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by **DharmaBum** » Wed May 13, 2009 10:15 pm UTC

Looking for a book on differential equations that specifically describes Bernoulli's principle and Torricelli's law.

by **SpallettaAC1041** » Tue May 26, 2009 6:55 pm UTC

For graph theory, I really enjoyed "Pearls in Graph Theory" by Hartsfield and Ringel. It introduces all of the material in an organized and fun way, and the problems do very well in making sure you know how to work with all of the theorems and definitions. Cool stuff, that graph theory.

by **distantorigin** » Wed May 27, 2009 10:06 am UTC

DharmaBum wrote:Looking for a book on differential equations that specifically describes Bernoulli's principle and Torricelli's law.

wiki has a proof of toricelli's, which doesn't use DE's
and also bernoulli's

by **Æshættr** » Sun May 31, 2009 10:02 pm UTC

I'm looking for a book on Complex Analysis that has emphasis on applications to physics (and/or other sciences and engineering.) The book that I have (Title: Introduction to Complex Analysis Author: H.A. Priestly ISBN: 978-0-19-852562-2) is entirely too focused on proofs, has scant hints at applications, and has no solutions to the exercises in the text.

Ideally, I'd like to get a book that is oriented more toward scientists and engineers. One that I've found to be decent is Fundamentals of Complex Analysis for mathematics, science, and engineering (Authors: E.B. Saff, A.D. Snider ISBN: 0-13-332148-7), but buying options for this book are scarce, and I'd like to know if anyone has had good experience with some other books on the subject.

by **doogly** » Sun May 31, 2009 11:40 pm UTC

Brown and Churchill has in the latter portion of the book a lot of fluid problems. That's an interesting part of physics (though our complex course never actually did any of these whatsoever, bah). You might be best off finding a book on the subject you'd like to see it applied to, and then getting the math in there and referring back to a pure complex book when you need it.

by **auteur52** » Thu Jun 11, 2009 8:47 pm UTC

Any suggestions for Algebraic Number Theory? Is the standard reference Lang? My professor suggested I look into Lang or Ribenboim. Any help would be appreciated.

by **Bob S7** » Sun Jun 14, 2009 11:53 pm UTC

I've not made it all the way threw the book yet, but I like Thomas/Finney Calculus 9th edition ISBN 0201531747

by **Quaternia** » Mon Jun 15, 2009 6:53 pm UTC

Hey everyone,
First post, and as it's probably important to get a better idea about the books, I'm going into a non-math program for my first year university, but teach myself math during my spare time.
These are the books I have, and have found useful. They are mainly published by Dover, which I find has a very rich line when it comes to math:
Mathematics: It's Content, Methods, and Meaning by A.D. Aleksandrov, A.N. Kolmogorov, and M.A. Lavrent'ev. This book is a goldmine, it's actually 3 books bound as one, and covers a ton of topics. The learning curve is quite nice, and just overall I can't recommend it more.
Optimal Control and Estimation by Robert F. Stengel. I have only taken a quick look at this book, having bought it recently. Looks very promising, though, and the review portion at the beginning is helpful.
Group Theory and Chemistry by David M. Bishop. Does what it says on the can, really. I found it a neat approach when teaching myself a little bit about groups, just because you can see it applied to molecules. If you're a visual learner, it's worth a shot. It's quite small, too.
Chaos and Fractals: New Frontiers of Science, by Peitgen, Jurgens, and Saupe. I've seen a lot of books on chaos theory and fractals, some math-heavy, others not, but this one in my opinion dwarves them all. First of all, it's massive, at 837 pages as a large hardback, but somehow it's still light (I think the paper's very thin). And in terms of contents, it's fantastic. It goes into a ton of details, and it's definitely math-heavy, but still explains the relevance with examples to real life of different effects. The illustrations are clear and large, some in colour.
Numerical Methods for Scientists and Engineers, by R.W. Hamming. To be honest I haven't read a lot of this book, because I was working on a project and just needed one specific portion. For what I needed it was worth it, and that's about all I can say.
Pearls in Graph Theory: A Comprehensive Introduction, by Nora Hartsfield and Gerhard Ringel. I'm a bit of a compulsive buyer when it comes to math books... I've read through the introduction, the rest seems very nice. I learned about it on this very thread. Overall this little book has my total respect :wink:

