handlers actually work.
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269You can't jump in the middle. Java is a language used at the basic level of many schools. For a reason! On the other hand, if someone has a first course in programming on C++ templates they will likely flame and burn.
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273[–]ballisticanimal 3 points 7 years ago 
274My first couple programming courses were in C++, and sure, it was a little rough at first but it also gives way more insight into whats really going on then Java, I think I would up learning a lot more and being a better programmer because of it. Just a thought.
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278[–]hbetx9Algebra[S] 2 points 7 years ago 
279The debate of 'what is the best language to start with' probably belongs somewhere else. Starting with C++ isn't my point, my point is trying to explain to someone who barely has an idea of what a class is, if at all, the idea of templates is near impossible. Think back to your C++ class, remember when cout was a completely mystery? Remember when you couldn't even conceive of a pointer or recursion seemed like complete black magic? This is not the time to hit someone with advance topics! In the same manner, one can't understand more advance topics until they understand these first!
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283[–]shimei 3 points 7 years ago 
284Remember when you couldn't even conceive of a pointer or recursion seemed like complete black magic?
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286In the places I've taught, recursion is taught in the first year intro programming course. It's not advanced or black magic at all, and the students understand it fine. Point is, intro programming shouldn't be about any particular language, but about how to think and approaching the task of writing programs for a particular problem. Teaching recursion as "black magic" is the "limit ourselves with a bad language" school of teaching programming. Although I think I'm in agreement with you here, just not on this particular point.
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288Basically, if you are new to programming, you shouldn't pick up a reference book and expect to understand anything. Like how you wouldn't pick up Dummit and Foote if you're starting college algebra.
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292[–]hbetx9Algebra[S] 2 points 7 years ago 
293(1) See my remark about this not being a debate about first year programming language selection and (2) Your last statement is...exactly...the...point...I...made.
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295Nothing of what I said is to limit oneself to a "bad language" its just simply that you really, simply, truly, cannot understand differentiable manifolds without understanding both calculus (analysis) and topology first. Just like you can't understand templates without classes, nor data structures without pointers (at least conceptually).
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297I think at the end we're saying the same thing.
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301[–]shimei 1 point 7 years ago 
302I agree, I just took exception to the point about recursion. Sorry if it seemed I didn't understand your point in the last sentence there, I just wanted to reiterate it in terms of math.
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306[–]hbetx9Algebra[S] 1 point 7 years ago 
307I probably just wasn't very clear.
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310continue this thread
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312[–][deleted] 6 points 7 years ago 
313This happened the other day. The guy said something like, "I really don't know anything about programming. Where should I start? Assembly?"
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315found it: http://www.reddit.com/r/compsci/comments/en2z9/besides_carlhwhich_is_great_what_would_you/
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319[–]Idiomatick 11 points 7 years ago 
320Assembly is an awesome place to start .... if you are rather young and very nerdy. If you are older you would have already learned a language if you were that nerdy. Or you aren't nerdy enough :S
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324[–]derleth 2 points 7 years ago 
325The single biggest problem with starting with assembly is that you have to spend a lot more time on stuff that's only going to be useful to one specific machine and, often, one specific assembler, as opposed to spending a few moments learning the syntax as needed and spending the rest of your time learning things you can easily apply elsewhere.
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327I'm also not convinced that learning how the machine does things at a low level provides some massive amount of insight into anything but how the machine does things at a low level. I'm not denigrating machine-level knowledge, but it has a definite shelf life and it won't help you understand compiler design any better.
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331[–][deleted] 2 points 7 years ago 
332Nothing wrong with assembly as a first language. One should probably stay away from x86 asm though. A nice microcontroller maybe?
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336[–]hbetx9Algebra[S] 0 points 7 years ago 
337lol, that would be a nightmare, truly a nightmare.
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341[–]derefr 7 points 7 years ago 
342Nothing wrong with it—an entire generation of programmers learned assembly language because that was all there was, and did just fine. Then those programmers, with their massively-swollen brains, invented compilers, because having a massively-swollen brain sucks.
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346[–]hbetx9Algebra[S] -1 points 7 years ago 
347To a degree, those programmers wouldn't survive in todays world.
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351[–]james_block 1 point 7 years ago 
352To a degree, those programmers wouldn't survive in todays world.
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354Absolutely not -- they were constrained not by their skills or choices in technology, because there was no choice to make: only one language existed in the world! And so they created the modern idea of programming languages.
