Math Books
Moderators: gmalivuk, Moderators General, Prelates
Re: Math Books
I'm asking for opinions on Cartan's Elementary Theory of Analytic Functions of One or Several Complex Variables and what books one thinks one should read in preparation for its study. Unfortunately, my introductory complex analysis course will be using it as a text next semester, so I'm desperately flinging myself through Topology (Munkres), Baby Rudin, Algebra (MacLane), Algebra (Artin), Naive Set Theory (Halmos, soon to become Set Theory by [Hausdorff]) and the professor's lecture notes he put online through the next three weeks.
Obviously I'm not going to get superfar through any of those books, but I've been making some good progress thus far and it'll be even easier once Christmas is past. The professor in question seems to be in love with category theory, order theory, and weird filternet interactions, so I'm brushing up on those. Mostly, I'm working on building up a certain intuition with a number of structures, which are coming much easier nowadays but are still not exactly friendly.
I've taken linear algebra (I really don't know this well, though), abstract algebra, metric differential geometry, an incompleteness/undecidability course, discrete math, game theory, calculus of all stripes, and real analysis. Most of those subjects are somewhat less than solid at this point, but then... what can one do. I'm about to be a secondsemester sophomore (long story involving withdrawing midsemester last time I tried secondsemester sophomorehood).
Anyway, any advice is helpful =/
Obviously I'm not going to get superfar through any of those books, but I've been making some good progress thus far and it'll be even easier once Christmas is past. The professor in question seems to be in love with category theory, order theory, and weird filternet interactions, so I'm brushing up on those. Mostly, I'm working on building up a certain intuition with a number of structures, which are coming much easier nowadays but are still not exactly friendly.
I've taken linear algebra (I really don't know this well, though), abstract algebra, metric differential geometry, an incompleteness/undecidability course, discrete math, game theory, calculus of all stripes, and real analysis. Most of those subjects are somewhat less than solid at this point, but then... what can one do. I'm about to be a secondsemester sophomore (long story involving withdrawing midsemester last time I tried secondsemester sophomorehood).
Anyway, any advice is helpful =/
Come visit the Bay12 Mafia subforum: http://www.bay12forums.com/smf/index.php?board=20.0
Re: Math Books
I think you might be panicking prematurely, especially with the background you already have.
Edit: If you want a slower paced book for reference, Brown & Churchill's Complex Variables with Applications is excellent, though it has different ordering of topics.
Edit: If you want a slower paced book for reference, Brown & Churchill's Complex Variables with Applications is excellent, though it has different ordering of topics.
Last edited by GyRo567 on Mon Jan 03, 2011 2:55 am UTC, edited 1 time in total.
I came here to read a cool post, a witty dialogue, a fresh joke, but stumbled upon a "bump"...
Way to go, jerk... ~CordlessPen
Way to go, jerk... ~CordlessPen
Re: Math Books
GyRo567 wrote:I think you might be panicking prematurely, especially with the background you already have.
I think I agree with you. Studying has calmed me down significantly.
Anyway, thanks for this.
Come visit the Bay12 Mafia subforum: http://www.bay12forums.com/smf/index.php?board=20.0
Re: Math Books
I guess this is a bit late, but I looked at the book on Google Books. I have to say that I think it is kind of strange, and I don't really like it very much. Judging from the pages I looked at, I do not think that there are many prerequisites for reading it (except a willingness to fight through Cartan's unnecessary and obfuscating Bourbakicity, and to look up the algebraic and topological concepts when necessary).
But it's possible that I looked only at the easy pages.
But it's possible that I looked only at the easy pages.
Re: Math Books
Yeah, the professor in question is kind of... weird... and Bourbaki's works have a certain impenetrability I've stumbled into before (albeit briefly). I can't understand anything they write without writing it out myself, along with copious sidenotes and explanations of where they're going with each step.
That laconic French style... *brrr*
Anyway, thanks for your input, as well. As I've been studying topology and algebra with some intensity over the last bit, I suppose I'll just hold onto my confidence and go for it.
