I'm in the 11th grade. At the bachelor exam, my main focus will be on mathematics and informatics.  I'm a hard working man, but due to the school norms, I can consider myself idiot at math. Why? Because the math that's studied at school is rubbish. It makes you reproduce, and not think. I'm also tutored at math, but with the same results.  I want to go on the same way I went with informatics, and this is by learning in private, alone.  Could you recommend me some books that can help me understand the whole high-school curriculum? A book/books that takes me from the very below (9th grade) till 12th grade?
123298
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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I am hoping you can give me some suggestions. I am teaching in a very diverse (made of minority groups) college and the students are mostly Psychology majors. Most students are fresh from high school but some of them are older returning students above 40. Most of the students have motivational problems and aversion to math. But I am still looking for a book that covers the basic curriculum: from descriptive to sampling and testing all the way to ANOVA, and all in the context of experimental methods. The department requires me to use SPSS in class, but I like the idea of building the analysis in a spreadsheet such as excel.  p.s. the other teachers use a book that I don't like because of the extensive reliance on computational formulae. I find using these computational formulas - rather than the more intuitive and computationally intensive formula that is consistent with the rational and basic algorithm- unintuitive, unnecessary and confusing. This is the book I refer to Essentials of Statistics for the Behavioral Sciences, 7th Edition Frederick J Gravetter State University of New York, Brockport Larry B. Wallnau State University of New York, Brockport ISBN-10: 049581220X Thank you for reading!
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This question recently appeared :     Slashdot posts a fair number of physics stories. Many of us, myself included, don't have the background to understand them. So I'd like to ask the Slashdot math/physics community to construct a curriculum that gets me, an average college grad with two semesters of chemistry, one of calculus, and maybe 2-3 applied statistics courses, all the way to understanding the mathematics of general relativity. What would I need to learn, in what order, and what texts should I use? Before I get killed here, I know this isn't a weekend project, but it seems like it could be fun to do in my spare time for the next ... decade.   It seems like something that would be a good addition to this site: I think it's specific enough to be answerable but still generally useful. The textbook aspect is covered pretty well by , but beyond that: What college-level subjects in physics and math are prerequisites to studying general relativity in mathematical detail?
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I'm a first year econometrics student with a great interest in mathematics. I very much enjoy my study, but still I am interested to learn about more topics in mathematics which are not part of my study. Some of the main topics which I am already familar with or which will soon be covered in my study are: calculus, linear algebra, optimization, statistics/probability/combinatorics.  Which topics in mathematics would you advise me to study still (that are not part of this list)? I have a general interest in mathematics, so any advice on interesting and or essential topics in mathematics that are worth studying is appreciated.   If possible, could you also give me advice on books/references which I should study from?  Thanks in advance.  Edit: To be more specific, I am looking for topics on which the general consensus is that they are essential to know of for any mathematician or very interesting to study.
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What's a good book (or other resource) for an advanced undergraduate/early graduate student to learn about ,  and ?   has a  that makes me wary of it, but something like it would be great.
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I am from mathematical background, and I always hated the way they teach elementary probability theory in schools without giving any clue about measure theory.   I want a theoretical book in probability theory, which starts with measure theory and defines everything in mathematical terms. I am also not looking for a measure  theory book. If there is such a book that instead of giving only an intuitive introduction to probability theory, it rather defines everything in details, I would be really grateful to know it.  I would be happy to hear about any reading experience. Being exact in mathematical  language and maybe exercises.  Thanks a lot.
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I have no idea if this question is appropriate for this forum, but I hope you guys can overlook the fact that I asked it on a wrong forum (if I did) and still help me answer it (of course, if this is indeed the wrong forum for the type of question I'm about to ask, do please say so).  I am a 16 year old guy who is passionate about physics and as a result wants to increase his knowledge in mathematics, the language of physics. I've read and heard a lot about Linear Algebra and how crucial it is to physics and I am deeply motivated to self study this intriguing part of mathematics. However, I have limited knowledge of maths. I (for example) know basic algebra, trig, diff/int calc and some analytical geometry, but I wouldn't say I master these subjects past the high school curriculum. Now my question is: Would you kind people say I am able to self study Linear algebra or is it too tough and/or does it require too much of a math background? And are there any good books out there for BEGINNERS in LA? I found this (free) e-book called: Elementary Linear Algebra by Kenneth Kuttler and another one called 'Linear Algebra: Theory and its applications' also by Kuttler? Are these any good? Or would you recommend other books? If you guys have any tips regarding books for LA but also tips in general, please, I'd appreciate them!