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358[–]hbetx9Algebra[S] -1 points 7 years ago 
359They had skills current programs don't because of the limitations. However, there have been plenty of times that I've worked with much older coders and they have a hard time adapting to new tech. quickly. This is a skill those coders didn't need and therefore never developed.
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361I am not saying all old coders do this! Just enough to merit a stereotype. Yes they created the modern idea of programming languages, like Fortran and C. They did not even conceive of things like python or more modern frameworks.
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365[–]derefr 1 point 7 years ago 
366There were Blub programmers even then; it was just impossible to distinguish them from the non-Blub programmers, because they wrote in the same language.
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368They did not even conceive of things like python
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370LISP (with "modern" features like GC, a REPL, tail-call elimination, closures, etc.) was invented in 1958, by these same assembly programmers (who also happened, more importantly, to be mathematicians.) It's all been done before.
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374[–]kfgauss 8 points 7 years ago 
375For those just trying to learn a little more math or develop some math literacy, you could make a really strong case that discrete math is much more important than calculus. I've really never understood why calculus is the class that's so often taken as a "one and done" math requirement. Statistics! Discrete math! Math literacy! Yikes. There's a really good math overflow post on the subject (I especially like Noah's answer).
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379[–]RattusRattus 2 points 7 years ago 
380No math whiz here--in fact calculus felt like banging my head against the wall. At the same time too, learning calculus helps a lot with physics, to the point where I don't understand why any school would teach physics to someone who doesn't know calculus. Again, I'm not offering an informed opinion, but rather an observation as to how those two disciplines fit together, hence giving calculus it's status. Statistics is the one math class I regret not taking, although in general I wish I understood math better.
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384[–]kfgauss 3 points 7 years ago 
385Agreed. Calculus is certainly great for physicists and engineers, and none of what I said really applies to them. I was thinking more about what one class should be taken by those who don't plan on following in a mathy discipline.
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389[–]RattusRattus 1 point 7 years ago 
390I honestly think everyone should take statistics, just to help them make sense of media. I've not taken statistics, but I would imagine it also helps with logic/critical thinking skills as well, as it's oftentimes counter intuitive. Also, is information theory considered part of math? If there's one thing that's changed my outlook on life, it's a reading of Charles Seife's book on information theory. Evolution makes much more sense from that perspective.
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394[–]hbetx9Algebra[S] 1 point 7 years ago 
395This point of view I totally understand and support. Completely. Though learning things like big-O notation (probably a topic of some interest) is made much better with calc and a lot of the posts I was directing at are "Help me learn X" where X usually has some kind of analysis in it. If you were to take one and only one course, yes DM is a better choice than calc for a lot of people.
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399[–]hbetx9Algebra[S] 1 point 7 years ago 
400Glad to help.
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404[–]thehotelambush 1 point 7 years ago 
405I think the main reason is that it's most useful for lots of people who actually use math in their career (engineers, economists, and physicists). Departments really like being able to lump non-majors all together into the same class.
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409[–]juliuszs 7 points 7 years ago 
410I'd like to chime in and suggest two topics that will destroy your joy of simple reception of the news: Logic and Statistics. I can't read newspapers without sputtering and cursing at the glaring errors in logic and don't even start me on statistical methodology ;-)
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414[–]CoreyN 4 points 7 years ago 
415Basic logic and statistics really should be required to graduate high school.
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419[–][deleted] 2 points 7 years ago 
420They are in Canada (or at least were part of the curriculum in the high school where I studied). Very basic, but there.
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424[–]hbetx9Algebra[S] 1 point 7 years ago 
425lol, I feel your pain.
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429[–]mian2zi3 5 points 7 years ago 
430Stop asking for a "good book on blah" or "I'm a novice and want to learn more" because these questions are either (1) easy/clear to answer from literally 10 seconds of google/reading older posts
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432I'd say: don't waste your breath. If someone can't do 10 seconds of google or read some reviews on amazon, posting a syllabus (that they'd also find in 10 seconds) isn't going to help them sit down and do 2 years of work. This echoes some of the "Will you mentor me? No." discussion going on elsewhere: save your effort for, as you say, questions like, "I'm studying measure theory and I'm stuck here. I tried A, B and C. Can you help?"
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436[–]magicmalthus 5 points 7 years ago 
437I partially disagree. There is a lot of legwork a person can do before they ask that question, sure, but it can actually be incredibly hard to pick out a good book on a subject.