That laconic French style... *brrr*
Anyway, thanks for your input, as well. As I've been studying topology and algebra with some intensity over the last bit, I suppose I'll just hold onto my confidence and go for it.
Come visit the Bay12 Mafia subforum: http://www.bay12forums.com/smf/index.php?board=20.0
 existential_squirrrel
 Posts: 401
 Joined: Mon Jun 14, 2010 3:57 pm UTC
 Location: San Rafael, CA
Re: Math Books
Has anyone on the forum had experience with using A Transition to Advanced Mathematics, 7th Edition?
courage is about knowing when to pick yourself up and whisper to yourself, "I will try again tomorrow"
http://http://stats.freedc.org/cpidtagb.php?cpid=f0b63432195be1a8665b08c414e36545&theme=12&cols=1
http://http://stats.freedc.org/cpidtagb.php?cpid=f0b63432195be1a8665b08c414e36545&theme=12&cols=1
 doogly
 Dr. The Juggernaut of Touching Himself
 Posts: 5321
 Joined: Mon Oct 23, 2006 2:31 am UTC
 Location: Somerville, MA
 Contact:
Re: Math Books
I have no experience with it at all, but I'm guessing from the "7th edition" it's crappy.
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
 existential_squirrrel
 Posts: 401
 Joined: Mon Jun 14, 2010 3:57 pm UTC
 Location: San Rafael, CA
Re: Math Books
doogly wrote:I have no experience with it at all, but I'm guessing from the "7th edition" it's crappy.
or rewritten / reworded to keep up with the times.
courage is about knowing when to pick yourself up and whisper to yourself, "I will try again tomorrow"
http://http://stats.freedc.org/cpidtagb.php?cpid=f0b63432195be1a8665b08c414e36545&theme=12&cols=1
http://http://stats.freedc.org/cpidtagb.php?cpid=f0b63432195be1a8665b08c414e36545&theme=12&cols=1
 doogly
 Dr. The Juggernaut of Touching Himself
 Posts: 5321
 Joined: Mon Oct 23, 2006 2:31 am UTC
 Location: Somerville, MA
 Contact:
Re: Math Books
You don't appear to be cynical enough yet. Let me introduce you to my friend, the publishing industry!
That book purports to introduce one to things like analysis and algebra. For comparison, the standard algebra text, Dummitt and Foote, has had three editions in over twenty years. The standard analysis text, Rudin, has had three editions in something like forty years. Seven editions in ten years? This is a warning sign.
That book purports to introduce one to things like analysis and algebra. For comparison, the standard algebra text, Dummitt and Foote, has had three editions in over twenty years. The standard analysis text, Rudin, has had three editions in something like forty years. Seven editions in ten years? This is a warning sign.
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Re: Math Books
Is Elementary Linear Algebra by Howard Anton a good book for beginning Linear Algebra?
Re: Math Books
Mike_Bson wrote:Is Elementary Linear Algebra by Howard Anton a good book for beginning Linear Algebra?
I've looked through it a little bit, and it is not the best. It's an expensive book but I really liked the book that I used for my Linear Algebra class (Elementary Linear Algebra by Larson and Falvo). That said, other users in this thread have suggested texts on linear algebra which are more affordable and probably better than the book by Larson and Falvo.
For example, this one which was recommended by Other_Calvin: http://joshua.smcvt.edu/linearalgebra/
 Marbas
 Posts: 1169
 Joined: Mon Jun 04, 2007 4:01 am UTC
 Location: Down down down at the bottom of the sea
 Contact:
Re: Math Books
So, after doing Measure Theory and such things, I want more analysis stuff. I have already gone through Royden, now I don't know where to go next. What kind of book would be good if I want to learn about things like Sobolev spaces? And other things in analysis? I know functional analysis is a place I can possibly go, what else is out there?
Jahoclave wrote:Do you have any idea how much more fun the holocaust is with "Git er Done" as the catch phrase?

 Posts: 10
 Joined: Mon Nov 22, 2010 10:40 am UTC
Re: Math Books
Marbas wrote:So, after doing Measure Theory and such things, I want more analysis stuff. I have already gone through Royden, now I don't know where to go next. What kind of book would be good if I want to learn about things like Sobolev spaces? And other things in analysis? I know functional analysis is a place I can possibly go, what else is out there?
