I'm taking a euclidean and plane geometry course and the bibliography given to us is scarce. The course covers the next topics: Trigonometry Coordinate systems Inversion in a circle Poles and polars Extension of the plane Transformations of the plane Would you recommend me books that covers such topics? It's important to mention that the course is mostly proof-based
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I consider myself relatively good at math, though I don't know it at a high level (yet). One of my problems is that I'm not very comfortable with geometry, unlike algebra, or to restate, I'm much more comfortable with algebra than geometry. I think that's mainly because my geometry education was sparse through the years, lacking in consistency etc. So I'd like to revise (and learn more) all at once, catching the basic axioms, understanding why such is such, etc. Essentially, a moderately rigorous textbook in plain Euclidean geometry (nothing fancy). Please don't say "The Elements" - I have browsed it at the bookstore, it is quite good, but not really what I'm looking for right now.
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I went through this thread on  asking about a text on number theory, but my question is slightly different.   I was looking for a short and sweet book on elementary number theory. I don't need it to be a definitive treatise on number theory. I just need to have book which covers enough material to advance to algebraic number theory. I have looked at the books by Niven-Zuckerman-Montgomery and the Jones' and the one by Burton. All of them were very readable and I would like to read at least one of them at some point. For now, I would just like a book (say 100 pages long) which can get me acquainted with most of the material needed for algebraic number theory. Basically there is a course on algebraic number theory that I wish to take which begins in a month's time and I have not done enough elementary number theory.
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I plan to self-study linear algebra this summer. I am sorta already familiar with vectors, vector spaces and subspaces and I am really interested in everything about matrices (diagonalization, ...), linear maps and their matrix representation and eigenvectors and eigenvalues. I am looking for a book that handles every of the aforementioned topics in details. I also want to build a solid basis of the mathematical way of thinking to get ready to an exciting abstract algebra next semester, so my main aim is to work on proofs for somehow hard problems. I got Lang's "Intro. to Linear Algebra" and it is too easy, superficial.  Can you advise me a good book for all of the above? Please take into consideration that it is for self-study, so that it' gotta work on its own. Thanks.
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Ok so I read the following article the other day:  and I wanted to learn more about lie groups. Using my exceptional deduction skills I thought "oh it must have something to do with groups" So I picked up a copy of Dummit and Foote's book on abstract algebra and skimmed through it. It didn't say anything about Lie groups however. $E_8$ is coming to be rather famous so maybe other people are interested in this question too. Lets suppose I wanted to learn about lie groups. What books should I read to be ready to learn about Lie groups and what is a good book that talks about Lie groups. I'm guessing its a combination of group theory (representation theory in specific) and also differential geometry. Is this correct? Thank you very much for your time.
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Possible Duplicate:          I'm looking for a good book on commutative algebra covering most of (but not limited to) :   Basic Galois theory and Module algebra Primary decomposition of ideals Zariski topology Nullstellensatz, Hauptidealsatz Noether's normalization Ring extensions "Going up" and "Going down"   The emphasis is on the approach, as I would like a book giving a good geometric intuition of ring theory that I could use as a solid basis to start learning algebraic geometry.  All in all, do you remember a book that gave you a deeper geometric insight of commutative algebra ?
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I am a student of 11th grade and i have completed the syallabus of both 11th and 12th grade maths with complete understanding and it was possible coz of the love for this subject that i have. I don't want to sound "larger than life" here, but my curiousity has now increased to learn maths at a deeper level. As of now i am reading "Linear algebra done right" by Axler. Thats an amazing piece of work and now i truly understand what "matrix" is all about. I also want to extend my knowledge on the following topics :  1) Algebra (groups,subgroups,homomorphisms etc)   2) Analysis   3) Geometry/Topology  Why i am here is because i wanted you guys to recommend a book on each of the above topic that would be appropriate for a beginner like me (I must mention here I have been working on Apostol's volume 1 calculus, thats a great text, but for a beginner, its best if the concept is explained in a broad manner and in as simple and easy words as possible) . I just want a book which explains the concept broadly rather than coming to the conclusion directly (which is not a great sight for a beginner like me) .   Having said that, no book is complete i understand. Thats why i am asking your recommendation as you guys are aware which text would be the best to start with for a beginner. I have searched on the net about this, but there are dozens of works available, and out of them all , i want the one which is the best (approximation) for a beginner .   Please don't misunderstand me in any way. I am just confused which text to go for, and i understand the books which u may suggest may be for undergraduate level course as these topics are for undergraduate level courses, thats not a problem at all . I need a easy to learn (i mean easy in terms of "broad" explanation) book. I hope you guys don't mind me questioning such a question on this forum . Thanks for all the help you guys have been providing me on this forum . Maths Maths Maths... the world is beautiful coz of u! :))
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Is it possible to get into algebraic geometry by just knowing calculus and linear algebra or is this too far of a stretch?  If not could anyone give me a list of book/lecture notes recommendations in chronological order to dive into algebraic geometry with my state of knowledge?  Thanks
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I'm currently in my 3rd year of my undergrad in Mathematics and moving onto my 4th year next year. I took a course in Real Analysis I, but the professor was very confusing and we didn't use a textbook for the class (it was his lecture notes) which was also very confusing as well. Although I got a good mark in the course, I don't think I learned anything from the class since I felt like I memorized how to do the questions rather than actually understood the questions.   So I was wondering what would be a good textbook for real analysis. I'm okay with a textbook with rigorous proofs, as long as everything is explained in good detail.  At the same time, I also want to teach myself Topology. I wanted to take it this year, but there was a conflict and hence I could not take the course. So I was also looking for a textbook for an introduction to Topology.  Any kind of recommendations would be great! I really do want to learn analysis and topology.
