# 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_.

230 views

### How can I find all the solutions of $\sin^5x+\cos^3x=1$

Find all the solutions of $$\sin^5x+\cos^3x=1$$ Trial:$x=0$ is a solution of this equation. How can I find other solutions (if any). Please help.
309 views

### Beginning with math

I am studying computer science since 3 years now. It is really math heavy and I like it. However the problem that I have is that I never really had math in school it was too basic and I lack some ...
440 views

### First Course in Linear algebra books that start with basic algebra?

I'm 30 years old, and the only math I can remember from college is basic algebra and some probabilities. Next month, I have a machine learning project I'd like to work on, but I'll need a solid ...
397 views

### Equivalence Relation between Derivative Being Odd and Function Being Even

In the exercise, I am required to prove that $f'$ is odd $\iff$ $f$ is even Moving from right to left was pretty trivial, however, I couldn't move from left to right. Note that we can only use very ...
370 views

### Books with fun exercises

As university is a bit slow, we organize a group activity of doing math exercises (after learning the basics of the subject separately). Thus I am looking for a book with many exercises that are ...
225 views

### Modeling Rain on a Windshield for various Speeds using Calculus

A question was recently posed to Click & Clack Talk Cars (http://www.greatfallstribune.com/story/life/2014/08/07/click-clack-rainy-day-raises-physics-question/13750681/). The topic is rain hitting ...
284 views

### What all maths do I need to know to become good at machine learning.

I am a computer science engineer and I took a couple of maths classes in my first year they were on Fourier series(not transform) partial differential equations, vector calculus, infinite series ...
2k views

### Importance of Neatness / Organization / Speed in Math?

Pretty simple question here but it does relate to math. I ask this as my writing is quite messy, possibly a cause of silly mistakes. How important is neatness in math? Does having messy writing put ...
272 views

464 views

### Want to learn differential geometry and Riemannian geometry by myself

I want to follow a Ph.D. programme on geometric analysis. The main focus are Monge-Ampere equations and convex level set of $p$-harmonic equations. The theory of PDEs is very familar to me. However, I ...
952 views

### Importance of the Artin-Wedderburn theorem

I feel silly asking this, but what is the importance of the Artin-Wedderburn theorem in Algebra? In A First Course in Noncommutative Rings, T.Y. Lam calls it "the cornerstone of non-commutative ring ...
375 views

### Capacity theory beginner resources

I'm currently studying a book on shape optimization: Variation et optimisation de formes: Une analyse géométrique By Antoine Henrot, Michel Pierre. The book introduces at some point capacity, and uses ...
183 views

### Soft Question: Suggestions on mathematics resources for problem solving.

I'm doing my final year of under graduation through distance education and would be appearing for entrance tests for various graduate schools in a few weeks. I am looking for a database of algorithms/...
1k views

### Proof verification that Q is dense in R

Hi everybody I'd like to know if the next argument is sound. Definitions: A real number x is said to be positive if can be written as a formal limit of a Cauchy sequence of rational numbers $(x_n)$ ...
2k views

### Strategy to improve own knowledge in certain topics?

My background is physicist/engineer, and at university we studied only particular topics in mathematics. Some of the courses were never used and faded away with time, and I need to refresh the ...
649 views

### Supplementary exercises for Herstein's Noncommutative Rings

I've been studying from the book Noncommutative Rings by Herstein (not as a part of some official course), but unfortunately it doesn't contain any exercises apart from a few simple ones in the body. ...
356 views

### What would be an effective way to learn group theory on my own?

I've read the basics of this branch and I found it extremely interesing, and I would really love to learn more about it. I want to study as much as I can on my own, as my course doesn't have group ...
1k views

### What are some good resources for brushing up on geometry and trigonometry?

I'm brushing up on my calculus, and geometry and trigonometry keep coming up. However, these are probably my weakest areas mathematically. Are there any good sites or free PDFs/ebooks that I can use ...
94 views

### How to relearn undergrad and tackle grad mathematics? Want to become a better mathematician!

I am a student who has just completed their degree in pure math. Unfortunately, my undergrad was a very... Unpleasant time for me due to personal reasons. Although math is accepted as a very "poorly-...
91 views

### Self-studying Information Geometry

I was recently exposed to the topic of Information Geometry by a friend of mine, and was looking for a good book to begin self-studying this topic. Any suggestions? Also, what subject matter would ...
95 views

### Concrete examples and computations in differential geometry

I've been studying differential geometry by myself for some time now. I studied a fair amount of the basic general theory and gone through a lot of the exercises from several textbooks. Lately I ...
125 views

### Who wants to learn set theory? [closed]

So set theory is something I really want to learn. I found this document that I really like, except the fact that it doesn't prove all of it's theorems in with a lot of detail (a lot of times they say ...
449 views

### Analysis or (abstract) algebra first?

Which one would you recommend? I only know calculus and linear algebra when it comes to university-level mathematics. Is one required to understand the other?
200 views

### Transitioning to Higher Level Mathematics

I am just finishing grade 12 pre-calculus at my school and have strong interest in math. The problem is, it seems some important elements of higher level math are not in my schools curriculum that are ...
243 views

### What is the best way to go about learning math?

I know this is a very subjective question, but after struggling on my own for a while I figured I might as well ask it. I did all the normal math classes in college (LinAlg, MultiVariable Calc, etc......
192 views

I know it is hard to ask for the perfect method for doing mathematics, but I hope there are some paths that are more preferable over others. I am a engineering student who has switched to mathematics ...
224 views

### The high road to learn algebraic geometry

Suppose that a student has a basic knowledge in commmutative algebra at the level of the Atiyah-MacDonald. What do you think about the following steps to learn algebraic geometry? step 1: read "...
237 views

### Is integration by parts the best method for $\int_0^1 x^3(1-x)^6 dx$?

It came up when finding a constant such that the integral is equal to 1 and thus behaves like a pdf. I used the parts method but have made an error, just curious how others might approach the problem.
833 views

### Follow-up to Baby Rudin

I would like to continue my study of analysis, albeit temporarily in self-study, and I was wondering what would be the best "sequel" to baby Rudin. Thank you very much for your advice.
280 views

### Studying mathematics: Is proving things yourself worth the time?

When studying mathematics, is proving things yourself (before reading the proof given in the text) worth the time? This approach takes significantly longer than simply trying to follow along, but you ...
93 views

### What is the value of $a+b+c$?

What is the value of $a+b+c$? if $$a^4+b^4+c^4=32$$ $$a^5+b^5+c^5=186$$ $$a^6+b^6+c^6=803$$ How to approach this kind of problem. Any help. UPDATE: Thank you all for answers. Now I ...
5k views

### Learning trigonometry on my own.

I have been self teaching myself math beginning with a grade 10 level for a while now and need learn trigonometry from near scratch. I am seeking both books and perhaps lectures on trigonometry and ...
396 views

### Beyond the Exercises? [closed]

I've entertained and become bored with quite a few interests, though mathematics has more or less been my central passion throughout my high school/middle school life. I've only recently started into ...
102 views

### Let $R$ be a finite ring (with unity) and $S$, $T$ be subrings of $R$. Is $S \cup T$ a subring of R?

Let $R$ be a finite ring (with unity) and $S$, $T$ be subrings of $R$. Is $S \cup T$ a subring of R? (Counterexamples are easy to find to me when $R$ is an infinite ring or a finite rng.) P.S. I am ...