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439My background is in computer science and math, but I still struggle just about every time in finding a good place to start when diving into a new field. many books on amazon will only have two or three reviews, and many have wildly different ways of approaching a topic. getting a personalized answer to the question (which is probably not possible with the lack of detail provided in the posts by the people the OP is talking about) can easily save many hours and possibly be the difference between the person succeeding or giving up and moving back to more familiar subjects.
440
441all that said, it is why /r/learnmath exists :)
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445[–]shimei 3 points 7 years ago 
446My background is in computer science and math, but I still struggle just about every time in finding a good place to start when diving into a new field.
447
448This is a good point, but on the other hand there are many resources on this reddit (see sidebar links) that already point to many suggestions for exactly this purpose. I wish more new readers would look there first. The sidebar even says to read the FAQ before asking question. Ah well.
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452[–]hbetx9Algebra[S] 2 points 7 years ago 
453You know what I never see though...."I just picked up this book and am stuck on this question on the first chapter". It seems like people get this info, read the book for a minute, learn a new buzzword and ask for another recommendation. The culture is wrong, that somewhere there is a fantastic reference that will make it all clear. First try a reference or two, and give some feedback about what you don't like about it. That way, the community can help you find a book that fits your learning style (intuitive vs systematic for example).
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457[–][deleted] 1 point 7 years ago 
458I think people tend to take specific questionsfrom textbooks to /r/cheatatmathhomework or /r/casualmath. Or at least they should.
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462[–]hbetx9Algebra[S] 1 point 7 years ago 
463I don't follow.
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467[–][deleted] 1 point 7 years ago* 
468I'm saying you don't see questions from specific chapters of specific books that people just picked up because, in general, they should and they do post such questions in the appropriate subreddits. (not here)
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472[–]hbetx9Algebra[S] 1 point 7 years ago 
473Ah yes, thanks.
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477[–]hbetx9Algebra[S] 4 points 7 years ago 
478I guess my thought process here is that if the /r/math community stands together we can create a culture on this subreddit where people phrase questions in useful ways. So I not only encourage ignoring poorly phrased questions, I encourage answering them in a way that that OP is reminded of what they need to do, and not just given the info.
479
480This also comes to questions of the form: "Should I learn X?". This is impossible to answer! And we, as a community, should stand up and say so. I get the feeling there are a lot of professionals who have no problem donating their time and dare I say, enjoy helping others here, however I for one am very frustrated with the lack of focus. This is my effort to vent and help address the problem.
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484[–]mian2zi3 2 points 7 years ago 
485I agree. I think the usual solution to this problem is to have a FAQ that (1) answers common questions like "How do I learn X?" (Your post would be a perfect start) and (2) explains how to ask questions/what questions are appropriate for the community. Then the community needs to enforce the standards by downvoting/moderating/closing inappropriate questions. (I for one downvote questions that are vague, can't be answered, or could be answered with a few minutes of research.) I think math.SE/mathoverflow do a great job articulating their goals, for example.
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489[–]shimei 2 points 7 years ago 
490My hope was that the community would downvote posts that are too vague to be useful. I find that most of the time, posts like this are actually downmodded to zero, though enough people respond with Khan Academy to hopefully make the poster read it. Usually when I remove a post on /r/math/ it is because it is either obvious spamming/trolling, links to blogspam, or totally offtopic.
491
492Also, the FAQ has been updated with a section for learning math (probably needs expanding). The FAQ should be editable by any user, so please feel free to add anything you feel is necessary.
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496[–]hbetx9Algebra[S] 1 point 7 years ago 
497Thanks.
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501[–]RattusRattus 1 point 7 years ago 
502I'm not really qualified for editing your FAQ, but your link for recommending math books is really advanced, so maybe include some basics for those trying to relearn calc., etc. in their spare time. This may help with cutting down basic questions, which seems to be your aim. Also, I don't know if it's appropriate, but I always really enjoyed Charles Seife's book on information theory. I don't know if it belongs in programming, or what, but it's an excellent book which links evolution and information. More so than anything, I suspect your average math nerd would enjoy it as some light reading.
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506[–]hbetx9Algebra[S] 1 point 7 years ago 
507Exactly, I agree completely. Is there a way to get something like this done?
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511[–]mian2zi3 1 point 7 years ago 
512I'm not sure. The closest I've gotten to formal participation on reddit was trying to run a (failed) universityofreddit/math class.
