Can you please suggest some books or websites for higher secondary school student for easy understanding of calculus?(Just I want to learn to carry out basic calculations)
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This question is a  of the common question asking for calculus references. It is here to  away the repetition, and give a canonical resource for calculus references.      I'm looking for a resources to learn single-variable calculus.
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Could you recommend some beginner books for Riemannian geometry to me?  I am completely new to Riemannian geometry, but have some basic knowledge of differential geometry.   I am looking for a book in Riemannian which is similarly as light as Tu's "Introduction to Manifolds" for differential geometry. I know that the classical reference is the book of do Carmo, but I have heard some students complaining that its not a book for the absolute beginner.  For the moment, I am just looking for a source to introduce me Riemannian metrics, Riemannian manifolds, curvature, geodesics in a way as clear as possible.  Thank you
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I'm currently trained in Algebra, Calculus and Statistics in high school level. Basically, I've no knowledge at all in number theory as this subject is not taken seriously in my country.  I was thinking to self-learning number theory by books. But the books I found in the internet are really hard and complicated for me as I've no number theory background at all.   Recently, I was asked by a 10 years old kid for a question which is related to number theory. I've no idea at all how to solve that, it was really embarrassed.   So can anyone recommend me some books for number theory which are suitable for me?
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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.
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I have read Calculus by Michael Spivak. Now I want to learn additive combinatorics though I have no experience with combinatorics or probability theory. To my understanding, there is a book on the subject by Terence Tao and Vu. Do you think I'll be able to read it thoroughly? Do you have any other suggestions?
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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 am currently undergoing a full Apostol Calculus I reading, and with few chapters left I've began planning what other books to read. I was thinking about finishing both Apostol Calculus l and ll, and then read Apostol mathematical analysis. I'm not pretty sure whether these are the best books or if they will provide me with a strong math basis. I've already taken calculus i, ii, iii and linear algebra. The reason I've chosen Aapostol volume 1 and 2 is that I've heard they cover almost all the topics I've seen and will see in the next semester/s. I would appreciate if somebody could give me some advice about this. I really like to have a book that really gives me hard and challenging problems. I don't know whether to read Spivak Calculus book or not.
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I have just learnt about the chain rule but my book doesn't mention a proof on it. I tried to write a proof myself but can't write it. So can someone please tell me about the proof for the chain rule in elementary terms because I have just started learning calculus.
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Can you suggest some useful things we can do with higher order derivatives?    A fellow student in my Calculus and Analytic Geometry I class asked what some applications of higher order (e.g., ( $y^{(n)}$, $n\geq 4$) ) derivatives might be.  Our instructor (masters level faculty) did not know of one.  It's got me curious...  This question doesn't require a rigorous example, just illustrative concept(s).  Thanks.
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I recently graduated with a degree in bachelor of science with a focus interactive and multimedia design. I had to opportunity to take 1 C++ course and 1 HTML course. I was also only required to take one math class, introduction to calculus (and it was hardly calculus, it was more of a math class for designers)  Since graduating I have pursued a career in web development. I'm considering going back for a MS in computer science or MS in web technologies.   I feel my math has suffered dramatically as I have always been behind most others on my math studies (middle school through college). I want to learn calculus as I feel it's an integral part of any CS degree.   Does anyone have any recommendations on any great books that I can read through and teach my self a bit of calculus or other advanced math topics?  Thanks for any advice
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I am looking to study mathematical logic, however, I find that introductory books are very daunting, which kind of disheartens me. You see, slowly but surely, I started to realize that the maths which I have learned did not just pop out of thin air, but is a collection of systems, which must of been developed via some other system, i.e, maths did not develop itself.  So I began to look into the origins of mathematics, and read that it was developed via a type of logic, which exists sort of by 'default', via a set of axioms, and then of course I looked up the definition of axioms.   So given that I'd be studying a type of logic whose origins are self evident axioms, naturally I believed there would be no prerequisites. However, in looking up mathematical logic, I have come across things such as Boolean algebra, sets, first order logic, some other type of logic, called 'traditional logic', as well as references to a sort of calculus, though not in a mathematical sense, I think.  So all in all, I am trying to develop a type of mental spider web, and I am trying to find out the strands which lye at the absolute bounds so that I may learn this mystique logic. Though I have no idea where to start.  Side note: This is the book I have started reading:   Credit goes to Wolfgang Rautenberg.
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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 is your recommendation for an in-depth introductory combinatoric book? A book that doesn't just tell you about the multiplication principle, but rather shows the whole logic behind the questions with full proofs. The book should be for a first-year-student in college. Do you know a good book on the subject?  Thanks.
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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 know this is a subjective question, but  I need some opinions on a very good book for learning differential equations.   Ideally it should have a variety of problems with worked solutions and be easy to read.   Thanks
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I am in search of a good book for learning Stochastic Calculus from a purely mathematical/statistical point of view. Almost all the books I see are based on Finance. Also, please specify the pre-requisites for this course.  Actually, I am quite knowledgable in Measure Theory, Markov Chains and Martingale Theory. I believe this knowledge should suffice.  I am planning to self-study this subject. Please suggest me good books.  Thank you.
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During this summer break, I want to use my time to broaden my knowledge of mathematics. I am a very motivated high school student searching for some challenging material to learn, and the two subjects I had in mind are complex analysis and probability theory.  For probability theory I already choose a book, but I am struggling a bit with finding the right complex analysis textbook. I already found two textbooks which seem pretty good to me:  by Sara Maad Sasane and  by Zill.  As to requirements for the book:   The textbook must not be too broad, since I only have 6 weeks to study intensively (yes, I know it's a challenge to study most of complex analysis in 6 weeks). The textbook must not require a lot of prerequisities other than knowledge of single variable calculus (not a course in proof writing) and must not be too rigourous (some pictures and intuitive explanations can come in handy).   I hope someone could give some advise as to if the books I found suit my needs, if someone has experience with those books or if someone knows a book other than the two I found which suit my needs better.  Thanks in advance.