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I'm a mathematics undergrad student who finished his first university year succesfully. For this post, it should be interesting to note that I already took a course in group theory.  I also had a course in linear algebra where we treated the following topics:  1) Vector spaces; basis; span; linear dependency; direct sum   2) Linear transformations, matrices, rank  3) Linear varieties, system of linear equations  4) Determinants  5) Eigenvalues and eigenvectors, diagonalisation, triangalisation, cayley-hamilton,  6) Euclidean spaces: inner products, norm, hermitian transformations, orthogonal basis, Gramm-Schmidt, orthogonal transformations  7) Prehilbert spaces  8) Isometries  9) Bilinear forms and quadrics in $2$ and $3$ dimensions  Now, I want to revise these topics, but it would be too boring to reread these books again, so now I look for a book that has all these topics, but also some additional requirements:   Focus on intuition (e.g. connections between linear algebra and geometry). This is a hard requirement for me, since there was no attention given to this in the course I took) Additional topics such as Jordan form of matrices, quotient vector spaces, ... Good exercises (preferred with solutions somewhere) The book must be rigorous   In the course I had, we mainly discussed finite-dimensional vector spaces, but I am also interested in a theory of infinite dimensional vector spaces.  Can someone hint me towards a good book that would suit me? If I have to add any information, please leave a comment and I will edit my post.  Thank you for your time.
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I've taken up self-study of math. (How smart can that be?) I've just about finished a course in real analysis which spent a lot of time on metric spaces and some time revisiting calculus.  I was thinking of trying abstract algebra. I would appreciate any book recommendations.  Thanks in advance.  Andrew
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I'm looking for a textbook or set of lecture notes on gauge theory for mathematicians that assumes only minimal background in physics. I'd prefer a text that uses more sophisticated mathematical concepts like principal bundles and connections, and categorical language whenever convenient.
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How am I to "[u]se induction to show that $n$ straight lines in the plane divide the plane into $\frac{n^2+n+2}{2}$ regions"? It is assumed here that no two lines are parallel and that no three lines have a common point. Further, this is not a non-Euclidean problem, but I wouldn't mind a discussion on the non-Euclidean nature of the problem.  I was thinking it might be easier to show using the unit sphere.    A GOOD REFERENCE I FOUND THAT WILL BE USEFUL TO ANYONE COMING ACROSS THIS PROBLEM IS Concrete Mathematics, Graham, Knuth, Patashnik pp. 4–8.
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I'm a PhD student in math and am really excited about celestial mechanics.  I was wondering if anyone could give me a roadmap for learning this subject. The amount of information about it on the internet is overwhelming, and I honestly don't know where I should start.  Any help would be greatly appreciated.
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I have a hazy notion of some stuff in differential geometry and a better, but still not quite rigorous understanding of basics of differential topology.  I have decided to fix this lacuna once for all. Unfortunately I cannot attend a course right now. I must teach myself all the stuff by reading books.  Towards this purpose I want to know what are the most important basic theorems in differential geometry and differential topology. For a start, for differential topology, I think I must read Stokes' theorem and de Rham theorem with complete proofs.   Differential geometry is a bit more difficult. What is a connection? Which notion should I use? I want to know about parallel transport and holonomy. What are the most important and basic theorems here? Are there concise books which can teach me the stuff faster than the voluminous Spivak books?  Also finally I want to read into some algebraic geometry and Hodge/Kähler stuff.  Suggestions about important theorems and concepts to learn, and book references, will be most helpful.
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I was wondering if you could tell me about some self-learning resources for linear model theories. My professor has been using "A First Course in Linear Model Theory, Ravishanker and Dey. Publisher: CRC." I found this kinda difficult. My major is mathematics. Thank you so much for your time!
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I tried to learn Algbraic Geometry through some texts, but by Commutative Algebra, I left the subject; many books give definitions and theorems in Commutative algebra, but do not explain why it is needed.  Can one suggest a good reference to learn this subject geometrically, which would also give ways to translate geometric ideas in algebraic manner, possibly through examples?  Particularly, I am interested in differentials on algebraic curves, Riemann-Roch theorem, various definitions of genus and their equivalences, and mainly groups related to complex algebraic curves such as group of automorphisms, monodromy group etc.
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I am reading now E. Soper, Classical Theory Of Fields, now and sometimes it is very hard to follow the equations. So I need a side book on  to read it comfortably. Landau &amp; Lifshitz's book is not helping as its content and topics are very much different.