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Ask HN: How to self-study mathematics from the undergrad through graduate level?
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Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?
#22There's a set of basics that you will want no matter which direction you go: calculus/real analysis, linear algebra, differential equations/dynamical systems, and sets, groups, rings, and lattices. Calculus: learn to extract qualitative information about a function (it goes up here, has a maximum there, goes down there, oscillates with an increasing period, goes to this value at infinity...) and to numerically comput…
Any suggested reading on rings and lattices? I took a lot of math classes in undergrad but was never exposed to these concepts.
Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?
#23There's a set of basics that you will want no matter which direction you go: calculus/real analysis, linear algebra, differential equations/dynamical systems, and sets, groups, rings, and lattices. Calculus: learn to extract qualitative information about a function (it goes up here, has a maximum there, goes down there, oscillates with an increasing period, goes to this value at infinity...) and to numerically comput…
Any suggested reading on rings and lattices? I took a lot of math classes in undergrad but was never exposed to these concepts.
Herstein Topics in Algebra or Dummit and Foote.
Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?
#24Earlier quoted context omitted.
Any suggested reading on rings and lattices? I took a lot of math classes in undergrad but was never exposed to these concepts.
Herstein Topics in Algebra or Dummit and Foote.
goofy suggestion. those are both either grad or senior undergrad books depending on where you are. much better suggestion is
A Book of Abstract Algebra by Pinter (really gentle)
or
A First Course in Abstract Algebra by Fraleigh
Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?
#25There's a set of basics that you will want no matter which direction you go: calculus/real analysis, linear algebra, differential equations/dynamical systems, and sets, groups, rings, and lattices. Calculus: learn to extract qualitative information about a function (it goes up here, has a maximum there, goes down there, oscillates with an increasing period, goes to this value at infinity...) and to numerically comput…
Any suggested reading on rings and lattices? I took a lot of math classes in undergrad but was never exposed to these concepts.
Any standard abstract algebra textbook will cover rings in gross detail. Dummit and Foote is a much beloved standard, but is also used in graduate classes. I've heard good things about Pinter's book (http://www2.math.umd.edu/%7Ejcohen/402/Pinter%20Algebra.pdf).
For lattices, there's Birkhoff's book on lattice theory, which is where I learned what I know about it. I haven't spent any time with other books.
Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?
#26Don't study "math." Find a topic or a problem you'd like to understand, look up the prerequisite knowledge for it, and start there.
You need to know what you want to do before you go looking for resources. There is no set agreement on what should constitute an undergraduate applied mathematics curriculum, and you are likely to get lost in the deluge of conflicting information. On the other hand, the undergraduate pure mathematics curriculum has been more or less stable for half a century. Any college curriculum will do at this point, and many are freely accessible online.
Either way, there is no shortage of information and resources available. Any topic you'd choose as a layperson likely already has a course or a seminar covering it, and the corresponding syllabus should give you what you need.
Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?
#27John Baez (physicist / category theorist / smort dude) has a list of books to learn math and physics. Is an interesting source to crib from.
http://math.ucr.edu/home/baez/books.html
Gerhard t'Hooft has a page on how to become of a good physicist. http://www.goodtheorist.science/ Not math though.
I'm not necessarily suggesting that a mountain of books is the best way to go about it. I think I respond best to video lectures. I'm not sure where you're starting from or how applied/pure you want. Here's a quick mind dump some of my favorites and some that I haven't watched. Roughly in order of how much I liked them.
Gilbert Strang's Computational Methods for engineers was life changing for me. It is a two part MIT opencourse. https://ocw.mit.edu/courses/mathematics/18-085-computational...
A Stanford course on the Fourier transform https://see.stanford.edu/Course/EE261
Bartosz Milewski's Category theory for programmer's https://www.youtube.com/watch?v=I8LbkfSSR58
Stephen Boyd's courses are online. http://web.stanford.edu/~boyd/ Linear Systems, convex optimization. Useful stuff.
Francis Su's Real Analysis is very good https://www.youtube.com/watch?v=sqEyWLGvvdw
Indian universities have an astounding collection of videos https://nptel.ac.in/ I have a tough time with the accents, which is a bummer.