You have a few options. If you want more "pure" analysis, I would get a text on functional analysis. Rudin's Functional Analysis is excellent but lacks any sort of motivation. Lax's book covers an incredible range of topics, but can be tough as a first exposure. I've heard Conway's Course in Functional Analysis is great, but I haven't read it myself.
A second option in pure analysis is Fourier analysis (or harmonic analysis). If you feel comfortable enough with real analysis, Duoandikoetxea's Fourier Analysis is excellent. Nothing is required beyond basic real and complex analysis, but you get into some very deep material rather quickly.
If you really liked the measure theory aspect of analysis, there is the subject of geometric measure theory, which has applications ranging from PDEs to the Plateau problem (see Wikipedia). The book by Morgan is very good, as is the book by Krantz (Geometric Integration Theory).
You could also try a different area of math in which you would use the analysis you learned. Obvious choices are ODE, PDE, and differential geometry. My personal specialization is analytic number theory, which uses analysis to study problems in number theory.

 Posts: 77
 Joined: Tue Aug 11, 2009 9:17 pm UTC
 Location: Champaign, IL
Re: Math Books
I'll elaborate on forgetful functor's suggestions about functional analysis, because, well, I'm a functional analyst.
While it's probably possible to learn functional analysis from Rudin's book, I feel like that's a tough route. Conway's book is a good suggestion; while I may not always love his writing, he takes an interesting approach to presenting functional analysis. He begins by developing the basic ideas of functional analysis in Hilbert spaces, where they're simplest, then generalizes those ideas to Banach spaces, where they're slightly more complicated, then generalizes to locally convex spaces, where they're again slightly more complicated. He finishes off with a decent treatment of the basic theory of operator algebras (which appeals to me bc I'm an operator algebraist). After you feel comfortable with a topic, Rudin is a great place to read about it in more depth. He generally deals with topological vector spaces from the very beginning, and proves a lot of the same theorems you'll find in Conway for Hilbert or Banach spaces in a great deal more generality.
While it's probably possible to learn functional analysis from Rudin's book, I feel like that's a tough route. Conway's book is a good suggestion; while I may not always love his writing, he takes an interesting approach to presenting functional analysis. He begins by developing the basic ideas of functional analysis in Hilbert spaces, where they're simplest, then generalizes those ideas to Banach spaces, where they're slightly more complicated, then generalizes to locally convex spaces, where they're again slightly more complicated. He finishes off with a decent treatment of the basic theory of operator algebras (which appeals to me bc I'm an operator algebraist). After you feel comfortable with a topic, Rudin is a great place to read about it in more depth. He generally deals with topological vector spaces from the very beginning, and proves a lot of the same theorems you'll find in Conway for Hilbert or Banach spaces in a great deal more generality.
Re: Math Books
I took calculus 3 (multivariable and vector calculus) two semesters ago and I didn't quite get all that I wanted out of it as the professor was kind of soft on us. Is there a book that covers calculus 3 stuff with quite a bit of rigor? Preferably a book that just covers multivariable and vector calculus as my knowledge of single variable calculus is sufficient. I still remember a bit from the class so it doesn't need to be a textbook that spoonfeeds me things and I think I should brush up on the subject before I take an analysis class at my university where I would have to prove things I've either never learned or don't know in detail.
 doogly
 Dr. The Juggernaut of Touching Himself
 Posts: 5321
 Joined: Mon Oct 23, 2006 2:31 am UTC
 Location: Somerville, MA
 Contact:
Re: Math Books
If you want to brush up on things, something like Div, Grad, Curl and All That covers the computation. But for rigor, you approach things from a different sort of perspective. It becomes important to distinguish between differential forms and vectors, and it's generally done in the context of manifolds rather than just R^n. Munkres and Spivak have some great books on this subject. (or at least, in the case of Munkres, canonical. I haven't used it myself so should reserve personal endorsement as great.)