513
514There is an existing FAQ linked on the sidebar. There is also a "message the moderators" link. Maybe they could help?
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518[–]hbetx9Algebra[S] 2 points 7 years ago 
519message sent.
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523[–]baruch_shahiAlgebra 5 points 7 years ago 
524Gallian's Contemporary Abstract Algebra is fantastic for an undergraduate course in algebra. Dummit and Foote is too advanced for a beginner, in my opinion, but a great reference.
525
526Munkres' Topology is awful. I hated this book. He builds absolutely no intuition, and he seems to have a hard-on for highly pathological examples, which wouldn't be an issue if there were presented better.
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530[–]hbetx9Algebra[S] 2 points 7 years ago 
531Well, opinions abound. Though I agree that Dummit/Foote is too much for a beginner, which I why I followed up with Rotman. As for Munkres, as I said, everyone has strong feelings it seems.
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535[–]oddthink 2 points 7 years ago 
536What about Herstein? That's what I read for an intro to algebra, and I thought it was a lot of fun. I've not looked at the others.
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540[–]hbetx9Algebra[S] 1 point 7 years ago 
541Herstein is classic and solid.
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545[–]rberenguel 1 point 7 years ago 
546I would add Guillemin & Pollack's Differential Topology as an addendum for "standard" topology (be it Munkres, which I own or another reference). I just love this book.
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550[–]hbetx9Algebra[S] 1 point 7 years ago 
551Haven't read this, but it looks interesting. Guillemin is usually a very good writer.
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555[–]wavegeekman 3 points 7 years ago 
556It would help a lot if you gave the titles and authors of the books eg I searched on amazon for Introduction to Topology Munkries and no obvious match appeared. Let alone "Grab Baby Rudin" - WTF is that?
557
558Here are some of my suggestions (I am currently working through math/physics on my own - currently at mid second-year college level doing vector calculus in preparation for electromagnetism).
559
560Do the exercises.
561
562Make sure you buy books with answers you can check.
563
564Start with a little revision of what you already know.
565
566Take your time and work through things carefully. You can't read a math book like a newspaper. I take my books and go for long multi-hour walks, a little reading, a little thinking; repeat until done.
567
568Have an objective and work back from that using prerequisites from course descriptions. Eg if you want to do physics you really do not need all of abstract algebra. Group theory and some topology are most important.
569
570Be aware most math books exist to show how clever the author is, not to teach you anything. Choose carefully an author who cares about his readers.
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574[–]acetv 3 points 7 years ago 
575The book hbetx9 was probably referring to is simply titled Topology. It's the first thing that comes up in the list when you search "Introduction to Topology Munkries" on Amazon (even though the author's name is spelled Munkres).
576
577When you search for "Baby Rudin", you get the right book at the top of the list too: Principles of Mathematical Analysis.
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581[–]hbetx9Algebra[S] 1 point 7 years ago 
582Sorry in my zeal, I could have been more clear. I disagree that a good book comes with answers you can check (I assume you mean there is an answers section to selected problems). I think in the last remark, no one writes a book to show how cleaver they are, however remember that not all books are written for beginners, not all books are self-contained, and not all books are well written. Just because it has a hard cover and says "intro" on it, doesn't mean its for you.
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586[–][deleted] 6 points 7 years ago 
587There is no reason anyone in the world "has to learn measure theory" -- period. Or Galois theory, or anything in mathematics, unless you are becoming a mathematician or a professional in a mathematical field (abstract theoretical academic computer science for example, NOT programming/web developing).
588
589Honestly, I think this is a big thing—not to diss programmers at all, because I came from that community, but so many posts on /r/programming and even Hacker News and other similar communities are of the form "Learn X because it will help you program/enterprise/win at life". While it's true that learning new skills is awesome and can often give you new and different insight into what you are doing in your everyday life, so much of mathematics just simply does not overlap with the work that programmers/web developers do on a daily basis. So software people come to math, having heard that it'll make them better at what they do, but they don't realize that looking for immediate, surface-level connections to what they do in what we do is not going to help anyone, and usually comes off as a waste of time.
590
591Again, not to sound like a pompous asshole and not to create any sort of "us-and-them" bullshit, but philistine, you do not understand what I've been through to get to where I am mathematically today and you do not understand what mathematics does for me and to me. If you want to learn math, you cannot simply expect to waltz in, buy the classics of mathematical literature, and emerge after a month and a half of bedtime reading as a newly mathematically competent individual, ready to apply your skills to your latest web project. It takes math people hours and hours of hard work to "get math", and to begin to make forays into the field, you need to work at it, not just ask what books you should read.