Penguin Dictionary of Mathematics, by David Nelson. I got this for a math research project, and it proved very, very useful. It goes in enough depth to briefly explain the topic required, but remains very small and light. I used it a lot when first starting out.

by **534n** » Sun Jun 21, 2009 8:40 pm UTC

So I just finished Pre-Calculus and I am looking to teach myself some calculus concepts before taking Calc BC next year. I have already used Calculus Made Easy by Malthus and, shamefully, Calculus for Dummies which was very informative. I am starting work on basic differential equations and looking for books on differential equations, as well as more texts about derivation and integration- I understand these topics and can integrate and derivate, but more advanced things like trig substitution is lost on me.

by **elucipher** » Tue Jun 30, 2009 5:32 pm UTC

I've found I have a strong interest in mathematical logic (i.e. set theory, proof theory, model theory, etc). As a first step, is there a good introductory book (or even a standard book) to the field that covers the basics of formal logics and, at a minimum, explains the Löwenheim–Skolem theorem and Lindström's theorem?

by **TathagataISC** » Thu Jul 02, 2009 9:08 pm UTC

stockford wrote:I'm looking for books that cover all the important subjects in maths prior to calculus. So far, that I can think of:

Algebra, Geometry, Trigonometry, Functions and Graphs, Sequences and Sums.

So far I'm reading "Basic Mathematics", by Serge Lang. It's a horrible book because of the way he goes about things, and some of the answers are wrong, but I enjoy the application free, "proofiness" of it, and am I looking for more books with that kind of tone. Sullivan has a comprehensive "Algebra and Trigonometry" book but I'm worried it's going to be chock full of word problems and applied problems. I want to get good at pure maths, applications don't interest me. Another set of books is the Gelfand books (Algebra, Trigonometry, Functions and Graphs and Method of Coordinates). The Trig book looks good, but Functions and Graphs didn't look so good.

So yeah, any treatments of pre-calculus topics would be much appreciated, I want to be very comfortable with all kinds of functions, sequences, series, etc. For instance, I have no idea how to solve something like \frac{1}{x-a} + \frac{2}{2x-a} + \frac{5}{x+3a} = \frac{4}{x+a}. That's how good I want my algebra to be. Or how to work with sequences and sums- I know nothing about them, really.

This is exactly what I am looking for. I am looking for my pre-calculus knowledge to reach a level such that I would be able to solve the problems on the IMO, since I feel that my high school math education was pitiful. I want books that prove everything that they state, and have them state a lot of theorems and equations. I just picked up an e-book called "Geometry Unbounded", essentially a compilation of geometry notes and proofs that a past IMO student put together. I like the level of depth in the book, but it is still very informal and without figures. If anyone could recommend something like this except formal and with figures, I would appreciate it.

Additionally, for anyone that is looking for a Linear Algebra text, I've found "Linear Algebra" by Friedberg to be quite nice. It is certainly a book written for the pure mathematician - applications given in the text are minimal, and the proofs have improved in a really nice way since the first edition. Should you decide to see what other people have written about the book on other websites, you may hear them say that it is a book intended for or used in a second year course in Linear Algebra. While this may be true, I think that this book is more than accessible enough to be one's first exposure to Linear Algebra.

by **Jk.d** » Sat Jul 11, 2009 1:46 pm UTC

Hello everyone.
I'm in year 11 and I haven't really been doing much with all my extra spare time so far, so I'm hoping to find some maths books to read over the rest of the summer. Next year I will be taking Maths and Further Maths so I thought it would be a good time to start reading ahead a bit. The A level is offered by MEI and I am doing C1-4, M1, S1 for Maths and then FP1-2, M2, S2, D1, NM for Further Maths. So far I have done GCSE Maths and Statistics (though I probably need a refresher course on the stats) and OCR Additional Maths FSMQ. What books should I look into?

Thanks in advance.

by **oliver_** » Mon Jul 20, 2009 7:58 pm UTC

Hello,

I'm looking at some books for the semester break and wanted to ask if anyone could share some thoughts on Michael Atiyah's "Introduction to commutative Algebra".