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Re: Math Books
doogly wrote:If you want to brush up on things, something like Div, Grad, Curl and All That covers the computation. But for rigor, you approach things from a different sort of perspective. It becomes important to distinguish between differential forms and vectors, and it's generally done in the context of manifolds rather than just R^n. Munkres and Spivak have some great books on this subject. (or at least, in the case of Munkres, canonical. I haven't used it myself so should reserve personal endorsement as great.)
I've seen Div, Grad, Curl and All That mentioned in this thread before but I can't find the table of contents and it seems to be a book more geared towards scientists and engineers which might make it worth picking it up but it's not what I'm looking for right now. In my calculus 3 course we used McCallum, HughesHallett, et al. but I didn't really like it as the examples weren't good and now that I remember, the theory in it is quite light. I also have Stewart's book which is very good for learning it but the theory in it is even lighter than McCallum's text. Basically what I'm looking for is a book that is more rigorous than Stewart's and McCallum's book (in terms of theory) but less rigorous than a real analysis text. From the few that I've seen so far, Lang's text seems to fit the bill but I'm not entirely sure about that. I don't quite think I'm ready for differential forms stuff as of yet or at least Spivak's as I've read that it's dense reading to say the least.
 doogly
 Dr. The Juggernaut of Touching Himself
 Posts: 5321
 Joined: Mon Oct 23, 2006 2:31 am UTC
 Location: Somerville, MA
 Contact:
Re: Math Books
Yeah, I don't think a level of rigor exists between calc 3 and calc on manifolds. Maybe take a look at the Munkres book? Same sort of stuff as the Spivak but decompressed.
You're probably ready for those things if you've also had some linear algebra. It's tricky but fun stuff.
You're probably ready for those things if you've also had some linear algebra. It's tricky but fun stuff.
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?

 Posts: 638
 Joined: Thu Jan 27, 2011 5:23 pm UTC
Re: Math Books
Could you please help me find a precalculus book with the most difficult exercises available? Or a good online resource for difficult problems.
The precalculus course I'm taking at my high school is extremely competitive and I can't find any books with problems at the level of the quizzes/exams we'll be taking.
Here are some sample problems to give you a feel for the problems.
1. Suppose the lines ax+by+c=0 and dx+ey+f=0 intersect at the point (p,q). Show that every equation of the line that passes through (k,l) can be expressed as m(ax+by+c)+n(dx+ey+f)=0 where m,n are constants.
2. Let the distance between two points (x1,y1) and (x2,y2) be defined as d = (x1x2)^2 + y1y2.
Graph a circle centered at the origin with a radius of 3.
The precalculus course I'm taking at my high school is extremely competitive and I can't find any books with problems at the level of the quizzes/exams we'll be taking.
Here are some sample problems to give you a feel for the problems.
1. Suppose the lines ax+by+c=0 and dx+ey+f=0 intersect at the point (p,q). Show that every equation of the line that passes through (k,l) can be expressed as m(ax+by+c)+n(dx+ey+f)=0 where m,n are constants.
2. Let the distance between two points (x1,y1) and (x2,y2) be defined as d = (x1x2)^2 + y1y2.
Graph a circle centered at the origin with a radius of 3.
Mighty Jalapeno wrote:Tyndmyr wrote:Роберт wrote:Sure, but at least they hit the intended target that time.
Well, if you shoot enough people, you're bound to get the right one eventually.
Thats the best description of the USA ever.
Re: Math Books
Unfortunately, I don't know of any good precalculus books. Maybe just try working through math competition problems to get a grasp on problemsolving?
Does anybody know of any good introduction to combinatorics books? All that I know of combinatorics is basically fuzzy notions from algebra 2 of what a combination and permutation is.
Does anybody know of any good introduction to combinatorics books? All that I know of combinatorics is basically fuzzy notions from algebra 2 of what a combination and permutation is.
Re: Math Books
To be honest, looking at those problems makes me think that you aren't quite understanding how they workthat is, by applying principles you should understand from other problems in new ways.
Try going through the process you'd use for the "usual" version on those problems, and see what happens. You may find that your main problem is anxiety visavis new things, rather than actual lack of knowledge.
