# Tagged Questions

The process of studying mathematics without formal instruction. _Don't_ use this tag just because you were self-studying when you came across the mathematical question you're asking; it is only for when the fact that you're self-studying is what your question is _about_.

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### A Book for abstract Algebra

I am self learning abstract algebra. I am using the book Algebra by Serge Lang. The book has different definitions for some algebraic structures. (For example, according to that book rings are defined ...
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### Book on the Rigorous Foundations of Mathematics- Logic and Set Theory

I am asking for a book that develops the foundations of mathematics, up to the basic analysis (functions, real numbers etc.) in a very rigorous way, similar to Hilbert's program. Having read this ...
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### History of the theory of equations: John Colson

This is an EDIT version of my original question: Recently I've been interested in the history of the Theory of Equations. The thing is that I learned about this mathematician named John Colson, he ...
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### Math blogs, pros and cons for writers?

I regularly read blogs by three mathematicians, and occasionally run into others. Definitely they help me a lot studying mathematics. But now I am more interested in the writers' perspective, and I ...
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### Grasping mathematics

First, I'm not trying to make this sound like a "poor-me" story. I understand fully that every decision I've made leading to this is my fault. I am genuinely looking for advice. So, I am a high ...
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### Do equal bases imply equal powers?

$$x^a = x^b \Rightarrow a =b$$ So, this is a concept I used in multiple math problems and they often turn out right. The thing is, today my math teacher told me that this is not necessarily true. (...
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### Relearning from the basics to Calculus and beyond.

Assume someone has very limited knowledge of math. (low level high school, 5-6 years ago) How would they learn from the basics of algebra, geometry and trigonometry to a solid foundation for calculus ...
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### What are the prerequisites for stochastic calculus?

I am not a math student, and only kind of picking up something whenever I need it. After emerged in the field of machine learning, probability, measure theory and functional analysis seem to be quite ...
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### Introduction to ring theory?

I've been teaching myself algebra these couple of months. I already went through the basics of group (Lagrange, action, class equation, Cauchy and Sylow theorems etc.) And I already have some linear ...
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### How to Self-Study Higher Math Without Solutions

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 ...
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### IMO programs of different nations?

