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How to Study Mathematics (2017)

math.uh.edu

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Re: How to Study Mathematics (2017)

#21

Post by ivansavz »

jamiek88 wrote: post #19
ivansavz wrote: post #16

Earlier quoted context omitted.

I have two books that might be a good fit for you since they are specially written for adult learners in mind. (disclaimer: I wrote these books and I have a financial interest in promoting them) The No Bullshit Guide to Math & Physics [1] is a condensed review of high school math, followed by mechanics (PHYS 101) and calculus (CALC I and II). It's not as rigorous as other more proof-oriented textbooks, but it still c…

Ah I had a vague recollection of your work, I think I read a pirated multi scanned janky pdf once - but I couldn’t remember who it was written by, just had ‘Russian’ stuck in my head and Ivan triggered it! I’ll buy your book now I’m a man of means and ready to learn properly.

Yeah the Russian pirated books site (libgen.li right now) has a version, but it's outdated.

I recommend getting the print version because it's easy to read (and flip back and forth with page references). We have a free-eBook-copy-when-you-buy-print policy—just get in touch with me by email and I'll send you the PDF with matching page numbers.

Re: How to Study Mathematics (2017)

#22

Post by danck »

I dropped out of my maths degree after struggling for six years (!) at university - I had fallen too far behind. I can't just blame my part-time jobs for that.

Especially early on I often dismissed problems and assignments that I felt I wouldn‘t be able to tackle in terms of time or intellect.

This wasn‘t what the successful students did. They took on every problem with determination and focus. No matter how hopeless. Along the way of failing they quickly developed their skills whereas I was falling more and more behind.

I then applied this lesson on my second attempt at university. A CS degree. Again I struggled at the beginning, but I became competent much quicker and in the end the degree was a breeze.

Still wish I‘d known this from the beginning...

Re: How to Study Mathematics (2017)

#23

Post by mindcrime »

dvfjsdhgfv wrote: post #13
no_wizard wrote: post #8

Earlier quoted context omitted.

What would anyone recommend to someone who really only had high school math[0] to get up to speed on enough math to handle more advanced computer science concepts? I’m really interested but all the material I can find is either for kids (which just isn’t sufficiently stimulating for an adult) or aimed at college kids with a decent background in math that is fresh [0]: not even calculus just what they called technical…

In theory, any introduction to discrete mathematics would do. In practice, there are many differences in depth and breath of the material. You probably will do well if you choose Rosen, but there are several great alternatives, such as Levin[0] that you can start right away with. http://discrete.openmathbooks.org/dmoi3.html

I highly recommend the Susanna Epp book[1][2] for Discrete Math. I found her book to be much better written, and more understandable, than Rosen.

[1]: https://www.alibris.com/Discrete-Mathematics-with-Applicatio...

[2]: https://www.youtube.com/watch?v=FPr5-X9nZc4

Re: How to Study Mathematics (2017)

#24

Post by alisonkisk »

danck wrote: post #22

I dropped out of my maths degree after struggling for six years (!) at university - I had fallen too far behind. I can't just blame my part-time jobs for that. Especially early on I often dismissed problems and assignments that I felt I wouldn‘t be able to tackle in terms of time or intellect. This wasn‘t what the successful students did. They took on every problem with determination and focus. No matter how hopeless…

Doing the assigned work is good way to learn the material.

Most teachers know better than most students what is need to do to succeed in the class.

Re: How to Study Mathematics (2017)

#25

Post by galaxyLogic »

I think that lot of math curriculum does not really make clear to students the rationale for why they cover the topics and proofs in the order they do. The students lose the big picture of the path they are on, why is it important for me to be working on this right now, so that I will be able to tackle the next subject when that comes along. The structure of theorems and proofs and how they all build upon one another is not presented clearly. The point of a proof is not to prove something, but what further proofs this proof makes possible. NO?

Re: How to Study Mathematics (2017)

#26

Post by baby »

alisonkisk wrote: post #24
danck wrote: post #22

I dropped out of my maths degree after struggling for six years (!) at university - I had fallen too far behind. I can't just blame my part-time jobs for that. Especially early on I often dismissed problems and assignments that I felt I wouldn‘t be able to tackle in terms of time or intellect. This wasn‘t what the successful students did. They took on every problem with determination and focus. No matter how hopeless…

Doing the assigned work is good way to learn the material. Most teachers know better than most students what is need to do to succeed in the class.

When you spend most of your time in class, when do you have the time to do the assigned work? That’s what I struggled with.

Re: How to Study Mathematics (2017)

#27

Post by spekcular »

bollu wrote: post #5

Also, use computers! I use SAGE extensively to get a feeling for lots of mathematical objects! 1. Grobner bases: http://bollu.github.io/computing-equivalent-gate-sets-using-... 2. Localization: https://github.com/bollu/bollu.github.io/blob/8cd335687ff3ef... 3. More broadly, an answer on math.stackexchange on how to debug math: https://math.stackexchange.com/questions/1769475/how-to-debu... 4. (WIP) continued fraction…

You might enjoy Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra by David Cox.

Re: How to Study Mathematics (2017)

#28

Post by sn9 »

no_wizard wrote: post #8
jdlyga wrote: post #2

I would love to get back and really learn math. I was really interested back in High School with Geometry and Algebra. But my interested totally burned out with poorly taught and punishing Calculus classes in College.

What would anyone recommend to someone who really only had high school math[0] to get up to speed on enough math to handle more advanced computer science concepts? I’m really interested but all the material I can find is either for kids (which just isn’t sufficiently stimulating for an adult) or aimed at college kids with a decent background in math that is fresh [0]: not even calculus just what they called technical…

The Art of Problem Solving books are great if you want to relearn pre-college math at a deeper and more advanced level so that your foundation is all the stronger for university level math.

Re: How to Study Mathematics (2017)

#29

Post by TrackerFF »

My only real critique of academic books, was that the exercises varied A LOT in difficulty. Some books had exercises that seemed to assume that the reader had been a honors student, and thus able to pre-process/setting up the problem with intricate identities and what not, before coming to the part where you apply some theorem.

Now - no big problem if you worked with very keen math students, and they'd show you that, or if your TA could give some pointers. But you could easily get completely stuck, if you were using these texts for, say, self-study.

Re: How to Study Mathematics (2017)

#30

Post by benrbray »

jdlyga wrote: post #2

I would love to get back and really learn math. I was really interested back in High School with Geometry and Algebra. But my interested totally burned out with poorly taught and punishing Calculus classes in College.

For abstract algebra self-study, I highly recommend "A Book of Abstract Algebra" by Charles Pinter. Each chapter starts with a few definitions and examples, and the rest of the chapter is a series of exercises meant to help you discover algebraic concepts for yourself.
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