I hope I'm being helpful, rather than trivializing your troubles in some sense =/
Rosen's book on discrete mathematics is a nice introduction, I thought. If you're more interested in graph theory, there's always Bollobas and so on.
Try going through the process you'd use for the "usual" version on those problems, and see what happens. You may find that your main problem is anxiety visavis new things, rather than actual lack of knowledge.
I hope I'm being helpful, rather than trivializing your troubles in some sense =/
ahazaq2 wrote:Does anybody know of any good introduction to combinatorics books? All that I know of combinatorics is basically fuzzy notions from algebra 2 of what a combination and permutation is.
Rosen's book on discrete mathematics is a nice introduction, I thought. If you're more interested in graph theory, there's always Bollobas and so on.
Come visit the Bay12 Mafia subforum: http://www.bay12forums.com/smf/index.php?board=20.0
Re: Math Books
In a few weeks, I'm going to attending a math team state competition. One of the tests I'll be taking is on the History of Prime Numbers. Does anyone have any good books, or internet sources, that I could read that covers prime numbers well?
Re: Math Books
Kurushimi wrote:In a few weeks, I'm going to attending a math team state competition. One of the tests I'll be taking is on the History of Prime Numbers. Does anyone have any good books, or internet sources, that I could read that covers prime numbers well?
The Prime Pages at the University of Tennessee at Martin.
http://primes.utm.edu/

 Posts: 272
 Joined: Thu Jul 09, 2009 9:26 am UTC
Re: Math Books
Can't say I've personally read it, but Music of the Primes by Marcus Du Sautoy sounds like it would fit the bill.
Re: Math Books
greengiant wrote:Can't say I've personally read it, but Music of the Primes by Marcus Du Sautoy sounds like it would fit the bill.
I've read it, and yeah, it would be absolutely perfect.
Come visit the Bay12 Mafia subforum: http://www.bay12forums.com/smf/index.php?board=20.0
Re: Math Books
Does anyone know a good LaTex book covering some basic stuff like text formatting, maths formatting, figures and drawing with TikZ?
God does not care about our mathematical difficulties — He integrates empirically.
—Albert Einstein
—Albert Einstein
 jestingrabbit
 Factoids are just Datas that haven't grown up yet
 Posts: 5963
 Joined: Tue Nov 28, 2006 9:50 pm UTC
 Location: Sydney
Re: Math Books
Most of those are in lshort.pdf, but not TikZ.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.
Re: Math Books
Can anyone give me any suggestions for a good problem based calculus book? I already have Calculus (3th Ed) by Michael Spivak; which I really like, but would love to have a few more problems to work with (in the same style) for pretty much every chapter. In other words... I guess I'm looking for a book much like the one I have, but with more or different problems.
Thanks in advance!
Thanks in advance!
 Metaphysician
 Posts: 519
 Joined: Tue Apr 12, 2011 10:58 pm UTC
 Location: WV, The Tenth Circle of Hell
Re: Math Books
Hello everybody, this is my first post here on xkcd. I've recently started to become very interested in mathematics. My experience with math is limited. I coasted through Algebra 2 and Trig in highschool and never pursued any further knowledge in math as I've always been more interested in philosophy, literature and language. I dropped out of college for financial reasons and never had the opportunity to take any of the mathematics electives I was interested in. As I've studied philosophy over the years I've begun to realize how much philosophy draws from the mathematical world. Thus, I have decided to construct a math curriculum for myself. I have no illusions of becoming an influential mathematician or even entering a profession requiring copious practical application of mathematics or pursuing mathematics as anything more than a hobby. I'm simply a 26 year old college dropout philosophy junkie that desires understanding for the sake of understanding. Now, I have read through most of this thread and compiled a tentative reading list to start out with and would like some input on my selections. I'm basically looking for an idea of what may be within my reach and what may be too advanced and obviously any suggestions if you feel I'm missing something... well honestly any advice would be great at this point as the world of math is massive and I have no idea where to start. I believe most of my selections are more about the philosophy of math rather than actual instructional texts so any input on instructional texts (preferably texts that focus on explaining the theory and underlying thought process behind the techniques rather than just saying "here is how you solve this or that type of problem") would be helpful. My tentative reading list is as follows.