44295
I'm starting a very long quest to learn about math, so that I can program games. I'm mostly a corporate developer, and it's somewhat boring and non exciting. When I began my career, I chose it because I wanted to create games.  I'm told that Linear Algebra is the best place to start. Where should I go?
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I'm a sophomore in university and seriously feel that I'm bad at solving mathematical and algorithmic problems (be it discrete math, calculus or just puzzles). I noticed that I'm only good at solving questions that are similar to the ones that have been taught to us.  Here's how I generally approach it:   What is the problem? What do I need to do here? Does it look like I've encountered this before?  Can I think of a smaller problem to solve instead?   If the answer is no to all the above then I sort of blank out. I stare at it and force my brain to run through a wide variety of stuff, almost like a brute force attempt of solving it. Obviously that leads me to nowhere everytime. I simply can't think "outside the box."   What can I do to improve my situation?
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This is a question about studying for the Putnam examination (and, secondarily, other high-difficulty proof-based math competitions like the IMO). It is not about the history of the competition, the advisability of participating, the career trajectories of former participants, or other such things. This is a question about how one can most effectively prepare to do well.   Many such questions have been asked before on this site. The answers, while helpful, all seem to boil down to recommendations of the same standard canon of books with the encouragement to do more problems. This is very good advice, but I want to approach the topic from a different angle.   We have a wealth of talent on this website, and in particular many users who have done quite well at these competitions. I would like to hear their personal stories. In particular, how did you prepare, and what kind of time commitment did you put forth? And advice, especially practical study tips, is always welcome. :)  edit: Also, it seems to me that the majority of people who do very well at the Putnam had developed the majority of their skill in high school, and focused mainly on their classes in college (while attending whatever Putnam seminar their college offered). I would appreciate comments on this matter too.   (Motivation: It seems to me like the role of talent is vastly overestimated in mathematics, and in mathematics competitions in particular, to the point where the Putnam exam gets used as a sort of pseudo-IQ test. Of course the people who do well have gifts, but it also seems that, without fail, they all have a history of doing many hours of mathematics a day for years on end. For example, I recall reading an interview with Tao where he admitted his childhood consisted of nothing but math and computer games. I am trying to gather some evidence on this matter [and advice for Putnam preparation!]. Please keep the answers focused on the actual question, though.)
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I'm a high school student who is trying to figure out a complete course of self-study for each year of high school. How can I self-learn grades of math without devoting too much time? This is a complex issue for me, as other students at my competitive high school have tutors and the like. Please recommend textbooks that have detailed explanations and progressive practice problems, for self-study for each area such as:  Algebra  Geometry  Trigonometry and Analytic Algebra  Pre-calculus  BC Calculus  Other people have skipped grades of math due to help from tutors and parents. Can I cover all of geometry and trigonometry in 8 months without going insane and be able to skip a grade?
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For a high school student interested in majoring in math and learning more about math, what kinds of mathematical research can a student in high school get involved in? How can a high school student get involved? If a high school student does conduct research, what mathematical journals would be willing to publish their work? Also, what other ways are there for a high schooler to get involved in more complex mathematics?
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I am taking a course in Mathematical Methods for physicsPhysics (Junior Level).   We are working from   > Mathematical Methods for physicists, George B.Arfken .    I just need online resources covering ( Matrices, Determinants, Vector Analysis, Tensors and differential forms and Vector spaces...etc) to study and understand from.
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This question is motivated by a little anecdote. I was at home teaching some secondary school math to a relative. At some relax time, he glanced at a book I had over the table - it was some text about analytical number theory that I had recently bought, second hand- and I  explained him that that was an area of mathematics quite arcane to me, that I'd like to learn something about it in some future, but I had little hopes...   He looked puzzled for a moment, and then asked me: "But, wait a moment... You don't know all the mathematics?"  This happened months ago, and I'm still laughing. But also (and here comes the question) I'm still thinking about how to make some picture of this issue: the big extension of "the land of mathematics", in diverseness and ranges of depth - and the small regions that one has explored.  I was specifically looking for some kind of bidimensional (planar?) chart, perhaps with the most basic/known math kwowledge in the center, and with the main math areas as regions, placed according to its mutual relations or some kind of taxonomy.   (I guess this should go in community wiki)
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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 am reading about decision making and I came across this subject. Fortunately it has a  , but the point is I want to see some examples, and learn to solve regular problems of this field. Of course I can go for the book by Pontryagin but then I don't think that would be an educative book. Does anyone has a suggestion? I would be happy if it also covers LQ problems. P.S. I studied math, therefore I appreciate a book with rigorous approach to the subject.
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I want to start signal processing and I need a book that satisfies my mathematical requirements: I am in the third grade of high school and I don't know any useful thing about limit, differential, ...  Please help me.