We in Albania have a good team in the IMO, and this year I will probably be part of it. Since Albania does not have a public training programme, I have to consult the training programmes of other ...
I want to show that for $n>0$, $2^n$ and $2^n + 1$ have the same number of digits. What I did was I found that the formula for the number of digits of a number $x$ is $\left \lfloor{\log_{10}(x)}\... 9answers 1k views ### Suggest an Antique Math Book worth reading? I'm not a math wizard, but I recently started reading through a few math books to prepare myself for some upcoming classes and I'm starting to really get into it. Then I noticed a few antique math ... 9answers 2k views ### A linear operator commuting with all such operators is a scalar multiple of the identity. The question is from Axler's "Linear Algebra Done Right", which I'm using for self-study. We are given a linear operator$T$over a finite dimensional vector space$V$. We have to show that$T$is a ... 2answers 5k views ### Why is cross product only defined in 3 and 7 dimensions? [duplicate] Why$3$and$7$? I know from some reading that Hurwitz's Theorem explains this, but can someone help me build some intuition behind this or perhaps provide a simpler explanation? It still seems ... 6answers 2k views ### How do I teach university level mathematics to myself? [closed] So here I go, I have enrolled myself in maths major this year but due to less marks in SSC I couldn't secure admission in a good university so I have to take admission wherever I could get with my ... 3answers 1k views ### Careers in Math I am a highschool freshman, and I really like to have goals for my life, one of the big ones is my career of choice. Previously, I have always wanted to be a programmer, and I have written a lot of ... 2answers 2k views ### Baby Rudin: Advice I am working through the first chapter of Principles of Mathematical Analysis and I am wondering how many of the twenty exercise problems I should do. I think the first ten are very to moderately ... 2answers 939 views ### Am I reading Bott - Tu right? Summary: I'm finding Bott - Tu to be too brief and terse. I constantly have to look elsewhere to fill in details. This is not time-efficient. Am I missing something? If not - what other books do ... 1answer 2k views ### Which is better strategy to learn and read books, traditionally one by one OR re-read carefully on perfect books (Just focus on how to learn and master the stuff pretty well, not involve the aspect of courses or exam) Because recently I always feel that the time and energy are pretty limited, I want to try ... 7answers 2k views ### Why is a square root not a linear transformation? The question says: Prove that the function$f(x)=\sqrt{x}$is not a linear transformation (particularly$\sqrt{1+x^2}≠1+x$) I think that this is because the exponent of$\sqrt{x}$is$1/2$, ... 4answers 6k views ### How to do well on Math Olympiads I'm a high school student who really likes maths and I'm quite good at school. I want to start training maths by myself but I think I need some guidelines. I want to do well on IMO but I don't know ... 5answers 400 views ### Is 'Algebraic Number Theory' the study of the theory of algebraic numbers, or is it the study of the theory of numbers from an algebraic viewpoint? Asked differently: Is Algebraic Number Theory the study of the theory of algebraic numbers? Or is it Number Theory from an algebraic viewpoint? Or is it both? I know I can just find a wiki article ... 3answers 2k views ### Learning schemes Could someone suggest me how to learn some basic theory of schemes? I have two books from algebraic geometry, namely "Diophantine Geometry" from Hindry and Silverman and "Algebraic geometry and ... 6answers 2k views ### Self studying math, how can I learn the most? I am currently studying Pre-Calculus on my own. I have a few texts I am working with but feel like I could learning a lot more than I am. When people typically ask these kind of questions the common ... 1answer 7k views ### How to self study Linear Algebra 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 ... 2answers 627 views ### Yoneda Lemma Exercises Can you please suggest some (relatively simple) exercises to practice the use of the Yoneda Lemma? Harder exercises are welcome too, but I would like to start with simpler ones. The answers to this ... 2answers 914 views ### Importance of Exercises in Mathematics for Self-Studying I am a high school student wanting to major in Mathematics in the future. I started to like Mathematics recently, starting a year ago and I watched some interesting math videos on YouTube for fun (ex: ... 1answer 566 views ### How to fill my mathematical gaps? To do the story short, I became interested in mathematics in a serious way like two years ago, I'm currently in graduate school, but the problem is that my mathematical background is not as good as ... 3answers 467 views ### Being mathematically critical: how should a student approach statements that appear to be obvious? Very occasionally, I will read or hear a theorem, and think: isn't that obvious? Not in a contemptuous "I can immediately see how to prove this" way, but rather in a "I would have thought this was ... 1answer 211 views ### What's the motivation of the definition of primary ideals? $$xy\in\mathfrak q\:\Rightarrow\:\text{either x\in\mathfrak q or y^n\in\mathfrak q for some n\gt0}.$$ Primary ideals can be regard as the generalization of prime ideals and radical. But why ... 1answer 853 views ### How to improve mathematical creativity? To introduce myself: I'm an undergraduate mathematics student in Germany. Currently I'm studying in the second semester and until now I'm doing well, but I still got the feeling that my ability to ... 1answer 219 views ### How to stay productive while you are studying math? [closed] Not sure that this question is a good fit for this site, but I will try. When I am working through a chapter of a mathematical book first two hours are normally very productive (easily remember ... 3answers 9k views ### Difference between continuity and uniform continuity I understand the geometric differences between continuity and uniform continuity, but I don't quite see how the differences between those two are apparent from their definitions. For example, my book ... 6answers 299 views ### Sources for mathematics outside the mathematics world In this question I would like to ask you about material showing the uses (or occurrences) of mathematics in the everyday world. The aim is to encourage with it a group of young undergraduate ... 3answers 1k views ### Book series like AMS' Student Mathematical Library? I had the joy of discovering AMS' Student Mathematical Library book series today, and I have been pleasantly surprised by how enticing some of the titles seem: exciting and expositionary, a perfect ... 7answers 1k views ### Strategy for reading math books, is it better to prove the theorems yourself or just read them? Context: I'm self-studying some mid to upper level undergraduate math subjects. For example, right now I'm reading Munkres' Topology book. Usually, the approach I use is to go through the book in ... 3answers 1k views ### What should a math graduate know? [closed] There are a lot of undergraduate courses out there and most of them agree on certain things, with regard to the subjects covered. Courses that include mathematics (engineering, physics, etc) are ... 2answers 588 views ### Computation of$\operatorname{Tor}_1$and$\operatorname{Ext}^1$Can you please give some examples of computation of the derived functors$\operatorname{Tor}_1$and$\operatorname{Ext}^1$for some simple cases, say$R=\mathbb{Z}$or$R=\mathbb{Z}[G]$for some ... 1answer 510 views ### How to Self-Study Mathematical Methods? Edit: Ok, user Chinny84 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 ... 1answer 685 views ### Looking for an easy lightning introduction to Hilbert spaces and Banach spaces I'm co-organizing a reading seminar on Higson and Roe's Analytic K-homology. Most participants are graduate students and faculty, but there are a number of undergraduates who might like to participate,... 5answers 7k views ### Multivariable Calculus books similar to “Advanced Calculus of Several Variables” by C.H. Edwards I am currently trying to teach myself multivariable calculus using C.H. Edwards' "Advanced Calculus of Several Variables", but the text unfortunately doesn't have very many problems with solutions. I'... 7answers 938 views ### Making up for wasted high school years - where should I begin? I realize this question is long and quite personal but any help will be greatly appreciated. I'm a senior high school student. I've learnt maths at precalculus level. I have had little exposure to ... 2answers 720 views ### How can I pick up analysis quickly? I have a 2-3 week recess from university for winter break. In this time, I would like to learn analysis, starting with Walter Rudin's Principles of Mathematical Analysis, and then, if at all possible, ... 2answers 4k views ### Is Aluffi's book a good second text for Algebra? I have been trying to relearn parts of algebra (mostly module theory and (advanced)linear algebra) from Lang, which, frankly, is not going too well. Now, I have managed to get my hands on 'Aluffi - ... 2answers 2k views ### Learning Abstract Algebra for a graduate degree I would like to do a graduate degree in mathematics, and I have a full year before I will be able to do so (for personal reasons). I mainly have my weekends available to study. I am interested in ... 1answer 734 views ### How to begin self study of Mathematics? I'm aware that this question has been asked several times, but I have specific questions hence why I'm asking again. I began to appreciate the beauty of mathematics when I glossed over the ... 4answers 181 views ### Is there a closed form expression for$\int_{- \infty}^\infty \int_{-\infty}^y \frac{1}{2 \pi} e^{-(1/2) ( x^2+y^2 )} \mathrm{d}x\,\mathrm{d}y$? I have been trying to evaluate the integral: $$\int_{- \infty}^\infty \int_{-\infty}^y \frac{1}{2 \pi} e^{-(1/2) ( x^2+y^2 )}\mathrm {d}x\,\mathrm{d}y$$ I know of course that the integral equals ... 3answers 1k views ### Why are we interested in irreducible representation but not faithful representation? I am reading some materials of representation theory (of a group). The motivation of representation theory is to represent (by a homomorphism$h: G \to GL(V)$, from the group$G$to a vector space$...
I am preparing for Mathematics Olympiad , can any one suggest me some books to prepare for olympiad ? The topics that usually come up involve: congruence modulo $n$, inequalities , number system, ...