A Mathematician’s Apology by G.H. Hardy
Mathematics: A Very Short Introduction by Timothy Gowers
Makers of Mathematics by Hollingdale
Fermat’s Last Theorem by Simon Singh
Does God Play Dice by I. Stewart
From Here to Infinity by Ian Stewart
Solving Mathematical Problems by Terence Tao
What is Mathematics? by R. Courant and H. Robbins
Beyond Numeracy by J.A. Paolos
Chaos by J. Gleik
EDIT: And after doing some research, I find that my Algebra is incredibly rusty after eight years of nonuse.
A Mathematician’s Apology by G.H. Hardy
Mathematics: A Very Short Introduction by Timothy Gowers
Makers of Mathematics by Hollingdale
Fermat’s Last Theorem by Simon Singh
Does God Play Dice by I. Stewart
From Here to Infinity by Ian Stewart
Solving Mathematical Problems by Terence Tao
What is Mathematics? by R. Courant and H. Robbins
Beyond Numeracy by J.A. Paolos
Chaos by J. Gleik
EDIT: And after doing some research, I find that my Algebra is incredibly rusty after eight years of nonuse.
 doogly
 Dr. The Juggernaut of Touching Himself
 Posts: 5321
 Joined: Mon Oct 23, 2006 2:31 am UTC
 Location: Somerville, MA
 Contact:
Re: Math Books
You are going to have to soldier on through some frustrating math then. If your algebra is rusty and you want to deal with 'the theory behind' it, it won't work. Algebra, trig, these are things that require drilling. Pieces of paper with lots of repetitive problems, and you solve them all. I'm not sure there is any way around this.
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
 Metaphysician
 Posts: 519
 Joined: Tue Apr 12, 2011 10:58 pm UTC
 Location: WV, The Tenth Circle of Hell
Re: Math Books
doogly wrote:You are going to have to soldier on through some frustrating math then. If your algebra is rusty and you want to deal with 'the theory behind' it, it won't work. Algebra, trig, these are things that require drilling. Pieces of paper with lots of repetitive problems, and you solve them all. I'm not sure there is any way around this.
Ah, well, in that case, any suggestions as to what resources would be best for brushing up then?
What should young people do with their lives today? Many things, obviously. But the most daring thing is to create stable communities in which the terrible disease of loneliness can be cured.
Kurt Vonnegut
Kurt Vonnegut
Re: Math Books
I got a copy of Introduction to LOGIC, 2nd Edition, by Irving M. Copi from a used book sale from my library. Is this book any good?
 doogly
 Dr. The Juggernaut of Touching Himself
 Posts: 5321
 Joined: Mon Oct 23, 2006 2:31 am UTC
 Location: Somerville, MA
 Contact:
Re: Math Books
Metaphysician wrote:doogly wrote:You are going to have to soldier on through some frustrating math then. If your algebra is rusty and you want to deal with 'the theory behind' it, it won't work. Algebra, trig, these are things that require drilling. Pieces of paper with lots of repetitive problems, and you solve them all. I'm not sure there is any way around this.
Ah, well, in that case, any suggestions as to what resources would be best for brushing up then?
It's not stuff I've looked at in a while, but basically anything with a lot of problems should do the trick. You just need to be very solid on algebra and trig, and some essential function stuff. Plotting things. I don't have any specific books I know of for these things.
If you enjoy geometry, there are books like "Elementary Geometry from an Advanced Standpoint," by Moise. That might be a good one for you. It does cover everything you need, but it is a little more sophisticated about why everything is happening.