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595[–]xamdam 3 points 7 years ago 
596You forgot probability and statistics.
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600[–][deleted] 2 points 7 years ago 
601This has been incredibly helpful, thank you! I love math and have always wanted to dive deep into it, but I'm in a less math-oriented scientific field (genetics) and there have always been non-math related classes I felt I ought to take instead of a math one. But with this, I know what to do should free time permit. I'm keeping this bookmarked!
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605[–]hbetx9Algebra[S] 2 points 7 years ago 
606Glad to help.
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610[–]donkeyhaut 2 points 7 years ago 
611Graph theory.
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615[–]drbaskin 2 points 7 years ago 
616If you're not a fan of Baby Rudin, I recommend Spivak's Calculus. It will redo your single variable calculus, but pretty darn rigorously. If you do all of the exercises, then by the time you get to the end of the book, Baby Rudin won't seem that hard to you. (And will have new material, so you can still go through Baby Rudin if you want!)
617
618Also, there is some fun material in this book -- the irrationality of pi, the transcendence of e, and elementary (ha!) definitions of trig functions (in terms of arc length) and logarithms (as an integral).
619
620Really, I cannot recommend this book highly enough to somebody who wants to learn how to prove some things in the context of mathematics that seems familiar. Sure, Spivak can be a little long-winded, but that's part of his charm!
621
622One more thing: This book is not that interesting if you don't do the exercises. Do them! It's good for you. I promise. Also, some of them are pretty hard, so there's something for everyone.
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626[–]greenknight 1 point 7 years ago 
627Thanks, I'll probably pick one of the two up with the gift cards from the holidays.
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631[–]GrishaPerelman 1 point 7 years ago 
632I'm going through spivak now. i like the texts, but exercises in chaps 1 and 2 are impossible. hoping chap 3 will be more reasonable.
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636[–]conoverPDE 2 points 7 years ago 
637Upvoted into next Thursday.
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641[–]FUUESTTAAA 1 point 7 years ago 
642anyone have recommendations on online lectures that are worth watching on subjects past calculus?
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646[–]tdyo 7 points 7 years ago 
647http://www.khanacademy.org/ for linear algebra and diff eq. Incredibly easy to follow and understand his technique.
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651[–]Idiomatick 1 point 7 years ago 
652He only gets mid way through a couple courses of 1st year uni...
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656[–]hbetx9Algebra[S] 1 point 7 years ago 
657True but its a start and hopefully will inspire the committed user to learn more.
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661[–]CoreyN 3 points 7 years ago 
662http://www.uccs.edu/~math/vidarchive.html
663
664It requires registration, but it's free and easy :)
665
666I've only watched 4 videos from the 'Modern Analysis' series but I've enjoyed them quite a bit. The only other real analysis videos I could find were from Harvey Mudd(on Youtube), but while the professor seemed great, the video was only 240p and reading the board was quite difficult.
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670[–]cdsmith 2 points 7 years ago 
671I go to that university. The mathematics department there is FAR and away better than other departments at the same university... but it's still no MIT. Still, for free videos, hard to complain.
672
673G. Abrams is my thesis advisor, and I believe has some videos there. Unfortunately, I think only his basic courses have been filmed. It would be awesome if you could see some of his graduate algebra seminars.
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677[–]hbetx9Algebra[S] 2 points 7 years ago 
678I know Gene fairly well and I agree UCCS is a fantastic program! You are lucky to have him as a thesis advisor, he's really good.
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682[–]hbetx9Algebra[S] 1 point 7 years ago 
683Again, it depends on the subject! There is a whole lot past calculus. If you're a professional MSRI posts a lot of their lectures. If you mean sophomore level mathematics, try MIT OCW.
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687[–]FUUESTTAAA 1 point 7 years ago 
688Alright, thanks! I'm aware of the MIT lectures but didn't know about MSRI. What subjects would you say were most enlightening for you personally?
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692[–]hbetx9Algebra[S] 1 point 7 years ago 
693Well here's the thing. You won't understand much if any on MSRI without basically a year or two of graduate school, at least, and maybe not even then. For me personally, learning abstract algebra was a maturing concept as as learning discrete mathematics. I loved for example learning about how to construct the integers from the naturals, the rationals from the integers, then coming to understand how so many seemingly separate topics come together around senior year or so. Graduate school only strengthened that, and now for example I'm loving relearning things I thought I learned before but can now approach them with a much better perspective.
