# Tagged Questions

Questions asking for advice on various mathematical matters. Be careful that your question is answerable, and also that it is not a polling question (e.g. "What is the best / your favorite way to...").

56 views

### What should one do if one works on a problem and submits a paper only to find that it is already in some book?

What should one do if one works on a problem and submits a paper only to find from the editor, that the work is already in some book? The work is is not really easy to find on the internet and was ...
3k views

### Mathematics needed in the study of Quantum Physics

As a 12th grade student , I'm currently acquainted with single variable calculus, algebra, and geometry, obviously on a high school level. I tried taking a Quantum Physics course on coursera.com, but ...
488 views

### Analysis on manifolds after course on Lebesgue integration

I am an junior currently taking a course on measure theory and Lebesgue integration using Royden's text. Before this, I took a standard intro to analysis course covering the first seven chapters of ...
446 views

### What area of Abstract Algebra do you find most interesting? [closed]

For my Abstract Algebra class, we will be doing small presentations (2 class periods) covering some topic in Abstract Algebra. Thus far, I have studied groups, rings, fields, modules, tensor ...
155 views

### What happens if your manuscript is accepted as a filler?

I just got a responce from a journal of the MAA that my manuscript is accepted as a filler. The email says : "The Editorial Board likes your submission and has asked me to move it to the ...
91 views

### Linear Congruence Theorem - Are these solutions too? Where'd they hail from?

(1) Can't the signs - I colored them in red - of x and y be switched? Aren't $x = x_0 - bn/d$ and $y = y_0 + an/d$ also solutions? They satisfy $ax + by = c$? (2) How can I remember these ...
130 views

### Intuition - Divisibility results - If c divides some integers, then c divides any linear combination of them. [closed]

Not querying about proofs here. I don't want to memorize, thence are there intuitions or illustrations for them? As a student, how else can I remember these results? Origin - Elementary Number ...
270 views

### Struggling with Topology. Any advice?

I'm a Junior Mathematics major at a small Liberal Arts college. I'm currently taking first semester topology (Munkres text). I feel like I'm barely able to tread water in this course. I was able to ...
152 views

### What are some ways to practice mathematical problem solving?

I am currently a high school senior and, naturally, I have participated in many math competitions in my years. In fact, in preparation for such competitions, I have probably spent upwards of $250$ ...
118 views

### My first simple direct proof (very simple theorem on real numbers). Please mark/grade.

What do you think about my first simple direct proof? What mark/grade would you give me? Besides, I am curious about whether you like the style. Theorem Let $I = [a,b]$ be a non-empty closed ...
255 views

### Learning to understand proofs faster?

There are many books, written by highly decorated academics, which feature proofs that I can hardly comprehend in an acceptable amount of time. Roughly each week, it happens that I find myself having ...
38 views

### Integration Exercise.Help!

I have to integrate the function F(x,y)=x+y on the line segment x=t , y=1-t , z=0 from (0,1,0) to (1,0,0) .So what i did is think the line segment as a vector function(curve) σ(t)=(t,1-t,0) with ...
180 views

### Time managment while self-studying rigorous mathematical textbooks

Lately I have been introducing myself to Calculus.But I have an issue with time. Namely I have found that on average I need about 2-3 hours per page of material.This of course includes finishing all ...
67 views

### Tools or Resources for pictures and visualizations

The popularity of books like Visual Group Theory and Visual Complex Analysis validates the importance of pictures and visualization for complex subjects. Unfortunately, I'm not aware of similar books ...
682 views

### When should I start learning Set Theory?

I started to learn a few disciplines on my own over the break after my first year in college and one of them was Real Analysis. In the process I came across many issues in Analysis texts concerning ...
366 views

### Difference between Vector Functions and Vector Field

I understand that a vector function is a function that has a domain $\mathbb{R}^n$ and range on $\mathbb{R}^m$ so it takes vectors and gives vectors right? So what is a vector field?And how can I ...
64 views

### Where can I find good examples about Algebra (but not only): Usual counter-examples, but also limit cases, rare ones, etc [duplicate]

I recently discovered the importance of examples and couter-examples in mathematics. Where could I find good examples books or anything related to it ? I am particularly looking for rare limit-cases, ...
573 views

### How to proceed doing number theory?

I'm an undergrad majoring in mathematics. Being in first year I'm still exploring new branches of mathematics and till now, It is analysis and Number theory that I've come to have a great interest ...
4k views

### How to be a successful math undergraduate student? [closed]

I am an undergratuate student in my first year of combined bachelor of electrical engineering and bachelor of mathematics. For my mathematics degree, this year I am supposed to take two math courses ...
2k views

### Topics on Number theory for undergraduate to do a project [closed]

Im an undergraduate in the mathematics field ..So i wanna be alittle more productive and wanted to do an essay or project mostly on number theory or Algebra(Rings or Groups) and i want to ask if you ...
101 views

### Breaking Out of Algorithmic Thinking

I have been taught my whole life to solve math with an algorithm or method. My teachers in school trained us to identify patterns in equations and then use a method to solve it. No one has ever ...
942 views

### Some Questions regarding preparing for Math Olympiads (searched but didn't get answers)

Many questions have been asked on this site regarding preparation for olympiads like the Putnam. I've read those questions and accordingly decided to start with Engel's "Problem Solving" but I have a ...
11k views

### How do you describe your mathematical research in layman's terms?

"You do research in mathematics! Can you explain your research to me?" If you're a research mathematician, and you have any contact with people outside of the mathematics community, I'm sure ...
808 views

### A book with simple proof exercises and full answers

I am quite bad at basic proof strategies, and in order to get some practice at this, I'm working through Daniel Solow's How to Read and Do Proofs (third ed.) Unfortunately, I'm having the problem I ...
631 views

