#122 in Science & math books
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Reddit mentions of Elementary Number Theory: Second Edition (Dover Books on Mathematics)
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Reddit mentions: 10
We found 10 Reddit mentions of Elementary Number Theory: Second Edition (Dover Books on Mathematics). Here are the top ones.
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- Cambridge University Press
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Specs:
Height | 8.52 Inches |
Length | 5.48 Inches |
Number of items | 1 |
Release date | September 2008 |
Weight | 0.63052206932 Pounds |
Width | 0.52 Inches |
You are in a very special position right now where many interesing fields of mathematics are suddenly accessible to you. There are many directions you could head. If your experience is limited to calculus, some of these may look very strange indeed, and perhaps that is enticing. That was certainly the case for me.
Here are a few subject areas in which you may be interested. I'll link you to Dover books on the topics, which are always cheap and generally good.
Basically, don't limit yourself to the track you see before you. Explore and enjoy.
Several good books have already been mentioned in this thread, but some good books are hard to get into as a beginner.
I recommend Elementary Number Theory by Underwood Dudley as a good starting point for a beginner, as well as something like Apostol or Ireland-Rosen if you want more details.
I think it makes sense to start with something like Dudley to get an overall framework, and then rely on more detailed books to flesh out the details of whatever topics you're interested in more.
In particular, I think Dudley's book has an approach to Chebyshev's theorem (i.e. there is always a prime between n and 2n) that's great for beginners, even if someone with a bit more experience can streamline that proof a little.
Elementary Number Theory, 2nd edition by Dudley, it's a fantastic book on number theory, deals with all sorts of old theorems by Euclid and Euler. Written in a really easy-to-comprehend way, and if you're really stuck on an exercise the internet can help.
Sure, there are lots of cool websites that don't ask for crazy prerequisites. One which I share with all of my friends who are starting out in math is the Fun Facts site, hosted by Harvey Mudd College.
As far as learning specific materials, you can try Khan Academy for what are perhaps some of the more elementary topics (it goes up to differential equations and linear algebra). If you want to learn more about number systems and algebra I think that either picking up a good, cheap book on number theory, or even checking out the University of Reddit's Group Theory course (presented by Math Doctor Bob) are both very strong options. Otherwise, you can check out YouTube for other lecture series that people are more and more frequently putting up.
Set Theory:
Naive Set Theory
Number Theory:
Elementary Number Theory
Introduction to Analytic Number Theory
A Classical Introduction to Modern Number Theory
Topology:
Topology
Introduction to Topological Manifolds
There's a couple options. You could pick up a basic elementary number theory book, which will have basically no prerequisites, so you'll be totally fine going into it. For instance Silverman has an elementary number theory book that I've heard great things about. I haven't read most of it myself, but I've read other things Silverman has written and they were really good.
There's a couple other books you might consider. Hardy and Wright wrote the classic text on it, which I've heard still holds up. I learned my first number theory from a book by Underwood Dudley which is by far the easiest introduction to number theory I've seen.
Another route you might take is that, since you have some background in calculus, you could learn a little basic analytic number theory. Much of this will still be out of your reach because you haven't taken a formal analysis class yet, but there's a book by Apostol whose first few chapters really only require knowledge of calculus.
If you decide you want to learn more number theory at that point, you're going to want to make sure you learn some basic algebra and analysis, but these are good places to start.
Also pick a book on Number Theory, pretty useful in computer science. I would recommend: https://www.amazon.com/Elementary-Number-Theory-Second-Mathematics/dp/048646931X/ref=sr_1_1?ie=UTF8&qid=1500074415&sr=8-1&keywords=elementary+number+theory+dudley
I would highly recommend spending some time learning number theory first. Much of crypto relies on understanding a fair amount of number theory in order to understand what and why stuff works.
The book antiantiall linked is fantastic (I have a copy), however if you don't have a strong foundation in number theory will likely be a bit over your head.
Here is the textbook that was used in my number theory course. It isn't necessarily the best out there, but is cheap and does a good job covering the basics.
Number theory is pretty cool. I enjoyed Dudley's book for a number of reasons.
I like Underwood Dudley's book, and it's now available cheap from Dover: https://www.amazon.com/Elementary-Number-Theory-Second-Mathematics/dp/048646931X/ref=sr_1_1?s=books&ie=UTF8&qid=1468275037&sr=1-1&keywords=dudley+number+theory