Math Books

For the discussion of math. Duh.

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gorcee
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Re: Math Books

Postby gorcee » Mon Apr 23, 2012 2:12 pm UTC

Incidentally, the latest Notices of the AMS contains a review of the series. However, the review was authored by Charles Fefferman, a colleague of Stein's at Princeton, and includes commentary from former students and colleagues. So, it's not terribly objective, and it's unsurprisingly very praiseworthy. So, I'm still on the fence about buying the series...

In unrelated news, years ago I lent my copy of Brown and Churchill to a friend, who never returned it. That fucking book is still $150+!

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Re: Math Books

Postby Giallo » Fri Apr 27, 2012 9:37 pm UTC

For those of you who don't live in America, Springer is doing some great sales on mathematics books. You can find a list of the titles in discount (up to over 50% of the price!) at this link, if you are interested: http://www.polybuchhandlung.ch/data/html/Springer_Yellow-Sale_Mathematik_2012.pdf

Personally, I'm buying some for the next semesters :wink:
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Re: Math Books

Postby fourhalfmats » Tue Jun 05, 2012 3:50 pm UTC

I'm looking for a very specific kind of book. Something that reviews everything up to and inside undergraduate's statistics. Kind of like this http://www.amazon.com/All-Mathematics-You-Missed-Graduate/dp/0521797071 but for stats.

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Dason
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Re: Math Books

Postby Dason » Wed Jun 06, 2012 11:07 pm UTC

Are you starting a graduate program in stats soon? If so what school? I don't have anything quite like that but some programs are more applied, some much more theoretical - and a recommendation can depend on the type of program.
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Re: Math Books

Postby fourhalfmats » Sat Jun 09, 2012 4:03 pm UTC

Dason wrote:Are you starting a graduate program in stats soon? If so what school? I don't have anything quite like that but some programs are more applied, some much more theoretical - and a recommendation can depend on the type of program.


edited because I sounded like an ass in the original; excuse me, I was sleepy

I'm not going into graduate school (quite yet). The best way I can put it is: I'm very familiar with the basics, but I've forgotten a lot of what I learned. I'm interested more in theory.

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Re: Math Books

Postby Twistar » Sun Jul 15, 2012 11:14 am UTC

Marsden, Ratiu, Abraham - Manifolds Tensor Analysis and Applications

Does anyone have experience with this textbook? I'm trying to use it to preemptively teach myself differential geometry. I've taken some undergraduate classes in Linear Algebra (though not a good one,) Analysis, Topology, basic abstract algebra and some other stuff like PDEs and Fourier analysis. Also mutlivariable calculus in the introductory sense. It's been one of goals to learn differential geometry. I'd like to learn it for its applications to physics (I'm a physics major) but I also just really like it. I also want a very rigorous treatment, lots of times in physics classes we take mathematical shortcuts that (for me) make it hard to understand the physics on the deepest level.
This book seems like it is good because it seems completely rigorous and it is also seems to be self contained. In my head this says to me "I have more than enough background to understand this book if I just take it slow and work through each argument, everything is there." The issue I am having is that it is very hard (duh.) I've spent months on the second chapter.
I guess my question boils down to two things. First, is this a good book to approach in this self teaching manner or am I banging my head against a brick wall? Should I try something more mellow first? Second, are there any tips for teaching myself this subject? I have a hard time deciding what to spend a lot of time on and what to gloss over. For example, chapter 1 in the book is basically a review of topology, there's a few things I didn't study in detail but I'm confident I could learn them if they turned out to be very relevant later on. But maybe I should look closely at these things just to train my brain? I don't have infinite time.

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Re: Math Books

Postby gorcee » Wed Jul 18, 2012 3:35 pm UTC

Modern calculus books: who's using what?

I need to freshen up on some basic Calculus. I still have my older edition Larson, Hostetler, and Edwards book, but I am curious what books people are using these days for Calc 1 and 2, which would include up through multiple integration (though perhaps less emphasis on vector calculus).