### Thinking of mathematics in terms of analogs

I think the way that I've come to think about mathematics is becoming problematic and I'm wondering if I should abandon it. When I study mathematics, I find myself trying to compare the mathematical ...
464 views

### best book for real analysis for undergraduate [duplicate]

I am in under graduate first year. I want to learn some advanced real analysis. Can you give me some suggestions? One suggestion I got is Rudin's mathematical analysis. Can I buy that?
78 views

### Writing mathematics one is only slightly familiar with

Reading Paul Halmos' book I want to be a mathematician, he emphasizes early his personal experience with writing mathematics - using long, clear sentences, claiming that it is more beautiful, engages ...
214 views

### Literature on Chern-Weil Theory and the Chern-Gauß-Bonnet Theorem

At my university there are plans for a graduate seminar on Chern-Weil Theory and Chern's generalisation of the Gauß-Bonnet Theorem. Unfortunately I am having a though time in finding adequate and ...
201 views

### How to write for phd? [closed]

I'm a professor in high school and I would like to get a phd but I don't know how to do research for some phd topic. Could you guide me how to do this? When I was a student I was very interested in ...
592 views

### Binomial Theorem Practical Problem

I have been studying the 'Binomial Series', Chapter 16, Pg.125 within the Engineering Mathematics Book by John Bird. After completing this section I have attempted to complete the exercises for ...
238 views

### Surveys of Current (last 50 years) Mathematics at Graduate / Research level?

I'm wondering if there are any books or broad survey articles that survey current mathematical areas, i.e. mathematics of the last 50 years. Ideally, these would continue in the style of the various ...
3k views

### How to test whether I am suitable to pursue mathematics? [closed]

I am a high-school student. I have developed a recent affection towards mathematics (especially proofs), although I was always into logic (I've been a programmer since the age of eight). Now I am ...
626 views

### What pure mathematics foundations should an applied mathematician have?

I'm studying mathematics, with some statistics also, and I've always chosen applied courses. I'm getting to the point where I'm studying 3rd year undergraduate to graduate level material. My first ...
327 views

### start studying advanced topics in number theory

I am a first year undergrad and have had elementary course in Number Theory which includes only basic introductory topics like: divisibility,gcd-lcm,primes,congruences, number theoretic functions etc. ...
537 views

### Mathematical logic book with answers to exercises

I'm sure a question similar to mine has been asked before, but I am looking for a mathematical logic book with answers to the exercises. I am studying independently and although I have good logic ...
163 views

### What will I be doing? [closed]

I'm a freshman studying discrete mathematics B.sc. It's easy to google ''typical mathematician jobs'' and get an idea of what mathematicians do for a living, but what sort of jobs can I expect to work ...
412 views

### How often should math students take day breaks and longer breaks or vacations? Any research?

John Edensor Littlewood wrote in page 197 of Littlewood's Miscellany "For a week without teaching duties - and here I think I am preaching to the converted - I believe in on afternoon and the ...
357 views

### Big geometry grad schools - for an average applicant [closed]

What are some schools that have a lot of geometry going on, but that might accept some middle-of-the-range applicants? Let me add some context... I left grad school (UC Davis) with an MS in 2012 ...
398 views

### Bachelor Thesis - Galois Theory Research Topics?

I'm on the last semester of my bachelor's degree (undergrad degree) and I will be writing my thesis next semester. I have talked to a professor at my university and one of the topics he suggested was ...
178 views

So, this is definitely a soft question and I apologize. I've been in point set topology for about a week and I have two questions, Everything spews from definition, so should I dismiss my geometric ...
110 views

### Greedy algorithm for reading a single paper in Dutch

I want to read the paper of Freudenthal and van der Waerden that proves there are only 8 convex deltahedra. (“Over een bewering van Euclides” Simon Stevin 25 (1946–7), pp. 115–121.) I have a copy of ...
799 views

### Mathematical Background for Computer Vision [closed]

I am a PhD student and would like to do deep research in the area of computer vision and pattern recognition. I know to be successful I need strong mathematical background. Could you please introduce ...
741 views

### Preparing for “differential forms in algebraic topology”?

I'd very much like to read "differential forms in algebraic topology". Apart from background in calculus and linear algbra I've thoroughly went through the first 5 chapters of Munkres. I'm thinking ...
94 views

### What textbook and chapters should I go through to study for a probability qualification exam?

In 7 months I will have to take a "Probability" qualification exam similar to the ones shown here: Fall 2013 Spring 2013 Fall 2012 Spring 2012 Fall 2011 Could somebody please recommend the best ...
273 views

### What's the right moment to learn Set Theory?

I've seen a question in which the OP asked when is the right moment to learn Category Theory, it seems this moment comes a little after a course of algebra, and indeed some books on abstract algebra ...
443 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 ...
98 views

### Let $x,y,z$ be integers and $11$ divides $7x+2y-5z$. Show that $11$ divides $3x-7y+12z$.

Let $x,y,z$ be integers and $11$ divides $7x+2y-5z$. Show that $11$ divides $3x-7y+12z$. I know a method to solve this problem which is to write into $A(7x+2y-5z)+11(B)=C(3x-7y+12z)$, where A ...
302 views

### Is it possible to learn differential topology before analysis?

Currently I'm self studying for my own enjoyment topology and algebra (munkres and herstein). Since I start at the university next year everything I'm learning now is for my own enjoyment and I will ...
168 views

### Is it better to teach or to grade?

As a graduate student at my university, I have the option many times of deciding what type of work I do for support. The two basic options are to teach either a calculus or college algebra course, or ...
731 views

### Generic elementary group theory problems.

This question is about generic group theory problems. here are examples for what I’m referring to: Prove that any group of order $p^2$, where $p$ is a prime, is abelian. Let $G$ be a ...