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697[–]cdsmith 1 point 7 years ago 
698Great resource. If I were to revise it, though, I'd do so by making discrete mathematics and algebra less of an afterthought. Differential equations and complex analysis (the complex-specific bits... this comment does NOT apply to analysis as a general field) are FAR less important to mathematics in general than the basic ideas of the algebraic method, such as you'd get from an introduction to abstract algebra. That is, you're far more likely to encounter algebra in superficially unrelated fields than you are to encounter complex analysis or differential equations in superficially unrelated fields. Hence, you should probably move algebra up a bit.
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702[–]hbetx9Algebra[S] 1 point 7 years ago 
703Thanks! I don't know if Alg is understated, in fact the only thing up there I feel is "optional" is diff eq. The list isn't ordered necessarily and I feel all of those are of equal importance. I slightly disagree that complex analysis is less important to mathematics in general, for example its theories are at the basic intuition for both number theory and algebraic geometry!
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707[–][deleted] 1 point 7 years ago 
708You mention Complex Analysis. Any recommendations for a good book on the subject? 2 criteria I have: First, I'm an engineer and will need to be able to crank out problems, so I need a book with plenty of worked examples as well as problems with the numerical answer in the back. Second, I'd like to have a good solid understanding of why the rules for Complex Analysis are the way they are.
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712[–]hbetx9Algebra[S] 2 points 7 years ago 
713I would say Complex Variables by Flanagin (spelling?) is pretty good and leads in with classic engr. problems and maybe the first half of it is just multi var calc. The other standard one is Churchill-Brown. I don't know if either have a tremendous number of examples, but both will address your latter point. I don't think I've seen any book loaded with examples, but these do have some.
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717[–]bobovskiDifferential Geometry 2 points 7 years ago 
718Marsden and Hoffman's Basic Complex Analysis, while having a wonderfully oxymoronic title, is a great intro to complex analysis.
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722[–]ludflu 1 point 7 years ago 
723I definitely lack a firm mathematical foundation, so the OP's advice definitely applies. However, my most satisfying mathematical adventures have always been as a result of going in over my head to accomplish something cool.
724
725For example, I was highly motivated to do some simple 3d graphics - and as a result I learned a bit of linear algebra. I got really excited when I learned I could stack multiple transforms (rotation,scaling, etc) into one matrix.
726
727It might have been easier if I had paid more attention when I took trig, but without the focus of something concrete to accomplish, I would not have been as motivated. Similarly, I've always been fascinated by cryptography and linguistics. In the course of reading on those subjects I picked up a little statistics and information theory because of the practical focus. I might have found statistics too dry without an application.
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729My point is that its a journey, and when people ask me overly general programming questions, I try to redirect it by countering with the question: what exactly are you trying to accomplish?
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733[–]hbetx9Algebra[S] 1 point 7 years ago 
734Going in over your head is fine! You just need to know that you're jumping deep and fill in the gaps as you go. That is also my point, one needs to have goals and "learning math" is simply too vague. A lot of the posts in this subreddit are people saying "I didn't learn math well enough" or "I forgot a lot of my older math". Okay, I hear ya, and love that you want to improve. Here is the classic, traditional tract in which to do so, that will keep you with the most available options.
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736If you're goal is to understand cryptography for example, fantastic. But heed my warning. An amazing amount of cryptography is based one number theory, both classic and more currently elliptic curves. These topics are not easy and are the fruit of many centuries of brilliant mathematicians dedicating literally their entire lives to understand. You won't get it in a semester, nor should you. But that also doesn't mean you shouldn't try! It means you should try, ask questions and keep at it, because the whole damn thing is just that damn cool.
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740[–][deleted] 1 point 7 years ago 
741When engineers use Finite Element Analysis to discover the flight characteristics of a plane and the structural integrataty of object, what type of math is involved?
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745[–]hbetx9Algebra[S] 1 point 7 years ago 
746FEA takes a simplicial mesh and utilize a numeric algorithm to give a close approximation to the solution to a multivariate differential equation. The important part here is that it is an attempt to approximate solutions to differential equations.
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750[–][deleted] 1 point 7 years ago 
751Differential equations is something I'm aiming to build a good base in. Anything else I should study before I get there?