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Math Books for a Recovering Liberal Arts Major

Postby friction » Tue Jul 31, 2012 8:55 pm UTC

I'm looking for an introductory / fundamentals text on math. Any formal training in mathematics is years behind me and my brain is getting fat from reading only blogs and escapist fiction. What do you recommend to the untrained and unskilled? I'm aware of the Math Links thread, but I'd like some dead-tree and ebook resources.

Thanks.

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Re: Math Books

Postby Giallo » Thu Aug 02, 2012 10:34 pm UTC

gorcee wrote:Modern calculus books: who's using what?

I need to freshen up on some basic Calculus. I still have my older edition Larson, Hostetler, and Edwards book, but I am curious what books people are using these days for Calc 1 and 2, which would include up through multiple integration (though perhaps less emphasis on vector calculus).


I have the two book by Zorich (in german, I don't know if they come in english, too; they're very good, though).

EDIT: Yes, they come in english, too (V.A.Zorich, Mathematical Analysis I & II).
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Re: Math Books for a Recovering Liberal Arts Major

Postby friction » Fri Aug 03, 2012 3:59 pm UTC

friction wrote: I'm aware of the Math Links thread, but I'd like some dead-tree and ebook resources.


The Paul Dawkins document from the math.lamar.edu link over in Math Links is serving pretty well as a "this is algebra, remember how to use exponents?" resource / primer. A more mathy friend recommended Abstract Algebra as he thinks it doesn't require much in the way of previous training, but didn't have any advice on books.

My purpose is to exercise mentally by learning a new discipline, so there isn't a particular 'real world' application I'm working toward.
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Re: Math Books

Postby Giallo » Thu Sep 13, 2012 10:29 am UTC

I'm looking for good textbooks on differential geometry and functional analysis. Any advice?
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Re: Math Books

Postby doogly » Thu Sep 13, 2012 1:05 pm UTC

I absolutely adore Spivak for differential geometry. His style is quite unique and intimately historical, so might not suit everyone.
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Re: Math Books

Postby rolo91 » Wed Sep 26, 2012 11:35 pm UTC

So, during next semester my subjects will be probability, methods of numerical analysis, and differential calculus. It's my sophomore year so all of them would be almost from scratch.

What books would you recommend as an introduction/complement to those classes?

Preferably something more focused on readability than... formality, for lack of a better word. I mean, math is always formal, but if possible I would like something explained as clearly as possible.

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Re: Math Books

Postby doogly » Thu Sep 27, 2012 12:41 am UTC

Grinstead and Snell is a lovely and free probability book.
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Re: Math Books

Postby OOPMan » Sat Nov 10, 2012 9:56 am UTC

A long time ago, in a galaxy far, far away...

I was a student studying Applied Computing (University of Caper Town, 2002-2005, Computer Science + History)

Unfortunately I never finished my degree (In part because I failed 1st year maths 4 years in a row) and to be honest it
hasn't stopped me from getting a nice coding job and doing well for myself.

However, I was recently helping my wife with her Masters (She's a molecular genetics researcher) and realised that:

  • I have forgotten most of the maths that I learned at University and some of the maths from Secondary School
  • I regret the above
  • I remember not actually being terrible at the maths, just having trouble with the exams (A general problem for me ;-) )
  • I also remember enjoying the maths, even as I failed it :-)

To this end I'd love it if someone could suggest some good, freely available textbooks in electronic form that would allow
me to return to 1st year maths (And maybe even try some 2nd or 3rd year stuff ;-) and refresh my knowledge.

I don't want to continue growing more ignorant, so please help...

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tl.
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Re: Math Books

Postby tl. » Sat Nov 24, 2012 5:25 pm UTC

my professor of Differential Geometry told us a story the other day. it goes something like this.

A good number of years ago, Graeme Segal taught a DG course (it could have been a geometry of surfaces or similar class). In the course of this class, he or someone close to him, made notes. these notes were very well written, very concise and covered precisely the topics my professor does in his class. As these notes were never published, they were (supposedly) used as basis for Pressley's Elementary Differential Geometry. According to my professor, Pressley's book is currently by far the best book to work with for his class, but Segal's notes, which, from what I understood, he actually had a copy of at some point, were better (more concise, Pressley included some topics we don't cover, etc.).

