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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2answers
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 ...
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2answers
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
3
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0answers
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 ...
4
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2answers
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 '...
4
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0answers
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 ...
0
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1answer
38 views

Equivalence of quadratic forms and general advice about “Number Theory” (by Borevich-Shafarevich)

At the very beginning of the "Algebraic Supplement" of "Number Theory" (Borevich-Shafarevich) I read: Any quadratic form $f$ can be written as $$\sum_{i,j=1}^{n} a_{i,j}x_i x_j,$$ where $a_{i,j}=a_{...
2
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1answer
3k views

How to use the AOPS books?

I just acquired the art of problem solving prealgebra book. I would like to ask, how does one use the AOPS books, are they meant to be supplementary to a full textbook? Or are they used for ...
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3answers
151 views

Should one prove all Dedekind-complete ordered fields are isomorphic before using the real numbers in any formal matter?

As mentioned in an early post I spent about nine hours cumulatively trying to construct the reals axiomatically from the bottom up using naive set theory. Though eventually I realized I made an error ...
3
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2answers
183 views

What are the mathematical topics most essential for an applied mathematician?

I am an undergraduate student of mathematics. My question regards those mathematical topics which are indispensable to applied mathematicians: what are they? My conception is that real analysis, (...
0
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1answer
791 views

Is it impossible to grasp Multivariable Calculus with poor prerequisite from Single variable calculus? [closed]

Would it be possible to keep up or would i be overwhelmed by a hopeless struggle trying to grasp the new material while at the same time looking back at as well as relearning a few core concepts from ...
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2answers
301 views

A simple reverse engineering of calculation. [closed]

I have a formula $x=\frac{1}{\frac{Y}{1000}}$ which is the calculation for converting Parallax to Parsec. I need to reverse it but can't remember how to reverse $1/$ . So for a Parallax of $49....
0
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1answer
43 views

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 ...
0
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5answers
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 ...
3
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1answer
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 ...
5
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3answers
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 ...
2
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2answers
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.
3
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1answer
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 ...
2
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2answers
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 ...
1
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3answers
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 ...
2
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2answers
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 ...
4
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2answers
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 ...
1
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2answers
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 ...
3
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2answers
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 ...
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2answers
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 ...
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2answers
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 ...
2
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2answers
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 ...
2
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2answers
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 ...
3
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0answers
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 ...
9
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4answers
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 ...
13
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2answers
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: "...
2
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1answer
287 views

How does one come up with regular expressions?

A regular expression is a sequence of characters and operators (concatenation, union, and Kleene $\bigstar$) that defines a pattern. Kleene $\bigstar$ operator: $S^\star=\{\epsilon\} \cup S \cup SS \...
0
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1answer
321 views

Extending Local Smooth Function $f : U\subset M \rightarrow \mathbb{R}$

I already know that one can extend a smooth function defined on a closed subset of a smooth manifold to the whole manifold using smooth bump function (John Lee : Smooth Manifold). So i wonder if we ...
9
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2answers
752 views

Study Tips and Techniques for Self-Oriented Students

I am asking for what, if any, the preferred study skills of approaching classes are like in higher math education are like **in general, ** and I am not asking necessarily for personal anecdotes for ...
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0answers
61 views

Advice: Which book/topic should I take first: Set Theory or Abstract algebra.

Some background about me. I study on my own and I am not a math major but I am interested in math. I am not even sure if I am mathematically mature enough to handle the 2 topics but I have read a few ...
2
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0answers
389 views

Study order of Fourier Analysis, Functional Analysis and Operator Theory?

I hope my question is in the scope of MSE. I want to study 1- Fourier Analysis, 2- Functional Analysis and 3- Operator Theory, all from scratch. Which one I need to study first? second? and third? ...
4
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2answers
152 views

Are we expected to “think outside the book” when answering the exercises for Courant's Differential and Integral Calculus?

I'm reading Courant's Differential and Integral Calculus, there is this session of exercises: My trouble here is that previously he talks about the rational numbers, why it is needed for them to ...
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2answers
1k views

Is it always possible to create a intuition for abstract algebra theorems?

I am a Ph.D student in computer science, and I work on graph isomorphism. My research work requires some level of mathematics (mostly group theory ). I have done basic level abstract algebra course. I ...
7
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3answers
260 views

How can I advance?

Right now I am 13. I have studied at the normal pace at my school, however, since this academic year I have felt that the pace the classes move at are too slow and I wish to advance faster. I would ...
2
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2answers
193 views

Theorems in Group Theory

A while ago, I took an introductory course on group theory, but have forgotten a good deal of the material. I therefore plan on spending the weekend reproving the theorems I once understood. However, ...
0
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1answer
382 views

Stick with Spivak or switch? [closed]

I've been working through Spivak's Calculus for a few weeks; however, I am stuck on Chapter 5 (limits, epsilon-delta, etc.). I'm finding that I need to reference his earlier chapters (on inequalities) ...
0
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1answer
55 views

Creating a math “loop”

Forgive me if I'm asking this question incorrectly, but I think I've hit the end of my mathematics knowledge on this one. I'm trying to create an equation for video games that takes the desired jump ...
8
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2answers
355 views

Motivation for learning about fundamental groups and covering spaces

I am about to give a seminar presentation in an algebra seminar (undergraduate level) about the Hopf fibration $SU(2) \longrightarrow SO(3)$ for which I will use an algebraic-topological approach ...
13
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2answers
458 views

Exploring Mathematica as a High School Student

I am a high school student and I am receiving a free one-year subscription for Wolfram Mathematica as a prize from USAMTS. How can I make the most of this one year with software that I have heard is ...
5
votes
1answer
642 views

What would be the effective way to study advanced mathematics? [closed]

I am a recent graduate with mathematics degree but I still don't think I truly understood all those difficult courses, especially the real analysis. My professor told me during his lecture that nobody ...
0
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0answers
54 views

Motivating undergraduates in learning about the Casimir element

Next week I will give a lecture about a chapter in Lie Algebras (I'm myself an undergraduate student). One of my topics is about the construction of the Casimir element (from Humphreys' book). I'm ...
5
votes
1answer
570 views

Advice on how to overcome obstacles in studying Abstract Algebra [closed]

I am studying math as an undergraduate, and I have run into a problem that seems to common among students- I enjoy analysis, followed by topology, and find the topics intuitive. However, the road has ...
1
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1answer
113 views

Field extensions and inverse $ \alpha$ of an element

I'm taking a second course of abstract algebra but I feel like I don't have the enough basis from the first course so it's very difficult the second one (well that's how I feel it). For example, I ...
9
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0answers
302 views

Applying to math graduate school out of law school [closed]

I was a former math college student with a 3.9+ GPA (overall, and in my math classes). I took most of the key classes to go to grad school, e.g. groups, rings, and fields, upper-level real analysis, ...
5
votes
2answers
325 views

Show all matrices very similar to the identity matrix are invertible

Please don't post completed solutions for 24 hours, as this is a homework problem, and I just need a bit of guidance. Given a $N\times N$ matrix A, let $|\mathbf{*}|_{2}$ be the sum of the squares of ...
4
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1answer
148 views

How to learn language to read math text? [closed]

I recently discover new mathematical wealth in non-English texts. Sadly, the two language that I speak are not German, Russian, Chinese, French, or languages that belong to the world leading math ...