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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Choice of $q$ in Baby Rudin's Example 1.1

First, my apologies if this has already been asked/answered. I wasn't able to find this question via search. My question comes from Rudin's "Princicples of Mathematical Analysis," or "Baby Rudin," ...
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6answers
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Best Math books or apps for adults to learn math from the beginning

I lost a possible job because I didn't know how to multiply and subtract negative valued integers. I also don't know how fraction manipulation works. What reference books can I read that can help for ...
17
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2answers
640 views

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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4answers
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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 ...
16
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7answers
818 views

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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6answers
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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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2answers
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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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2answers
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Path to Basics in Algebraic Geometry from HS Algebra and Calculus?

In this question, Why study Algebraic Geometry?, Javier Álvarez, develops a succint but encompassing description of algebraic geometry and its spread across different areas of mathematics. Indeed, it ...
15
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2answers
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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 ...
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2answers
1k views

Show that these two numbers have the same number of digits

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 ...
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9answers
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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 ...
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3answers
414 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 ...
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5answers
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Which calculus text should I use for self-study?

I am 36 years old, and have forgotten a lot of math from high school, of which I only took up to Algebra 2. However I am teaching myself mathematics and am now, as an adult, completely fascinated ...
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2answers
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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 ...
14
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3answers
915 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 ...
14
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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 ...
14
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0answers
390 views

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 ...
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1answer
5k 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 ...
13
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2answers
545 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 ...
13
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1answer
181 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 ...
13
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1answer
611 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 ...
13
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3answers
2k views

What is a good book to study classical projective geometry for the reader familiar with algebraic geometry?

The more I study algebraic geometry, the more I realize how I should have studied projective geometry in depth before. Not that I don't understand projective space (on the contrary, I am well versed ...
13
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1answer
646 views

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 ...
13
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1answer
261 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 ...
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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 ...
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5answers
1k 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 ...
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6answers
269 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 ...
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2answers
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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 ...
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3answers
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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 ...
12
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1answer
562 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 ...
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4answers
3k 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 ...
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8answers
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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 ...
11
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7answers
771 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 ...
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3answers
751 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 ...
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3answers
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I want to start mathematics from scratch. What should I begin with?

I've just finished high school but I don't feel my knowledge of mathematics is good enough. I'd like to start again from scratch, possibly adding a bit (a lot) of problem solving to it. What is the ...
11
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2answers
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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 ...
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2answers
520 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 ...
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1answer
125 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 ...
11
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1answer
508 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 ...
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5answers
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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. ...
10
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5answers
2k views

Advice for benefits to directly use analysis textbook to replace calculus

Main purpose: For self-learning performance, neither for exam nor degree courses. Calculus textbook using now[1]: Calculus I, Weinstein&Marsden, UTM, Springer Question Description: I've been ...
10
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5answers
869 views

Notes for Beginner Fourier Analysis?

Are there any good lecture notes or books on basic fourier analysis that authors publish freely online? It is very difficult to find rigorous mathematical theory of fourier analysis because google is ...
10
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2answers
3k 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 - ...
10
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3answers
409 views

Should I look at syllabi for math courses before beginning my bachelor's degree in math?

Next year I'll start my bachelor's degree on mathematics, but I want to study something about it while I'm idle. I've found this: http://webdocs.registrar.fas.harvard.edu/courses/Mathematics.html ...
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2answers
641 views

Modern research into Grassman's “theory of forms”?

I quote from Petsche's Hermann Graßmann: Biography (emphasis mine): The mathematical part of the book begins with the conception of the “General Theory of Forms”. Starting with a perspective on ...
10
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1answer
616 views

Undergrad Student Trying to Figure Out What to Study

this is my first time on stack exchange and I am seeking advice for my future studies. Some background first; I am a undergraduate student pursuing a degree in mathematics and I hope to pursue ...
10
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2answers
238 views

Suggestions for a learning roadmap for universal algebra?

I think a useful combination of resources for universal algebra would ideally, when taken together: Provide ample motivation behind the various developments in the field. Either provide powerful ...
10
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2answers
12k views

Tips for an adult to learn math — from the beginning.

First let me start with I am an adult and I can't do simple maths. I some how got through all of my math courses in University (after several attempts) but I honestly couldn't tell you how... I ...
10
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1answer
308 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 ...
10
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1answer
188 views

Soft question: How does basic differential geometry “fit together”?

I'm self-studying diff geom from Lee's Introduction to Smooth Manifolds. He warns the reader that there's a lot of machinery to construct, which is fine, and he explains things with wonderful clarity. ...