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How to Study Mathematics (2017)

math.uh.edu

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Re: How to Study Mathematics (2017)

#11

Post by flir »

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…

I'm working my way through this: https://pimbook.org/

I'm not very far in so I can't exactly recommend it, but I am enjoying it. In places where I'm rusty, I'm falling back on Khan Academy.

Re: How to Study Mathematics (2017)

#12

Post by dvfjsdhgfv »

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.

That's a shame, Calculus is a fascinating subject and a basis for many interesting applications. Basically, there are two ways to approach it: to pass your exams (and there are just a couple of rules to learn, it's not that complicated), and to really understand what it's about. If you choose the second approach, you don't even need to memorize any formulas, because you will be able to reconstruct all of them as you need them. Moreover, you won't be conceptually limited to the geometric interpretation (which is invaluavle in giving some intuition in the early phases but might get in your way later).

Re: How to Study Mathematics (2017)

#13

Post by dvfjsdhgfv »

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…

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

Re: How to Study Mathematics (2017)

#14

Post by ZephyrBlu »

Although the title is "How to Study Mathematics", I think a more accurate title would be "How to Study Mathematics as a Mathematician".

I am studying some maths right now with the goal of understanding some statistical methods. Having a rock solid understanding of all the underlying maths is counter-productive to my end goal though (Applying the statistical methods), because it would be extremely time consuming.

If you want to learn maths for the sake of understanding maths, then this could be the right approach. But it's definitely not a pragmatic approach.

Re: How to Study Mathematics (2017)

#15

Post by hyperpallium2 »

> How to make sense of a proof

> When you finish you should know why each step follows from what came before. You may not see how anyone could have thought to do the proof that way, but you should be able to see that it is correct.

Knowing that something is true is not the same as knowing why it is true.

I don't know what the problem is with understanding, but here's three thoughts:

1. You need a deeper level understanding - you can't understand a problem at the same level you encountered it. Perhaps, understanding different but related areas, so you see the same problem from a different perspective. Perhaps understanding the formal system that is used to define terms used in the problem description.

2. You need familiarity, which creates the feeling of "intuition". If you know how it behaves in all situations, you will feel you understand it, even if you don't. So, just lots of practice/exercises.

3. You need to fully understand the components from which the problem is formed. For example, the natural numbers and addition, and build up from there.

Re: How to Study Mathematics (2017)

#16

Post by ivansavz »

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…

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 covers all the material.

The No Bullshit Guide to Linear Algebra [2] is all about linear algebra and also includes three chapters on applications, so you'll learn the fundamental ideas but also what they are used for IRL.

Both books come with exercises and problem sets with answers, which is essential for learning. In fact one could say all math learning happens when you try to solve problems on your own, not just reading.

[1] https://minireference.com/static/excerpts/noBSmathphys_v5_pr... [2] https://minireference.com/static/excerpts/noBSLA_v2_preview....

See the reviews on amazon for what people say.

Re: How to Study Mathematics (2017)

#17

Post by ACosmicDust »

ZephyrBlu wrote: post #14

Although the title is "How to Study Mathematics", I think a more accurate title would be "How to Study Mathematics as a Mathematician ". I am studying some maths right now with the goal of understanding some statistical methods. Having a rock solid understanding of all the underlying maths is counter-productive to my end goal though (Applying the statistical methods), because it would be extremely time consuming. If…

I am sort of facing the same problem. On one hand I like math, abstract algebra, calculus etc but on the other hand I know I am not great with it. I am slow, I am not creative. So, when trying to learn something for programming like differential geometry, when I go deeper than I need to, I feel like I am wasting my time. And sometimes it is particularly hard to read a book written for mathematicians because my knowledge of it is not as "continuous" as theirs.

Re: How to Study Mathematics (2017)

#18

Post by harry8 »

yoaviram wrote: post #6

Slight tangent - any suggestions on none conventional ways to teach children math?

Depends on the kid(s), age, progress so far etc i would think.

Up to high school algebra level I can talk a little about but ymmv. Everyone is different.

The number Devil is an enjoyable story. Khan academy has a good problem bank with gamification of progress etc. Mathantics is a good substitute for school teaching of conventional stuff on video and has good worksheets. Mathific app is another source of practise and gamified progress.

Interested to hear other ideas and for other ages.

Re: How to Study Mathematics (2017)

#19

Post by jamiek88 »

ivansavz wrote: post #16
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…

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.

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