I'll hear a course called "Groups, rings, modules" next term and the lecturer mentioned the book in an introductory lecture. It's listed in last years recommended reading list too, but I can only find contradictory reviews on amazon. Some say it's okay for undergraduates with a modest knowledge of algebra while others say the opposite

I'm finishing my second term right now and hat two courses in linear algebra and analysis respectively so far. In groups, ring, modules we're going to do (suprise

) groups, rings and modules but an introduction in algebraic geometry up to Hilberts Nullstellensatz too.

Thanks

by **auteur52** » Mon Jul 20, 2009 8:11 pm UTC

I would not use that as an introduction to abstract algebra. It assumes you are very comfortable with rings and modules. It could be helpful when you are learning the Nullstellensatz, but you should probably wait awhile. It's an excellent book with very enlightening exercises and extremely concise and beautiful proofs, but you should definitely be comfortable with most of the first 12 chapters in Dummit and Foote (for instance) before you try to tackle Atiyah and MacDonald.

by **Odin1415** » Sun Jul 26, 2009 1:34 am UTC

I have a question about Algebra books. Next quarter I'm going to be enrolled in an Algebra class out of Dummit and Foote, so I thought I'd read ahead a bit. The only Algebra book that my local library had was Elements of Abstract Algebra by Clark. I have since attained a copy of Dummit and Foote, however I really like the workbook style of Clark. Does anyone know how these books compare? Dummit and Foote is certainly longer, but I'm not familiar enough with the subject to tell how much of this is due to important extra topics and how much is just a product of the different (and they certainly are different) styles of exposition. Also, I was wondering which is "harder" if there is even a definite answer to that question. Anyways, thanks in advance for any help/advice!

by **Paper Bird** » Sun Jul 26, 2009 1:57 pm UTC

oliver_ wrote:I'm looking at some books for the semester break and wanted to ask if anyone could share some thoughts on Michael Atiyah's "Introduction to commutative Algebra".

I agree with auteur52. While that book is excellent, if you've not seen any algebra other than linear algebra that book probably isn't the best place to start. The excercises in particular are not really suitable for someone seeing rings for the first time and it has no real coverage of the topics of basic group theory. I would recommend you start with a lower level book and perhaps look at Atiyah for a more advanced perspective when you are comfortable with the basic notions. Your university library should have a copy.

by **oliver_** » Sun Jul 26, 2009 2:09 pm UTC

Paper Bird wrote:I agree with auteur52. While that book is excellent, if you've not seen any algebra other than linear algebra that book probably isn't the best place to start. The excercises in particular are not really suitable for someone seeing rings for the first time and it has no real coverage of the topics of basic group theory. I would recommend you start with a lower level book and perhaps look at Atiyah for a more advanced perspective when you are comfortable with the basic notions. Your university library should have a copy.

I actually do have a basic knowledge of rings (polynomial rings for the most part) and groups from my linear algebra course and a seminar talk on characters that I held last semester. But nevertheless, I got myself a copy of Micheal Artin's Algebra after I had a look at Atiyahs book in the library ;-)

And while my original plan was to simply do the chapters on rings and modules, I've started at the beginning again, skipping the parts I know.

Artin can be a bit of a bother to read though. It certainly is different from the textbooks I've read so far ...

by **Paper Bird** » Sun Jul 26, 2009 3:16 pm UTC

oliver_ wrote:I actually do have a basic knowledge of rings (polynomial rings for the most part) and groups from my linear algebra course and a seminar talk on characters that I held last semester. But nevertheless, I got myself a copy of Micheal Artin's Algebra after I had a look at Atiyahs book in the library And while my original plan was to simply do the chapters on rings and modules, I've started at the beginning again, skipping the parts I know.

Ah sorry, when I learnt linear algebra the first time around they kept all the nice groups and rings stuff fom me so I assumed you were a complete algebra novice too :wink:

. In that case good luck with the Artin book, I hear it's good.

On a related note can anyone suggest an introductory book on Hilbert spaces?

by **Fafnir43** » Thu Jul 30, 2009 11:14 pm UTC

Can anyone recommend a good book on measure theory for a (soon to be) third year undergraduate? I've been recommended Taylor, but I'm having a tough time getting through it. This is for self-study in preparation for a course next year, so I'd rather have something accessible and light than something heavy and comprehensive. I know a decent amount of point set topology, which seems to be the main prerequisite, and analysis and probability, which seem to be the main applications. Thanks!

