Math Books

[gorcee]

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+!

[Giallo]

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

[fourhalfmats]

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.

[Dason]

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.

[fourhalfmats]

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.

[Twistar]

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.

[gorcee]

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).

[friction]

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.

[Giallo]

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).

[friction]

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.
Thanks.

[Giallo]

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

[doogly]

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

[rolo91]

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.

[doogly]

Grinstead and Snell is a lovely and free probability book.

[OOPMan]

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...

[tl.]

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.

[turidoth]

(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.

[Sebastiaan]

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?

[moiraemachy]

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]

How to purchase it?

[alessandro95]

Any good abstract algebra book? Undergraduate level!

[doogly]

I <3 Artin's.

[alessandro95]

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)!

[doogly]

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

[hairysun]

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.

[cjmcjmcjmcjm]

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.

[clonus]

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.

[Cleverbeans]

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.

[Anriasia]

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)

[skullturf]

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]

Any cheap introduction to complex analysis? (With plenty of excercises if possible)
Thanks
Alessandro

[cyanyoshi]

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!

[martfiunkar]

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.

[bitsplit]

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]

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?

[doogly]

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?

[onoresrts63]

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

[yvan]

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.

[Mambo4]

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 " ?

[doogly]

Indra's Pearls.