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755[–]musicalPDE 1 point 7 years ago 
756I am the only one who has hated Rudin? I read Introduction to Real Analysis by Bartle, and it was loads better. I mean, sure it doesn't get into the measure theory and the Lebesgue integral, but as something for an undergrad it is infinitely better than Rudin.
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760[–]hbetx9Algebra[S] 1 point 7 years ago 
761There are personal preferences. In my life, I'm surrounded literally by mathematicians and an overwhelming majority favor Rudin, not because they can't conceive of anything better but because that was the book that got them to where they are. None of them favor the measure theory part, that is not what I'm talking about. Its hard because its terse and you have to fill in the details. That is the process that you are intended to take! Filling in the details for yourself is an important step and even more so given the subject matter.
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765[–]musicalPDE 2 points 7 years ago 
766I'm not complaining about that, I like filling in the story, but Bartle was so friendly. There were always nice footnotes and reasons for things. And the theorems actually had names! Balzano-Weierstrass, Rolle's theorem, many many more all with footnotes telling you the history. It was great. Reading Ruding is like reading ancient latin. It seems as if there is no life to the mathematics that is there, it is merely a system of facts and definitions.
767
768Maybe I just liked my undergrad prof more than the current one. But it seems to me like there was a large gap between how Rudin and Bartle keep things interesting.
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772[–]coveritwithgas 0 points 7 years ago 
773I am ABD, and I think calculus sucks and is largely unnecessary. There's the math you need in your job, and the math you learn in order to be a reasonably well-rounded, educated individual. Thing about calculus, nobody teaches it as if they're trying to make you a reasonably well-rounded, educated individual. You don't get the history, all the controversy over infinitesimals, etc. You're taught calculus as if you're going to need it in your job, and then 95% of the time, you graduate, don't need calculus in your job, and think the whole exercise was a waste.
774
775Study noncommutative rings instead.
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779[–][deleted] 5 points 7 years ago 
780Algebra, category theory and discrete math has been way more useful than calculus since I started working as a programmer.
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784[–]hbetx9Algebra[S] 4 points 7 years ago 
785Again, this depends on your focus. Yes, if you are a "working programmer" than discrete math will necessarily be more useful than calculus (continuous math), however that doesn't mean it doesn't come up (how exactly do you compare running times without it?) or that it is not useful in general. There is a reason its required at univ, yes part of it is to understand physics, but there is a reason its required.
786
787Also, btw, I did a lot of work in graphics, and yes, there EVERYTHING I did was basically simple 2nd semester multivar calc.
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791[–]MidnightTurdBurglar 5 points 7 years ago 
792I hope this comment wasn't intended to be serious. Almost everything you wrote is nonsense.
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796[–][deleted] 2 points 7 years ago 
797Noncommutative rings are more useful than calculus? Surely you jest!
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801[–]bobovskiDifferential Geometry 1 point 7 years ago* 
802I am ABD, and I think calculus sucks and is largely unnecessary.
803
804A wild reverse ad hominem appears!
805
806Thing about calculus, nobody teaches it as if they're trying to make you a reasonably well-rounded, educated individual. You don't get the history, all the controversy over infinitesimals, etc.
807
808No one you know teaches it that way, perhaps. But, the world is not defined by your, perhaps limited, experience.
809
810You're taught calculus as if you're going to need it in your job
811
812Because engineering and physical sciences departments relegate the teaching of "useful" mathematics to mathematics departments, where it least belongs. The service class culture is a university system failure. Go find your favorite emeritus professor and ask him what his calculus class was like.
813
814then 95% of the time, you graduate, don't need calculus in your job, and think the whole exercise was a waste.
815
816Not needing calculus is different than being empowered with the opportunity to use one's understanding of it. It's service industry mentality like this that makes math education these days look bad and perform worse.
817
818Edit: spelling. Words are hard.
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822[–]hbetx9Algebra[S] 0 points 7 years ago* 
823Come...on....man! This is exactly the kind of thing I'm trying to avoid. Someone who doesn't know calculus won't understand noncomm. rings deeply (most of their main examples come from calc) nor many many MANY other areas of math. You can take issue with how its taught, but its importance is undeniable. PLEASE don't take him or her seriously.
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827[–]wasabijoe 1 point 7 years ago 
828Thank you for this.
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832[–][deleted] 0 points 7 years ago 
833Learn Algebra with Winnie Cooper