Currently, I'm studying a little about geometry and I was trying to find out some good book about it on internet, however I didn't find anything that I thought nice to me or what I really expected to which would be nice. What I'm looking for is a book with good proofs, in which show strategies to you reach the solution. and interesting exercises.  For instance :    , ,  ...  Something about mostly elementary geometry, proprieties of triangles, parallels lines, circles, triangle inscribed in a circle, so on.
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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've been lurking on this site for several months, and as someone studying higher mathematics independently (i.e., outside of a college/institutional setting), this forum has probably been the best reference for gleaning general information about college-level math.  However, recently I've come to realize that few of the major/popular math textbooks tend to have solutions to the exercises contained within them or available for free/online. As someone without access to a professor or peers who can check the accuracy of my answers, working through book solutions becomes very tedious. How do I know if I am getting the right answers and thus understanding the material? I know people are encouraged to post here for help with challenging problems, but it doesn't seem appropriate to post in a forum such as this to simply check the veracity of answers. In addition, certain books (e.g., Pugh's Real Mathematical Analysis) contain hundreds of exercises throughout the text, and it would be neither plausible nor acceptable to constantly ask for help with problem after problem for an entire textbook.  I am not in school nor do I plan to enroll anytime soon, so there's not really an option of waiting until college to talk things over with someone more knowledgeable about mathematics. I am learning math out of pure curiosity and not in preparation for future classes or career goals, and while there are a plethora of resources available to the independent student of mathematics now more than ever before, being able to assess how well the material is being absorbed remains a difficult obstacle to overcome.
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Well I have not started calculus yet but I am really keen to. I would love if you suggest some books.  Points to be noted:   I really don't like the way textbooks are written so please no "textbooks"  I am COMPLETELY beginner in calculus. I know a little bit of trigonometry and what functions are but not really in depth.The book should start from the base, I mean really from the base. I may require a precalculus book too if the books don't cover that. I would really love if the book shows how calculus was developed, why it was developed and things like that.   Well,thanks in advance!
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Edit:  Ok, user  made comment that truly helps narrow the focus of my question. Basically, I'm asking for a self-study course of Mathematical Methods.  Thanks to his recommendation I identified a book that is very close to the answer:  Mathematical Methods in the Physical Sciences by Mary L. Boas  Supposedly, the book covers most of the Math a person needs to learn in order to understand the simulations I presented.  Does this book suit my needs?    Hello,  I have always been interested on the idea to study Math at an Undergraduate level to be able to implement simulations like the followings:  Finite Difference Simulation of the Wave Equation    Heat Equation in Two Dimensions    Besides my precollege experience in Math, I have only been able to do very simple simulations due to my lack of knowledge of Advanced Math. Every time I ask about the inner workings of the simulations I get redirected to papers that look like foreign language to me and, unfortunately, I depend on easy-to-read tutorials to understand them, and while I have found   I'm more interested in reaching the solution myself.  I checked some of the questions related to book recommendations for self-study and while they are very helpful I'm interested in learning by example (There is a book called: "Accelerated C++ Practical Programming by Example" that fits very well my study habits)  Thanks in advance.
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What are some of the best books on graph theory, particularly directed towards an upper division undergraduate student who has taken most the standard undergraduate courses? I'm learning graph theory as part of a combinatorics course, and would like to look deeper into it on my own. Thank you.
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Is there any good book on Electromagnetism from a more mathematical point of view? By this I mean a book which makes use of differential forms and maybe De Rham cohomology. I was also searching for something that would include E&amp;M in the big picture of Gauge theories.
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I'm looking for mathematics books, courses + exercises for high school level. My daughter was high school certificated but she has stopped her studies for 5 years. She would like to be involved in new educational program but she needs to restore her mathematic capabilities.  Could you help me to identify which mathematics books can help her?  Thanks a lot for your reply,  FR.
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I want to self-study some abstract algebra and cryptography during the summer, so what are some of books that are suitable for self-study? I have very limited background in algebra and none in cryptography, and like to learn by examples. Also, please let me know if there are any books on these subjects with solutions to most of the exercises, so I can check on myself. (I saw 's post about good algebra books, but I would like to focus more on those with good exercises and detailed solutions.)  All suggestions are welcome! Thank you!!
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I'm interested in learning physics. I do realize that the subject is large and that it would be easier if I had a specific area of interest. However, I do not. I suppose I want to learn about the fundamentals of it all; the axioms that combine all physics fields. Or, in other words, a high school physics class.   Specifically, a book or series of videos would be helpful. I looked over MIT and unfortunately the material wasn't for me. I don't mean to be "picky" so I am not completely ruling out any resource just yet.   Thanks in advance.
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Which book is the best for me to self-study/improve at static mechanics problems?  I am looking for a book with a lot of ( only ) problems, not a theoretical book.  Not only basic problems, the ideal is a book with a lot of problems going from easy to hard.
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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 was wondering if some one here would please recommend an abstract algebra text book. In particular, I am seeking a text from among one of these:  1) Abstract Algebra by Dummit and Foote  2) Algebra by Michael Artin  3) Topics in Algebra by Herstein.  I was wondering which text is best for a high school student and has great exposition and good problems. My goal is study some algebraic number theory some time later in the near future as I liked elementary number theory.
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I need to find a good book on trigonometry, I was using trigonometry demystified but I got sad when I read this line:     Now that you know how the circular functions are defined, you might wonder how the values are calculated. The answer: with an electronic calculator!   I know a book which seems to be really good: Loney's Plane Trigonometry, I'm just not sure if the book is up to date.
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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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I searched on this site but I found posts asking for books on complex analysis which I guess is not what I want.   I want a book on problems concerning with roots of unity, argand plane, exponential form, inequalities etc. Some examples : , , .  I don't think these types of problems are covered in a analysis book but I don't know. I think I want a book on algebra of complex numbers.   Are these topics covered in analysis book ? If not, please suggests some books on this topic. I guess my question is bit vague, sorry for that. :).      As suggested in the comments I would like to have books similar to .
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Lately I've gotten a friend of mine interested in mathematics. He has no college-level education to speak of, but is well employed as a software engineer. So I feel he's competent to learn this stuff on his own.  He asked me recently if there was a 'mathematical' version of .  The point being, if there was an "introduction to proofs" book which took a more hand-holding approach. He's also expressed fondness for the .  However, metamath's proofs are obviously a bit too low level to learn anything serious.  At one point in our conversation, I mentioned the dependently typed programming language , but I felt it's not quite as helpful until he at least gets some experience with  (for which the target audience of Agda is Haskell programmers, hence the similarity in syntax).  Anyone have any good suggestions on a book?
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What is a good PDE book suitable for self study?   I'm looking for a book that doesn't require much prerequisite knowledge beyond undergraduate-level analysis.  My goal is to understand basic solutions techniques as well as some basic theory.