I was supposed to study for said class today and since I didn't feel like it too much, I decided to track down the notes (everything being on the internet and what not). I'm ashamed to admit, but I came up empty. Any ideas where to look or where to ask or where to go would be much appreciated.

Thank you for your time.

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Re: Math Books

Postby turidoth » Mon Jan 21, 2013 2:50 pm UTC

(for OP and OOPMan)

I think the Stewart textbook is great. To save $ just get an older edition; used, they usually go for 1/20th the original price after a few years. Abe books, or amazon may help. It's a series covering all undergrad calc topics, I found the first year Calculus - Concepts and Contexts very well organized.

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Re: Math Books

Postby Sebastiaan » Mon Feb 11, 2013 9:33 am UTC

Does anyone have any experience with "Adams - Calculus: A Complete Course"? I think that's the book (fifth edition) I've used during my first calculus/analysis class, but lost due to some accident, ahem, with open windows and heavy rain after dropping out/switching to another major. (I wonder what Freud would have to say about that...)

I've already worked myself through half of David Poole's "Linear Algebra: A Modern Introduction" and would like to renew my calculus as well. Is Adams a good enough book to do that or should I try another book?

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Re: Math Books

Postby moiraemachy » Fri Mar 08, 2013 10:35 pm UTC

I'm an engineering student who wants to get into math, but I honestly have no idea where to start. My desire to learn actual math came mainly because learning to use complex numbers, fourier and laplace transforms with absolutely no justification was really bothering me... and I realized that the most of the math I do isn't that rigorously justified (now I'm banging my head for blindly accepting the fundamental theorem of algebra year ago). So, I am looking for a book about the history of math that can teach me about the "techtree of math": when where certain topics discovered, and most importantly, which prior achievements were necessary for the discovery, and why. Does anyone have any suggestions? My candidate, at the moment, is Foundations and fundamental concepts of mathematics, by Howard Eves. Is it a good choice?

Jaswinder
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Re: Math Books

Postby Jaswinder » Wed Apr 03, 2013 7:44 am UTC

How to purchase it? :cry:

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Re: Math Books

Postby alessandro95 » Mon May 06, 2013 1:58 pm UTC

Any good abstract algebra book? Undergraduate level!
The primary reason Bourbaki stopped writing books was the realization that Lang was one single person.

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Re: Math Books

Postby doogly » Mon May 06, 2013 2:30 pm UTC

I <3 Artin's.
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Re: Math Books

Postby alessandro95 » Tue May 07, 2013 8:17 am UTC

The father or the son?

I found a book titled "algebra" from Michael Artin (the son) and a lot of books on more specific topics by Emil Artin (the father)!
The primary reason Bourbaki stopped writing books was the realization that Lang was one single person.

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Re: Math Books

Postby doogly » Tue May 07, 2013 1:15 pm UTC

The son's is a general purpose book suitable for undergraduates. The father's many things are all more specialized.
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Re: Math Books

Postby hairysun » Tue Jul 02, 2013 2:05 am UTC

dhokarena56 wrote:Does anybody have any suggestions for a good book about first-order logic? .



You might try an old book by Kleene called "Mathematical Logic", which is idiosyncratic and well-written enough to be engaging, and quite informative. It's a very sedate introduction to propositional and predicate logic. If you're interested in a fuller treatment of logic, you might consider "A Course in Mathematical Logic" by Bell and Machover, or something newer like Hinman's "Fundamentals of Mathematical Logic", though this is too terse to be useful before you've at least covered predicate logic.

There is also a wealth of easily accessible online material which you can find through a quick google search. You might scroll through those results and find something whose approach suits your preparedness and then proceed from there.

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Re: Math Books

Postby cjmcjmcjmcjm » Sun Aug 25, 2013 2:41 am UTC

I found a really thin old (as in published 1953, IIRC) volume called "Theory of Matrix" at a prof's retirement party (he was giving away books). Sadly, it vanished without trace before I could really get into it. Any recommendations on books I get on the subject? Old ones that are super cheap (~U$5) preferred.
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Re: Math Books

Postby clonus » Sun Aug 25, 2013 4:55 am UTC

Does anybody know of a good book for learning about algebraic varieties at a last year undergraduate/graduate level?
I'm trying to learn some of the work of Grothendieck but I don't really know where to start.

