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Ask HN: Ramping up math skills?

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Ask HN: Ramping up math skills?

#1

Post by fjellfras »

I went through a decent mathematical curriculum during college including calculus and linear algebra several years ago, and while I was nowhere near the best I had good skills. Recently I have been trying to implement machine learning and what I have found out is that I have lost most of the capacity for math, specifically following proofs etc.

I think this may have happened to other people as well, and while I am in no way averse to hard work or putting in long hours, a little direction to start off would be very helpful.

Keeping that in mind, are there books or tutorials that are useful when trying to refresh mathematical knowledge (refresh being the key here)? My area of interest is machine learning so the main topics I need to be good at are algebra and calculus. I have already ordered How To Prove It as it was recommended elsewhere to me.

Thanks a lot.

Re: Ask HN: Ramping up math skills?

#3

Post by billswift »

How to Solve It is a very good book, but it doesn't address the issue you want; it is mainly about problem solving and was intended for math teachers.

For review, I suggest getting cheap, out of print textbooks and working the chapter review problems. When the review suggests you are having difficulties, only then reading the appropriate section. That lets you target your problem areas without wasting time, and getting bored, doing a lot of unnecessary reviewing.

Re: Ask HN: Ramping up math skills?

#4

Post by fjellfras »

billswift wrote: post #3

How to Solve It is a very good book, but it doesn't address the issue you want; it is mainly about problem solving and was intended for math teachers. For review, I suggest getting cheap, out of print textbooks and working the chapter review problems. When the review suggests you are having difficulties, only then reading the appropriate section. That lets you target your problem areas without wasting time, and getti…

Thanks, solving questions before reading sounds like an excellent strategy, especially given that I'm supposed to have read it all before. Now I will try to make a list of books to work on.

Re: Ask HN: Ramping up math skills?

#6

Post by 1331 »

You may want to try working through Spivak's _Calculus_ [1] textbook. It is a bit more involved than most calculus textbooks used in universities today, so it will likely not feel like you are simply repeating something that you have already done. I would recommend this book to anybody who wants to brush up on calculus after studying it before.

[1] http://www.amazon.com/dp/0914098918/

Re: Ask HN: Ramping up math skills?

#7

Post by 1331 »

billswift wrote: post #3

How to Solve It is a very good book, but it doesn't address the issue you want; it is mainly about problem solving and was intended for math teachers. For review, I suggest getting cheap, out of print textbooks and working the chapter review problems. When the review suggests you are having difficulties, only then reading the appropriate section. That lets you target your problem areas without wasting time, and getti…

_How To Solve It_ [1] is indeed a good book, but I think fjellfras is referring to _How To Prove It_ [2], which prepares students "to make the transition from solving problems to proving theorems."

[1] http://www.amazon.com/dp/4871878309/ [2] http://www.amazon.com/dp/0521675995/

Re: Ask HN: Ramping up math skills?

#8

Post by 1331 »

As for studying proofs, _How To Prove It_ [1] is indeed a good book. You may also be interested in _Book of Proof_ [2], which is available under a Creative Commons license. (You can download the PDF for free, and you can order it from Amazon [3] if you want a hard copy.)

[1] http://www.amazon.com/dp/0521675995/

[2] http://www.people.vcu.edu/~rhammack/BookOfProof/index.html

[3] http://www.amazon.com/dp/0982406207/

Re: Ask HN: Ramping up math skills?

#10

Post by fjellfras »

1331 wrote: post #6

You may want to try working through Spivak's _Calculus_ [1] textbook. It is a bit more involved than most calculus textbooks used in universities today, so it will likely not feel like you are simply repeating something that you have already done. I would recommend this book to anybody who wants to brush up on calculus after studying it before. [1] http://www.amazon.com/dp/0914098918/

I have Spivak's book actually, I got the hardcover from a used book store several years ago. It did seem a bit daunting to me from what I recall, I had used Tom Apostle's book when studying calculus back then.

I'll give more time to working through Spivak, hopefully it feels more approachable this time around.

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