Felix Klein, a 19th century super star, wrote "Elementary Mathematics from an Advanced Standpoint," with an algebra/analysis volume and a geometry volume. These also have the benefits of being cheap.
http://www.amazon.com/ElementaryMathem ... pd_sim_b_1
And Gelfand wrote some elementary books. One of the greatest beasts of the 20th century will go over trig for you. This is crazy.
http://www.amazon.com/TrigonometryIM ... pd_sim_b_6
http://www.amazon.com/FunctionsGraphs ... pd_sim_b_5
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
 Metaphysician
 Posts: 519
 Joined: Tue Apr 12, 2011 10:58 pm UTC
 Location: WV, The Tenth Circle of Hell
Re: Math Books
doogly wrote:Metaphysician wrote:doogly wrote:You are going to have to soldier on through some frustrating math then. If your algebra is rusty and you want to deal with 'the theory behind' it, it won't work. Algebra, trig, these are things that require drilling. Pieces of paper with lots of repetitive problems, and you solve them all. I'm not sure there is any way around this.
Ah, well, in that case, any suggestions as to what resources would be best for brushing up then?
It's not stuff I've looked at in a while, but basically anything with a lot of problems should do the trick. You just need to be very solid on algebra and trig, and some essential function stuff. Plotting things. I don't have any specific books I know of for these things.
If you enjoy geometry, there are books like "Elementary Geometry from an Advanced Standpoint," by Moise. That might be a good one for you. It does cover everything you need, but it is a little more sophisticated about why everything is happening.
Felix Klein, a 19th century super star, wrote "Elementary Mathematics from an Advanced Standpoint," with an algebra/analysis volume and a geometry volume. These also have the benefits of being cheap.
http://www.amazon.com/ElementaryMathematicsAdvancedStandpointArithmetic/dp/048643480X/ref=pd_sim_b_1
And Gelfand wrote some elementary books. One of the greatest beasts of the 20th century will go over trig for you. This is crazy.
http://www.amazon.com/TrigonometryIMGelfand/dp/0817639144/ref=pd_sim_b_6
http://www.amazon.com/FunctionsGraphsDoverBooksMathematics/dp/0486425649/ref=pd_sim_b_5
These look pretty much perfect for me, I'll check them out. Hopefully I won't be embarrassingly ignorant on this subject for much longer. Thanks for helping a n00b out
What should young people do with their lives today? Many things, obviously. But the most daring thing is to create stable communities in which the terrible disease of loneliness can be cured.
Kurt Vonnegut
Kurt Vonnegut

 Posts: 2
 Joined: Wed Mar 30, 2011 3:58 pm UTC
Re: Math Books
Hello,
I am looking for a Statistics and Probability book. Now, the problem is, I don't know how 'advanced' the course is I am taking. We covered basic data collection and stats in 23 lectures and went on to probability (permutations etc) through normal distributions, z/t scores and test, and ending now with Null Hypotheses and tests associated with them with paired tests being last. If anybody could recommend a good book for review (for my final), I would appreciate it. I have a decent understanding of most topics but would like to have another explanation for them to see if I missed anything. I suspect that a intro book should be enough, but I don't know for sure if those don't stay with Statistics too long and don't cover Probability enough.
I am looking for a Statistics and Probability book. Now, the problem is, I don't know how 'advanced' the course is I am taking. We covered basic data collection and stats in 23 lectures and went on to probability (permutations etc) through normal distributions, z/t scores and test, and ending now with Null Hypotheses and tests associated with them with paired tests being last. If anybody could recommend a good book for review (for my final), I would appreciate it. I have a decent understanding of most topics but would like to have another explanation for them to see if I missed anything. I suspect that a intro book should be enough, but I don't know for sure if those don't stay with Statistics too long and don't cover Probability enough.
 doogly
 Dr. The Juggernaut of Touching Himself
 Posts: 5321
 Joined: Mon Oct 23, 2006 2:31 am UTC
 Location: Somerville, MA
 Contact:
Re: Math Books
Metaphysician wrote:These look pretty much perfect for me, I'll check them out. Hopefully I won't be embarrassingly ignorant on this subject for much longer. Thanks for helping a n00b out
They looked good to me, but I'm not intimately familiar with them, so if they work well for you let the thread know!
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Re: Math Books
Hi,
I am looking to develop my mathematical mind as much as possible. The "highest" classes I have taken are Calculus I & II as well as linear algebra. I'd be looking for either a bunch of books or some sort of guide (similar to the guide "How to become a good theoretical physicist" for physics) that ranges from algebra up to topology, complex analysis and partial differential equations.