I can't help much with a book on Hilbert spaces, sadly - I've got Linear Analysis, An Introductory Course by Bollabas sitting on my bookshelf, and it looks like a good (if somewhat brutal) read, but I haven't started it yet. Kreyszig's Introductory Functional Analysis is the only other one I've heard of. What sort of background do you have?

by **oliver_** » Fri Jul 31, 2009 12:27 pm UTC

There is one from Stein and Shakarchi: "Real Analysis: Measure Theory, Integration and Hilbert Spaces", which I wanted to have a look at myself since I saw it in our library. I own the first one in the series, which is about Fourier Analysis and is quite nice, at least the parts I actually read for my seminar last semester.

by **Captain Strychnine** » Sun Aug 02, 2009 9:54 am UTC

Fafnir43, I think you should look at "Lebesgue Integration on Euclidean Space" by Frank Jones. It's pretty much an ideal introduction to this material at the undergraduate level (i.e. friendly and concrete, rather than terse and fully general).

by **11-73-3-33** » Mon Aug 03, 2009 2:34 pm UTC

I'm looking for recommendations on introductory books on Knot Theory, at undergraduate (or not advanced graduate) level.

Thanks in advance!

by **Fafnir43** » Mon Aug 03, 2009 3:53 pm UTC

I found a copy of Lebesgue Integration in Euclidean Space in the maths department library - after reading the first chapter and a half, it looks perfect. Thanks!

by **doogly** » Mon Aug 03, 2009 4:56 pm UTC

11-73-3-33 wrote:I'm looking for recommendations on introductory books on Knot Theory, at undergraduate (or not advanced graduate) level.

Thanks in advance!

There is a pdf, Knots Knotes, that you can download from Justin Roberts that is pretty good, though you may have to check out before the last chapters set in. I also liked Lickorish's book. It requires you to have some solid point set topology, depending on how your undergrad works that may or may not be suitable.

by **Aladdin** » Sun Aug 09, 2009 7:42 am UTC

Hi,
My name is Aladdin Rajab , Australian living in Asia studying.

I've ordered Schuam's Calculus 5th edition book -- I'm in year 12 this year preparing for overcoming the faculity of engineeering.

Is this book helpful enough for this year and my coming years .

Thanks in advance.

Aladdin

by **Alpha Omicron** » Fri Aug 14, 2009 6:41 am UTC

Using regularly-sized text is helpful in getting people to read what you say.

by **osj1961** » Sun Aug 23, 2009 1:18 am UTC

elucipher wrote:I've found I have a strong interest in mathematical logic (i.e. set theory, proof theory, model theory, etc). As a first step, is there a good introductory book (or even a standard book) to the field that covers the basics of formal logics and, at a minimum, explains the Löwenheim–Skolem theorem and Lindström's theorem?

A friend of mine from grad. school (who, besides being brilliant was a really cool, nice guy...) wrote a logic/model theory text that might
fit your bill perfectly. Check out http://www.flsouthern.edu/academics/math/shedman/afcil.htm.

Cheers,
Joe

by **osj1961** » Sun Aug 23, 2009 2:02 am UTC

Also, I've written a free text about mathematical foundations (logic, set theory, combinatorics and cardinality)
and an introduction to proof techniques. It is called A Gentle Introduction to the Art of Mathematics (GIAM for short),
and is available at http://www.southernct.edu/~fields/GIAM. The students who have used preliminary versions
have given me a lot of good feedback, but I could always use more! So, I hope some of you will find it useful, and if you
have kudos or complaints, by all means forward them!

Cheers,
Joe

by **Ended** » Tue Sep 29, 2009 9:19 pm UTC

Does anyone have an opinion on either of the two books below (or other similar books)? I've been wanting a book which gives a mathematical introduction to QFT for self-study, and these look interesting. I'm fairly comfortable with functional analysis and quantum mechanics but a bit lacking in special relativity, Lie theory and differential geometry; I think I can fill in these gaps as necessary (though any recommendations for texts on these would be also useful). Thanks!

