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Everything you always wanted to know about mathematics (2013) [pdf]

math.cmu.edu

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Re: Everything you always wanted to know about mathematics (2013) [pdf]

#111

Post by cubefox »

pmoriarty wrote: post #79
sorokod wrote: post #77

Earlier quoted context omitted.

I doubt that having a "dictionary" attached to a math paper, something like 1. ∇ = nabla see https://mathworld.wolfram.com/Nabla.html 2. ... 3. ... would improve your understanding. Notation encodes ideas, it is the understanding of the ideas that is tricky, not the encoding.

It would actually help. I'd know what fields I need to study to more fully understand the papers I'm interested in. It would also help me figure out what to ask LLMs (or people) to explain to me.

GPT-4 can probably explain LaTeX formulas pretty well, but when they are compiled PDFs, the encoded PDF plain text is often garbage, so GPT-4 probably couldn't understand much.

Re: Everything you always wanted to know about mathematics (2013) [pdf]

#112

Post by cubefox »

SleekEagle wrote: post #80
pmoriarty wrote: post #73

One thing I've always wanted is a comprehensive guide to mathematical notation, which tells you what symbols mean or at least what field of mathematics they come from. I frequently come across all sorts of weird mathematical symbols in papers, and of course these symbols are virtually never explained, so I have no idea what they mean. Even better would be if there was some way an LLM could read through a paper itself…

many books will have a page in the preface that lays out the notation, even for very common objects. it's hard to make a cheat sheet for something like this because many symbols are used in different fields, and even if different subfields of the same field.

I think that's pretty rare?

Re: Everything you always wanted to know about mathematics (2013) [pdf]

#113

Post by alphameese »

bloemheuvel1 wrote: post #106
alphameese wrote: post #88

Earlier quoted context omitted.

Specifically these three courses [0][1][2] will take you from basic algebra to precalc. They're very thorough and I've found them extremely useful in upgrading my high school level math skills. I have heard that their calculus courses aren't sufficient though, and that it should be learned from somewhere else. [0] https://www.khanacademy.org/math/math1 [1] https://www.khanacademy.org/math/math2 [2] https://www.khanac…

Would you recommend this path over doing the Algebra 1 -> Geometry -> Algebra 2 …. etc path?

The Math 1-3 courses intersperse all of those courses and provide a more streamlined path. I would personally recommend using those 3 courses to learn up to pre-calc.

Re: Everything you always wanted to know about mathematics (2013) [pdf]

#115

Post by mjvmroz »

lmwnshn wrote: post #23
rickstanley wrote: post #20

Earlier quoted context omitted.

Does this replace the OP? Or is "An Infinite Descent into Pure Mathematics" a complementary book?

My link replaces; we did not use OP's book when I took the course. That said, OP's book looks more conversational in tone, which I personally have a slight preference for.

Great insight, thanks. I was tossing up on which one to take a stab at first, but I have a pretty strong preference for conversational tone.

Re: Everything you always wanted to know about mathematics (2013) [pdf]

#116

Post by sn9 »

GitPushOrigin wrote: post #86
evanmoran wrote: post #47

As a CS major who went to CMU years ago, my favorite book from all of my professors was for my 15-213 class called Computer Systems: A Programmers Perspective I remember at the time the book was in loose leaf paper so it warms my heart to see the book has a 3rd edition. It was used as a core part of teaching assembly, memory representations, and getting students ready for the operating systems class. When I help peop…

Is there a book or resource you'd recommend for operating systems? I recently finished CS:APP and really enjoyed it. Though I've been programming for ~7 years and felt that made it easier to digest.

The recommendations on https://teachyourselfcs.com/ are all pretty high quality and canonical.

Re: Everything you always wanted to know about mathematics (2013) [pdf]

#117

Post by sn9 »

no_wizard wrote: post #42

Does anyone know of an entry level book that could take someone through say, high school math to college alegbra / calculus? This is my singular biggest hurdle in going back to school to finish my degree and I'd love to fill the gaps I have around mathematics so I can not only finish my degree; I'd also like to participate in some more advanced computer science that rely heavily on underlying computation.

The aops books [0] will take you from prealgebra all the way to calculus and discrete math and will give you a foundation strong enough to enter any undergraduate math program in the world.

And the books all have complete solutions manuals available so you can get immediate feedback.

You could use programs like Anki to schedule your review of defintions you've understood and problems you've solved to supercharge your learning as well.

[0] https://artofproblemsolving.com/store

Re: Everything you always wanted to know about mathematics (2013) [pdf]

#118

Post by graypegg »

ivansavz wrote: post #75
no_wizard wrote: post #42

Does anyone know of an entry level book that could take someone through say, high school math to college alegbra / calculus? This is my singular biggest hurdle in going back to school to finish my degree and I'd love to fill the gaps I have around mathematics so I can not only finish my degree; I'd also like to participate in some more advanced computer science that rely heavily on underlying computation.

I think you might like my book "No Bullshit Guide to Math & Physics"[1,2,3], which contains a condensed review of high school math (a.k.a. algebra and precalculus), then explains PHYS and CALC topics in an integrated manner. [1] website https://minireference.com/ [2] PDF preview and sample chapter = https://minireference.com/static/excerpts/noBSmathphys_v5_pr... [3] concept map = https://minireference.com/static/conc…

Bought! Something in epub was exactly what I needed and loved your chill writing style in the sample chapter, cheers!

Re: Everything you always wanted to know about mathematics (2013) [pdf]

#119

Post by sanderjd »

How do people here like to read pdfs? It doesn't work on my ebook reader and I never actually read anything long-form on a computer screen, even when I think I will. Someone below mentioned using a service to print and bind into a book. Anyone have a better workflow for this kind of thing?

Re: Everything you always wanted to know about mathematics (2013) [pdf]

#120

Post by 70rd »

sanderjd wrote: post #119

How do people here like to read pdfs? It doesn't work on my ebook reader and I never actually read anything long-form on a computer screen, even when I think I will. Someone below mentioned using a service to print and bind into a book. Anyone have a better workflow for this kind of thing?

Some software has PDF reflow, like koreader.
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