UCCS MathOnline has quite a haul https://www.uccs.edu/math/vidarchive
I've been enjoying this Visual Group Theory course lately https://www.youtube.com/playlist?list=PLwV-9DG53NDxU337smpTw...
Math Doctor Bob https://www.youtube.com/user/MathDoctorBob/playlists
Wildberger has some interesting takes on elementary and non elementary topics https://www.youtube.com/user/njwildberger
https://www.perimeterinstitute.ca/training/perimeter-scholar... Perimeter scholars lectures. Physics not math. Good stuff.
Federico Ardila has a number of combinatorics courses. https://www.youtube.com/channel/UCWwECTsgjp_S-c73pO2c4gQ
Nonlinear algebra course https://www.youtube.com/playlist?list=PLRy_Pn1LtSpejKLClqbrW...
Also of course there is Coursera and edX stuff.
Godspeed.
Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?
#28The hard but maximally useful thing to do, in my opinion, is to regularly meet with at least two other people and a blackboard and beat your heads against it together for about 3 hours at a stretch. Do this at least weekly--and preferably more often. Self study in between meetings is obligatory. One of those people should be at about your level. The other should be farther along. All three of you should trust each ot…
this is an excellent recommendation. it did not work for though. i was not the one that was at the advanced level and the one that was got bored rather quickly with us minions. Happend 5 different times. if you could find one who willing, this recommendation will def help.
Other people's help is indeed one of the most effective ways to learn. My problem with that is simply finding such people - given my extremely introverted disposition it's much harder for me than for normies - and also what you say, ie. finding people who would not quit after three sessions.
Then I thought, why can't I just buy the time of someone competent? There are many students who tutor high school kids, shouldn't students who can teach first/second-year material for pay exist?
I wonder, have anyone tried this? To me, it looks like a perfect solution and I can't think of any downsides. I'm not sure how to approach this exactly - where to find such a tutor in the first place - but it should be possible, right?
I would use such private lessons for getting a summary/overview of the subject first, then after some self-study, I would ask about whatever I couldn't comprehend. It would have minimal impact on my schedule, shouldn't cost that much, and should be quite efficient.
Well, it's just an idea I had some time back, I didn't try it in reality yet, but I think I'll try going this way in the future. I'd like to ask what do you think, is it possible, could that really work out?
Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?
#29I had math through some introductory calculus when I was an undergrad 20 years ago, but I let my skills lapse. But I want to understand enough math so that I can do some more complex electronics projects and some statistics / ML / intelligence analysis. This level of math, as I recall, is more or less the math core of the undergrad engineering program I dropped out of in favor of a philosophy degree (cause I am dumb as dirt).
In March of '18 I started doing lessons on Khan and just played around until I couldn't do the problems easily, and for me that was, like literally adding fractions and using exponents. So I had pretty basic skills at that point.
At thus point, I'm finishing the unit on using derivatives to optimize functions around min/max. Not a big deal, but a long way from where I started 10 months ago.
I've had a lot of luck with:
a) khan academy
the lessons are very simple and well broken up, the teaching is interesting, and the site is gameified in a way that is rewarding
b) doing it as close to literally every single day as I can manage
Math fluidity feels (at least to me) very much like my fluidity with music theory or programming. As such I need to do it regularly. Even if I don't get all into a flow state about it (which, I think is necessary on the scale of any given week), I do need do it a little bit every day... that both keeps me doing it and keeps it in the forefront of my mind.
c) keeping a notebook
I do all my work in a single notebook and use it to both track my progress and as a reference. It's also been neat to see how far I've come.
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I dunno if any of that is useful to anyone else. But I feel like I've had a lot of luck educating myself in math. At this rate, I should be through integral calculus by the end of the spring and through the linear algebra class by fall, and then I will move my deep, long-term learning projects over to something else, hopefully a deeper dive into electronics design.
Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?
#30This book is fantastic and pretty much takes you through an entire undergrad mathematics course: https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...