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So you want to study mathematics

susanrigetti.com

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Re: So you want to study mathematics

#41

Post by pvg »

tptacek wrote: post #7
Mimmy wrote: post #6

Going from Strang to D&F seems like a steep jump. The former is an applied textbook for non-mathematicians and the latter is a proof-based text for advanced undergraduate / graduate-level math students. I would suggest working through a proof-based linear algebra book in between to ease the transition. Axler's is a good one. Alternatives include Hoffman and Kunze and the more modern Friedberg, Insel, and Spence.

Both Strang and D&F are extra-relevant for cryptography (I was struck by how much the earliest parts of D&F --- which I haven't gotten much further beyond --- read like the mathematics background chapter of a cryptography book), and I've been in study groups for both of them with non-mathematicians that went OK. But the D&F study group fell apart for logistical reasons, so maybe it would have hit a wall after a coupl…

read like the mathematics background chapter of a cryptography book

A lot of maths-related books, especially ones intended as textbooks will read like that in part because they aren't kidding about the 'abstract' in the title - they're trying to teach/re-summarize key concepts of mathematical abstraction. It's a good and true thing to notice.

Re: So you want to study mathematics

#44

Post by brimble »

susanrigetti wrote: post #40
brimble wrote: post #38

Earlier quoted context omitted.

Heh, I have a long-forgotten-due-to-complete-lack-of-use-for-15-years-straight background in calculus. Solid, it is not. Thanks for the tip, though.

In that case, I recommend starting out with Zill's Precalculus with Calculus Previews and then working through Stewart's Calculus: Early Transcendentals!

I'll check those out, thank you!

Re: So you want to study mathematics

#45

Post by atan2 »

paulpauper wrote: post #42

You can get good or better at something with effort, but few will ever make to leap to being great or world class at it, no matter how hard they try.

True! But sometikes getting better at something is all people really want, and that's ok. I see that most of my CS students just want to be able to not see math as an obstacle when learning new/interesting things.

Re: So you want to study mathematics

#46

Post by hintymad »

I find it hard to believe that the author started to appreciate physics by reading The Feynman Lectures on Physics before any exposure to physics or even algebra, and in less than three years went from barely knowing high school math to enjoying advanced mathematical physics and graduate-level quantum physics. It looks this is one-in-a-million level brilliance as learning the sheer amount of requirement knowledge in such a short time is amazingly challenging: analysis, functional analysis, complex analysis, linear algebra, abstract algebra, differential equations, mathematical statistics, and all the physics: mechanics, electromagnetism, thermodynamics, optics, statistical mechanics, relativity, and of course quantum physics, all in less than three years.

Kudos if the author is this talented.

Re: So you want to study mathematics

#47

Post by helpfulclippy »

brimble wrote: post #31

Are there any "math for people who just want to use it" tracks in math pedagogy? I don't care a bit about proving any of it's true, or even reading others proofs of same. "Recognize which tool to apply, then apply tool", all focused on real-world use (so, yes, it wouldn't be "real" mathematics). That's the math education I'd like—try as I might, I just can't make myself care even a little about math for math's sake.…

I did a degree in applied math. You’d think this would be “math you’ll use,” but the fact is that despite my program having a CS concentration, most of the stuff I did was not really applicable in practice.

However, one thing that has been VERY applicable is proofwriting. Although math proofs are far more rigorous than most real world stuff, the discipline I learned in writing proofs has carried over into pretty much everything from programming (will this algorithm work every time?) to executive decisions (why, specifically, should we believe X?). Obviously in the former case I wind up doing actual proofs, and in the latter I make strong arguments based on logical consequences of established or presumed facts, or find flaws or gaps in arguments that are being considered.

I really wish I’d spent a lot more time on proofwriting than say, vector calculus.

Of course you may want specific math to solve real problems, and that’s a real need too! Not to diminish your point at all, just advocating for proofs to be seen in a practical light.

Re: So you want to study mathematics

#48

Post by tunesmith »

How do you like to solve math problems in this day and age?

I'm partial to Jupyter notebooks lately - I run it locally from a docker container, and have a folder of notebooks. Mostly markdown cells, alternating between my narrative thinking and LaTeX math output.

Re: So you want to study mathematics

#49

Post by joatmon-snoo »

brimble wrote: post #31

Are there any "math for people who just want to use it" tracks in math pedagogy? I don't care a bit about proving any of it's true, or even reading others proofs of same. "Recognize which tool to apply, then apply tool", all focused on real-world use (so, yes, it wouldn't be "real" mathematics). That's the math education I'd like—try as I might, I just can't make myself care even a little about math for math's sake.…

My strong opinion as someone who majored in math is that, at least within the US, the standard calculus requirement should be replaced with statistics. So much more useful and so much more important as an adult.

The analytical type of thinking that proof-writing is certainly useful, but you can make much the same argument of many other curricula, and besides, it's not like most intro calc courses even do any proofs. The vast majority of them, I would assert, are simply pre-med weed-out courses.

I still remember freshman year, showing up to the standard intro calc course, and dropping it as quickly as I could in favor of my uni's equivalent of Math 55 (i.e. the hardest u/g intro math course) because of how asinine I found the content...

Re: So you want to study mathematics

#50

Post by auggierose »

musgravepeter wrote: post #2

I've been on a Math journey since I retired a couple of years ago and I agree with all the books mentioned that I know and look forward to picking up some of the one I do not know. I agree baby Rudin is essential, but I find it tough going. Some books I liked for self study because they have answers: Introduction to Analysis, Mattock. Elementary Differential Geometry, Pressley. There is also recently Needham's Visual…

Very pretty book (Needham's), will check it out! I think over 20 years ago I actually attended a house party that Needham was giving in SF. It's a small world.
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