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#1 general656  Icon User is offline

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Top Books to learn Calculus and Discrete Mathematics?

Posted 07 May 2017 - 02:58 PM

I've got a problem. I'm currently studying at the University.

As a self-taught programmer, I learned to learn this on my own. I'm not so into teachers to teach me things as I've discovered so far because I have no discipline to follow their orders, their schedule etc.

So, after some time thinking, I've decided to take the same way I've taken with Programming. Self-Teaching. And when I'll confront difficulties I'll ask the professor in the University what I'm doing wrong.

But to do this, I probably don't won't poor-written books that were made just to be sold. I want books that were made to actually teach, with simplicity, great writing and explanations all over the book.

I want Mathematics to be one of my Hobbies in the IT Culture. I mean I actually LIKE Mathematics. But every time I'm stuck somewhere and I don't know where to search, how to know the answer. It's not like in Programming where you will write "Why there is this bug". Because bugs that you can't fix yourself don't happen often, and programming in overall is not hard to be taught. Things like:

Why ....... Cn = c1 + 2 + ... + (n-2) + (n-1) + n
Equals to Cn = (N(n+1)) / 2

When I confront stuff like these I want to know WHY this equals to that. I want it to be like Programming, to know how to build a solution yourself from the bottom-up.

TL;DR; I'm not the best in Calculus and I just started learning Discrete Mathematics. What books are preferable in this case? So I can start Mathematics as a hobby and be good at it by practicing?

This post has been edited by general656: 07 May 2017 - 03:18 PM


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Replies To: Top Books to learn Calculus and Discrete Mathematics?

#2 jon.kiparsky  Icon User is online

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Re: Top Books to learn Calculus and Discrete Mathematics?

Posted 07 May 2017 - 03:20 PM

Absolutely you can study math as a hobby. There are some stumbling blocks that you're likely to run into - for example, mathematicians have devised an almost completely useless language for discussing their work, and most writing on math starts out from the premise that you already understand it all already so we can skip all of the bits where we explain things. This can be a bit frustrating, but it's honestly not that different from a discipline like history or sociology in that regard.

I don't know what the right books for calculus are going to be, but there was a pretty good MOOC on coursera. https://www.coursera...learn/calculus1
You might also talk to the people who teach the calculus course at your university and ask them what book they use and what they like about it.

For discrete math, there is a course on MIT open courseware: https://ocw.mit.edu/...video-lectures/

This has a pretty deep set of "course notes" associated with it. You might also be interested in looking through Knuth et al's Concrete Mathematics ("Concrete" here is a portmanteau of "continuous" and "discrete", a typical Knuthian pun) (http://www.powells.com/book/concrete-mathematics-a-foundation-for-computer-science-9780201142365/1-9, out of stock at Powell's but I'm sure you can find it somewhere)

The latter text is cited by Knuth as an effective preparation for his Art of Computer Programming, so that might be incentive to work your way through it.

You can also sort of fumble your way through the material on your own - Dover has published tons of great texts on the topics which make up discrete math, including set theory, graph theory, and so forth. They're typically in the $10-$20 range, which makes them kind of a steal as compared to new textbooks or titles from a publisher like Springer (typically 10X the price)

Andrews' introduction to number theory (http://www.powells.com/book/number-theory-9780486682525) and Rosenbloom's Elements of Mathematical Logic (http://www.powells.com/book/elements-of-mathematical-logic-2221124009698/2-0) are pretty readable and will help get you used to reading mathematical writing.


EDIT: Is there any reason you're not taking these courses through your university? Seems like a golden opportunity!
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#3 macosxnerd101  Icon User is offline

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Re: Top Books to learn Calculus and Discrete Mathematics?

Posted 07 May 2017 - 08:31 PM

Quote

I'm not so into teachers to teach me things as I've discovered so far because I have no discipline to follow their orders, their schedule etc.


Teachers, especially at the college level, aren't there to give you orders. They want to actually teach you. Granted there are ones in every crowd that aren't great, but most are actually interested in students learning.

Once you get past the number crunching sequences (e.g., freshmen calculus), the math becomes a lot more conceptual and abstract. And there is a lot of value in having a knowledgeable and articulate instructor. Most of what you will be doing is learning about concepts and techniques, and how to apply them. Lecture is designed to illustrate the important techniques, prove big theorems, and highlight outside connections. Homework is largely intended as practice for students to apply these techniques. At this stage of the game, each homework problem is like a small programming project rather than a syntax error. The goal should be to gain experience solving difficult problems. Googling for solutions to these problems is really comparable to Googling for completed programming projects.

On the flip side, it is very healthy to discuss these problems with your instructor and peers! Much of what you learn about mathematics will come from these discussions. And you'll make a lot of friends working late on homework; speaking from experience. :)

Quote

When I confront stuff like these I want to know WHY this equals to that. I want it to be like Programming, to know how to build a solution yourself from the bottom-up.

This is a really good attitude to have!


Quote

You might also be interested in looking through Knuth et al's Concrete Mathematics ("Concrete" here is a portmanteau of "continuous" and "discrete", a typical Knuthian pun) (http://www.powells.com/book/concrete-mathematics-a-foundation-for-computer-science-9780201142365/1-9, out of stock at Powell's but I'm sure you can find it somewhere)

I would not suggest this book until you've gained some experience in a couple upper level math classes. Knuth's book is a weight-lifting book. The real value in it is in working through all the problems, more than the exposition. My understanding is that the problems in this book are quite challenging. You'll get more out of it if you have a solid foundation.


If you're in a Discrete Math class, Epp and Rosen are the classic texts. Epp is a little more approachable, but it is ~$300. Rosen is still very readable, but it is intended for juniors/seniors.

Richard Hammack's Book of Proof is a good and free (legal) online text. It is a good place to start for learning both the language of math and how to write proofs.

Additionally, here are some resources:
CS Book Suggestions
Math resource thread
Paul's Notes for lower level math classes (such as Calculus)
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#4 alanafnc  Icon User is offline

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Re: Top Books to learn Calculus and Discrete Mathematics?

Posted 01 September 2017 - 03:24 AM

I learn similar to you. For discrete math, I've enjoyed Mathematical Reasoning by Ted Sundstrom the most. It's easy to read and is all basic, beginner stuff. The pdf is free, but I bought the book because I always prefer to hold what I'm reading.. it's only 20 bucks. I would have paid a lot more for it.

I haven't really found anything I liked for calculus. MyMathLab has been my favorite method assigned to learning calculus.
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