Unfortunately I have reached the maximum number of math classes I can take for my undergraduate degree. I still wish to study basic ODEs and basic number theory. What is a good textbook with an introduction to these? I would prefer a textbook that is not super rigorous or formal since I will be studying it on my own time.
Thank you.
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$\begingroup$ Similar questions: books on ODE/PDE math.stackexchange.com/q/3335/823 $\endgroup$– BaudrillardApr 21, 2011 at 8:37
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$\begingroup$ Books on introductory number theory: math.stackexchange.com/q/1774/823 $\endgroup$– BaudrillardApr 21, 2011 at 8:38
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1$\begingroup$ Wiki-hammered. For future reference: I highly encourage users of this site to be proactive in flagging this type of questions to the moderator for conversion to community wiki. $\endgroup$– Willie WongApr 21, 2011 at 11:53
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$\begingroup$ @Willie: I have a question for you, I wanted to know what is a community wiki and what is the difference between that and a normal thread? Thanks $\endgroup$– night owlApr 21, 2011 at 12:10
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$\begingroup$ @nightowl: please see meta.math.stackexchange.com/questions/445/… $\endgroup$– Willie WongApr 21, 2011 at 21:42
6 Answers
I think these two are quite good:
Elementary Differential Equations with Boundary Value Problems (Edwards &Penney)
An Introduction to the Theory of Numbers (G Hardy)
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5$\begingroup$ For Number Theory, Hardy and Wright is a great book, but not a great textbook (no exercises). The book by Joseph Silverman (Friendly Intro. to Number Theory) is fairly small, very nice. Niven, Zuckerman, and Montgomery is a classic text. $\endgroup$ Apr 21, 2011 at 5:45
For learning ODE's, a popular undergraduate book is
1.)Differential Equations with Boundary Value problems-Polking, Bogges, Arnold.
If you want to see many examples, I recommend you get the
2.)Schaum's Outline on Differential equations-Bronson,Costa.
From personal experience I highly recommend both of these books. If you want to see slightly more advance topics with a geometric taste I recommend
3.) Ordinary Differential Equations-V.I. Arnold
As for Number theory, if you want a computational approach, consider
1.) Elementary Number Theory-Burton
For a more theoretical approach,
2.) A classical Introduction to Modern Number theory-Rosen, Ireland 3.) Introduction to Analytic Number Theory-Apostol
Nonlinear Dynamics and Chaos by Steven Strogatz is a great book if you want to get a feel for how differential equations work. Wonderful explanations, fun exercises, and lots of interesting applications. (But don't expect any proofs of existence and uniqueness theorems and such things.)
There are two books I know of that deal with differential equations & include a chapter on the calculus of variations at an introductory level as well which you might enjoy.
1) Differential Equations and Their Applications - Zafar Ahsan
2) Differential Equations & the Calculus of Variations - Lev Elsgolts
Another book exclusively devoted to ODE's is Tenenbaum/Pollard Ordinary Differential Equations.
The NPTEL video lectures here are wonderful, do module 1 & 2 simultaneously (beginning with, & with more emphasis on, module 2).
The UCCS video's here use different books, you might like to buy one of the books & work along with the videos on there. Similarly the videos on number theory in that link use a book you might like to buy & read along with the lectures on there.
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$\begingroup$ @sponsoredwalk: Thanks for the links: I checked out the UCCS site and it seems to want a school email to access the online videos. Do you know a way around this or is this some new implementation that they have created you did not know about? Thanks $\endgroup$ Apr 22, 2011 at 3:00
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$\begingroup$ No it's fine you just need to give your own e-mail, i.e. just register when they ask you to as you try to access the videos, & you get access. Sorry, should have mentioned that! $\endgroup$– sponsoredwalkApr 25, 2011 at 10:50
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$\begingroup$ @sponsoredwalk: Okay thanks for the info, I will do that. $\endgroup$ Apr 26, 2011 at 8:09
Some books that I think work quite well and very well laid out in formatting and examples and exercise are the following two books:
1) Differential Equations & Linear Algebra, Third Edition: Edwards and Penney
2) Elementary Number Theory, Fifth Edition: Kenneth Rosen
There is a sixth edition out now on the Rosen's Number Theory book, but I would guess that there is not much change to it, but I can be unsure. The material should be still relevant in the Fifth with respect to the newer edition.
Okay, I hope that this helps out with your journey to self-learn.
Good~Luck and happy studying. :)
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$\begingroup$ To save someone else from having to click on the link, the ODE text refer to here is the Edwards & Penney text. $\endgroup$– cchApr 21, 2011 at 15:20
- An Introduction to Ordinary Differential Equations-Earl A. Coddington
- Fundamentals of Number theory-William J. Leveque