Basically, I want to master as much of the mathematical field as I can. I'd also be interested in a book (if any exists) that teaches maths at the same time as physics, as I think that learning one reinforces the other. (Is that what's called "Mathematical physics"?)
Thank you.
I am looking to develop my mathematical mind as much as possible. The "highest" classes I have taken are Calculus I & II as well as linear algebra. I'd be looking for either a bunch of books or some sort of guide (similar to the guide "How to become a good theoretical physicist" for physics) that ranges from algebra up to topology, complex analysis and partial differential equations.
Basically, I want to master as much of the mathematical field as I can. I'd also be interested in a book (if any exists) that teaches maths at the same time as physics, as I think that learning one reinforces the other. (Is that what's called "Mathematical physics"?)
Thank you.
 doogly
 Dr. The Juggernaut of Touching Himself
 Posts: 5321
 Joined: Mon Oct 23, 2006 2:31 am UTC
 Location: Somerville, MA
 Contact:
Re: Math Books
Mathematical physics is a whole branch of research. It's what I do! It is physics where you prove things. Formal results about quantum field theory, statistical mechanics, dynamical systems, general relativity, etc. These are the people whose eyes light up at "exact solutions." That sort of thing.
You've got some more calc type things ahead of you. Some vector calc, most likely  Div, Grad, Curl and All That, sort of thing. If you get some Purcell, Griffiths or Marion and Heald for electromagnetism, that should help out a bunch with the vectors in physics. And also in Heald you'll see some Fourier analysis peeking in, which is another great place to go next. The awesomest of partial differential equations, totally. I don't know a good PDE textbook.
Korner's book looks great for Fourier, actually. Might be worth a look.
These sorts of things are better considered "mathematical methods," rather than "mathematical physics." Everyone in any branch of physics would need to know these sorts of things.
You've got some more calc type things ahead of you. Some vector calc, most likely  Div, Grad, Curl and All That, sort of thing. If you get some Purcell, Griffiths or Marion and Heald for electromagnetism, that should help out a bunch with the vectors in physics. And also in Heald you'll see some Fourier analysis peeking in, which is another great place to go next. The awesomest of partial differential equations, totally. I don't know a good PDE textbook.
Korner's book looks great for Fourier, actually. Might be worth a look.
These sorts of things are better considered "mathematical methods," rather than "mathematical physics." Everyone in any branch of physics would need to know these sorts of things.
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Re: Math Books
As far as I can tell, almost all the math I've ever found myself using over the majority of the physics half of my degree has been covered in Boa's "Mathematical methods in the Physical Sciences".
It's also made most of the math courses I was obligated to take redundant, as my course equivalent of mathematical boot camp was taught primarily out of that book. It's not always where I've directly learned from, as most of the courses have their own book (indeed, most of my vector calculus came in the context of griffiths electrodynamics), but it seems to have everything in there and then some, so if you want a whackload of physics practical math in one book, it's well suited. It's generally not been my favourite book, but it gets the job done.
It's also made most of the math courses I was obligated to take redundant, as my course equivalent of mathematical boot camp was taught primarily out of that book. It's not always where I've directly learned from, as most of the courses have their own book (indeed, most of my vector calculus came in the context of griffiths electrodynamics), but it seems to have everything in there and then some, so if you want a whackload of physics practical math in one book, it's well suited. It's generally not been my favourite book, but it gets the job done.
 doogly
 Dr. The Juggernaut of Touching Himself
 Posts: 5321
 Joined: Mon Oct 23, 2006 2:31 am UTC
 Location: Somerville, MA
 Contact:
Re: Math Books
Yeah, I am usually unhappy with that sort of cookbook approach. I don't like to learn math and physics at the same time; I like math a la mathematicians, and physics a la physicists. Math as a pure tool just made it boring and confusing. But I am a minority among physics folk; most of them do not like abstractions as much as applications, and don't want to talk about math unless it "means something."
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Who is online
Users browsing this forum: No registered users and 6 guests