# Questions tagged [advice]

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...").

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224 views

### Learning Technique

I'm prepared for the competitive exam like this (a sample question). In order to solve the problems, first to familiarize with the prerequisite for the each concept. It's ok! My problem is: If I'm ...
42 views

### Either, Or, Both…a question in mathematical writing [closed]

I want to write that "this transformation changes either rank of effective matrix, or norm of effective matrix, or both" I want to avoid repeating "of effective matrix". How can I do this
94 views

### Is there active research on topological groups?

So I came across something called "Topological Groups". I have just taken a course on topology/and some basic algebraic topology which i really liked. My mind was blown. I said topological groups are ...
261 views

### Can I skip part III in Dummit and Foote?

I am reading Abstract Algebra by Dummit anfd Foote. I have already taken an introductory course in linear algebra, mostly at the level of Strang's MIT OCW Linear Algebra. My question is: Can I skip '...
115 views

### Can a profoundly gifted high school student directly enter a graduate program? [closed]

I'm a high school math teacher and I've been working with a profoundly gifted student. His case is highly unusual, and I wonder whether it is possible for him to enter a math grad program without ...
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### How do I manipulate a trio of equations for Acceleration / Velocity / Position such that if I change the number of iterations, the result is the same?

This is for a thought experiment I'm programming. Let's say I have 2 cars; 1 in front, 1 in back. I'm adjusting the rear car's acceleration so that it will never be closer than 1 second's worth of ...
160 views

### How to understand theorems and their proofs faster? [closed]

I am a PhD student works in group theory. I have did the course work required to do research. I am facing one big problem that my learning speed is very slow. I have spent around 6 months on a single ...
108 views

### Standard and/or advanced curriculum preparing for a grad school in Applied Math

I was wondering what would be a list of Applied Math courses (sort of like a road-map for an Applied Math student interested in a Applied Math PhD) which preferably contains absolutely essential ...
233 views

### How to explain proofs to audience smoothly?

I have given 5 to 6 presentations till now (on abstract algebra topics ). Many times to me it appears that most of the people in the audience have not understand the most of the part. Some people ask ...
71 views

### Recommended reading for a 15-year-old hopeful university mathematics student. [closed]

I am in the UK, studying GCSE, if that means anything to you. What would you recommend to me, to further my understanding of mathematics, of my current level or further? Thanks.
149 views

### How to learn math, such that we enjoy it? [closed]

I'm finishing high school now, and have the impression that anyone who studies math beyond high school does so because they enjoy it. Occassionally, I manage to solve a math problem, and feel a deep ...
88 views

### Resources for probability and counting

I'm currently taking a Discrete probability course at my University.It isn't going to well,the grad student taking the place of the professor is not able to teach the material effectively.Nor are ...
117 views

### Should I read non-mathematical courses if I want to go for a Ph.D? [closed]

I am an undergraduate student at a university in Sweden who am studying my second semester of a three year undergraduate degree. I have always loved mathematics and had a few years between high school ...
165 views

### Soft Question: What to do with proofs of nontrivial theorems?

A major part of reading any text in mathematics is understanding theorems and proofs. For me, I would try to find a proof by myself before reading the one given in the text. But sometimes the proof ...
128 views

### Are 'topological transformation groups' still studied in current research?

I was looking at the book by Gottschalk and Hedlund on Topological Dynamics; it uses topological transformation groups in the beginning and terms like Unimorphism, which seem obscure in current ...
183 views

### Is 117 something like a magic number?

Why is it that if you add the last 2 digits of your birth year + your age or the age you will become on any particular year it always adds up to 117? For example, I was born in 1975 and turned 42 ...
56 views

### If $\frac{\phi(n)}{n}=\frac{\phi(m)}{m}$ then $n$ and $m$ have the same primes in their prime factorization

Here $m,n\in\mathbb{N}\backslash \{0\}$ and $\phi$ is the Euler Totient function. I have been trying to prove that this statement is true but I'm stuck. I started with applying the product formula for ...
83 views

### How can one directly advance research from outside academia? Particularly Set Theory?

I recently received a bachelor's degree in Computer Science (which I pursued for pragmatic reasons) and would like to contribute to Mathematics as a mathematician would. My challenge is not knowing ...
197 views

### Question on Mathematical Logic & Book Recommendation

I'm in the last year of my undergraduate studies in mathematics and I would appreciate your oppinion in the following thought. Should I study Mathematical Logic, if I want to do further studies in ...
357 views

### How to excel at math?

I know this question has been asked at least a hundred times earlier but before you mark this as duplicate please read this cause I seriously need some professional help here. I'm a 15 year old kid ...
166 views

### Which definition of dual space is more common in research?

Generally, whenever I ask a question or talk about dual space of a vector space, people tend to understand this space as the space of linear functions from the vector space to the field. Lots of ...
411 views

### They say that pure mathematicians can easly found jobs in industry, but how? [closed]

It might seems that my question has already been asked, but in fact it's slightly different from the other similar question, so please read it. I'm in the middle of my last university year in a pure ...
1k views

### How to avoid getting “lost in notation”

Having just finished my first (and wonderful) year of undergraduate math studies, there is a certain "skill" I find myself still struggling with, as if I've made no progress regarding it since my ...
701 views

### How do you explain the use of studying higher mathematics to non-mathematicians? [closed]

Currently, I am an undergraduate studying math and will soon be taking my first courses at a graduate level. I'm often approached by my friends, my parents, or others, with an innocuous question: "...