Quantum field theory: a tourist guide for mathematicians (Folland)
Quantum Field Theory for Mathematicians (Ticciati)

by **doogly** » Tue Sep 29, 2009 9:29 pm UTC

I'd definitely also take a look at Araki's too, that is a highly delightful one.
If you are good friends with functional analysis, you might really like an approach like Haag's. This sort is dear to my heart, because if you want to do fields in curved space, C* algebras are absolutely necessary - all of the other state based approaches fail to generalise once you knock out things like Poincare symmetry and timelike killing vectors and so on.

by **Ended** » Tue Sep 29, 2009 9:51 pm UTC

Thanks doogly, both of those look good. I think a trip to the library is in order pretty soon.

by **RabidAltruism** » Mon Nov 09, 2009 12:02 am UTC

I'm looking for a good book on the general linear model at work in multivariate statistics.

I'm not looking for a multivariate statistics book with a chapter or a few special sections devoted to the general linear model; I already own a few multivariate stat's books, and am looking to improve my knowledge of the connections between each special technique (via the GLM).

Anyone know of anything that would suit that purpose?

by **doogly** » Wed Nov 18, 2009 4:45 am UTC

From A Scrabook of Complex Curve Theory - "...our point of view is romantic rather than rigorous." What a glorious book.

by **Luca_Tortuga** » Fri Nov 27, 2009 8:42 pm UTC

Good Day to all!(and happy holidays)
I'm looking for a comprehensive introduction to Undergraduate/Graduate level mathematics.
So far I have:

Mathematics of Classical and Quantum Physics. Fredrick W. Byron, and Robert W. Fuller.

and will soon acquire:

Ordinary Differential Equations. Morris Tenenbaum, Harry Pollard.

Linear Algebra, second edition. Kenneth Hoffman, Ray Kunze.

I am currently looking for a rigorous treatment of Differential and Integral Calculus, an introduction to proof writing, a text on Non-Euclidean geometry,and an introduction to Functional Analysis.
Do any of you have recommendations for books in those areas?
I am a first semester freshman currently taking calc. 1, so I have a very elementary understanding of more advanced mathematics.

by **doogly** » Fri Nov 27, 2009 10:44 pm UTC

What exact purpose do you want these books for?
For technical details, your course books are probably quite fine. Spivak has a very rigorous calc / intro analysis book, that might be a great one to pick up. I do quite like his style. And if you want a good overview, I've heard the Princeton Companion to Mathematics highly recommended.

by **Luca_Tortuga** » Sat Nov 28, 2009 1:13 am UTC

doogly wrote:What exact purpose do you want these books for?
For technical details, your course books are probably quite fine. Spivak has a very rigorous calc / intro analysis book, that might be a great one to pick up. I do quite like his style. And if you want a good overview, I've heard the Princeton Companion to Mathematics highly recommended.

I want to increase the depth of my understanding of math, for personal enjoyment, and also as a way to expand my skill set in the field of physics.
Thank you for the recommendation.
Do you have any recommendations for books on fractal geometry and complex analysis?

by **doogly** » Sat Nov 28, 2009 2:00 am UTC

Just make sure to actually pound out the problems, don't just leaf through the statements of theorems!
I don't really know a good fractals book. I think until you have some heavy analysis under your belt, the books on it are mostly of the "they're pretty and neat" variety.
Complex analysis also, sadly, no. I can tell you that Churchill's is boring and uninsightful, that was the one we used in our undergrad course.

by **Luca_Tortuga** » Sat Nov 28, 2009 6:03 pm UTC

doogly wrote:Just make sure to actually pound out the problems, don't just leaf through the statements of theorems!
I don't really know a good fractals book. I think until you have some heavy analysis under your belt, the books on it are mostly of the "they're pretty and neat" variety.
Complex analysis also, sadly, no. I can tell you that Churchill's is boring and uninsightful, that was the one we used in our undergrad course.

Most certainly I need to work alongside the book =].
I'm actually probably going to use these books are part of independent study courses as to get as many math credits as I can.

by **doogly** » Sun Nov 29, 2009 4:33 am UTC

I think the next thing you should look at is probably linear algebra. A bunch of books have mentioned here, I have no particular favorite myself, but that is something you may want to get into asap. And you could get going with it while you are still progressing through calculus, though there is probably a regular course and no need for an independent study, but your situation may vary.

by **Alpha Omicron** » Sun Nov 29, 2009 4:41 am UTC

534n wrote:I understand these topics and can integrate and ~~derivate~~ differentiate, [...]

FFS.

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