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Re: Math Books

Postby Cleverbeans » Sun Aug 25, 2013 9:47 am UTC

clonus wrote:Does anybody know of a good book for learning about algebraic varieties at a last year undergraduate/graduate level?


I found "Ideals, Varieties, and Algorithms" to be very palatable for self-study as an introduction.
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Re: Math Books

Postby Anriasia » Sat Sep 28, 2013 6:00 am UTC

Looking for introductory text on graph theory? I'm starting a undergrad research project in the spring and I want to at least get some basics under my belt before I start looking at the problem.
My advisor proposed the topic, so all that I really know is that it has something to do with graph theory and rings. :?

Edit: I've already went ahead and bought this book, because it was only four dollars and I figured it couldn't hurt to try it : Introduction to Graph Theory (Dover Books on Mathematics)

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Re: Math Books

Postby skullturf » Tue Oct 01, 2013 7:23 pm UTC

As an undergraduate math major, I very much enjoyed "Graph Theory" by Bollobas. I know I'm just one person, but take that as you will.

alessandro95
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Re: Math Books

Postby alessandro95 » Wed Feb 19, 2014 6:22 pm UTC

Any cheap introduction to complex analysis? (With plenty of excercises if possible)
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cyanyoshi
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Re: Math Books

Postby cyanyoshi » Thu Feb 20, 2014 5:58 pm UTC

It doesn't get much more cheap than free: Complex Analysis. In fact, this list of free online textbooks might keep anyone busy for a while!
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martfiunkar
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Re: Math Books

Postby martfiunkar » Fri Feb 21, 2014 8:45 am UTC

I am very much interested about the section of reading books. Every day, I do more practice on calculus subjects because more practice will be required to know it completely.

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bitsplit
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Re: Math Books

Postby bitsplit » Fri Apr 04, 2014 1:52 pm UTC

I had posted this as a separate topic, but then realized I should ahve posted here...

I recently (2012) took an introductory course in differential equations. I have since graduated, and am looking to learn more about partial differential equations and numerical analysis on my own. Are there any self-study friendly books or online sites/videos on the subject you guys would recommend?

Thanks in advance.

betta21
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Re: Math Books

Postby betta21 » Fri May 09, 2014 2:06 pm UTC

I'm afraid I don't really have enough linear algebra myself to recommend something for that (Anton is quite good, but only for a first course). I'd be interested in a good book on the subject myself after exams end, actually - does anyone have any ideas?

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Re: Math Books

Postby doogly » Sun May 18, 2014 12:55 am UTC

PDEs is a huge topic. I really enjoyed Garabedian, but I had a particular interest in Hadamard's method. His book could easily be useless for others. Did you have a particular application in mind?
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onoresrts63
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Re: Math Books

Postby onoresrts63 » Fri May 23, 2014 4:19 am UTC

What book would you suggest? A pre-calculus and calculus book for a college student :) (and where to buy)

yvan
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Re: Math Books

Postby yvan » Thu May 07, 2015 6:39 pm UTC

onoresrts63 wrote:What book would you suggest? A pre-calculus and calculus book for a college student :) (and where to buy)


For pre-calculus, I'd recommend Axler's Precalculus. It is the most comprehensive and not hard to understand. You could also try with Calculus by Gilbert Strang that is available for free. Hope this help.

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Following up Lockahrt's Lament

Postby Mambo4 » Tue Dec 01, 2015 8:38 pm UTC

Non-mathematician here.
I just read A Mathematicians Lament by Paul Lockhart
https://www.maa.org/external_archive/de ... Lament.pdf

One quote illustrates what I am looking for:
"Technique in mathematics,as in any art,should be learned in context.The great problems, their history,the creative process —that is the propersetting."

Is there a good book out there that explores math history and its context "The great problems, their history,the creative process " ?

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Re: Math Books

Postby doogly » Tue Dec 01, 2015 8:46 pm UTC

Indra's Pearls.
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