Questions asking for advice on various mathematical matters. Consider adding the tag (soft-question) as well.

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2
votes
3answers
312 views

Question regarding which book to use to study for an actuarial exam.

I am considering a career change and I would like to have some advice regarding the exam 1 (probability) that I need to pass as an actuary. The books that are recommended by SOA is the following. ...
5
votes
2answers
145 views

Is it a problem being unable to understand a mathematical definition without examples?

I was reading a book on coding theory, there was a definition fot the Hamming's Distance and also one example. Understanding purely from the definition was hard but the example helped to give meaning ...
1
vote
2answers
72 views

Question regarding education and master's degree in mathematics.

I am a UCB graduate with a BA in Education Centered Mathematics. Due to poor planning, I graduated without a teaching credential and ended up tutoring at a tutoring center. After 3 years working, I ...
2
votes
1answer
96 views

Are paraphrased theorems allowed?

In writing maths papers, if I want to present a theorem or definition from some other paper, would it be acceptable to cite the author and then present a paraphrased version of the theorem/definition ...
0
votes
1answer
238 views

Competition style mathematics

I'm currently 18 years old and only as of the part year taken a strong interest in maths. I'm working with my school curriculum (UK a-level) and receiving A grades so I am happy with this. However I ...
22
votes
6answers
4k views

Teaching a 4 year old maths

Im 18 years old and getting to grips with advanced mathematics (pre-university) and I have a younger brother of 4 years old (quite an age gap). I want to get him interested in learning (and away from ...
2
votes
0answers
170 views

Making Math a Job [closed]

As of now, I am pursuing a degree in math with my concentration being mostly on the applied side. I got into a grad level differential equations course over the summer and got an A. That being said, I ...
5
votes
0answers
216 views

culture of PhD students [closed]

I will be beginning my PhD program in a few weeks and I am adjusting to a lot of changes. Of course, there's the transition from undergrad to grad. Aside from this, I am pursuing it in the USA with me ...
16
votes
1answer
517 views

Strategies - What to do when stuck on some math?

Since math students will likely find themselves stuck on some math at some point, I am interested in pallating this ceaseness "fact." Thus, what are strategies, solutions, or resorts for getting ...
81
votes
10answers
3k views

what is expected from a PhD student?

As a PhD student in applied mathematics or mathematics in general, are you expected to be able to prove every problem, for example, in an elementary real analysis book? I know it sounds silly but I am ...
5
votes
0answers
130 views

which branch of maths studies Standard Logical Matrices

In classical logic you have truthtables like: & | T | F ---|---|--- T | T | F F | F | F In many valued logic you have tables like: (this one is ...
18
votes
3answers
622 views

How to Garner Mathematical Intuition

Motivated by Why Is Intuition so Important to Mathematicians but Missing from Mathematics Education? $^{1}$ by Leona Burton, I would like to learn about specific ideas or strategies to attain ...
2
votes
1answer
154 views

Ideas for mathematics club

I am planing to suggest founding Mathematics Club in next fall. Here is my attempt for first prototype: -Sources: films(such as Dimensions), interactive stimulation for some mathematical ideas(like ...
1
vote
1answer
164 views

Advice on career- interested in Mathemetics

I am sorry to post this question related to career over here. But I knew this is the place where my question can be viewed by the best people who can provide best advice. To introduce myself, I have ...
1
vote
1answer
749 views

Applications of number theory and functional analysis in the real world/ job market

what do you think are the application of pure mathematics in the real world except research. would like to pursue a masters in it because i love it but is it leading me any where in the job market? ...
1
vote
1answer
219 views

advice before i embark on my graduate studies in applied math

I'll be pursuing my graduate studies in applied math this fall. I'm hoping to gather advice in order to help me somewhat plan my courses as well as provide insight as to what is realistic or not. i ...
4
votes
0answers
242 views

Is Abstract Algebra Necessary For A Thorough Understanding of Real Analysis?

Background Info: I have been studying (self-study) Real Analysis for a few weeks now, and with the help of people from here I have, comfortably, made it 3/4 of the way through the first chapter on ...
11
votes
3answers
515 views

How to go About Undergraduate Research

I apologize in advance if this question is out of the scope or focus here. I was just wondering about the whole prospect of researching as an undergraduate. How to do it? Who to talk to in my ...
0
votes
1answer
106 views

Complex analysis knowledge that required to understand material in Riemann Surface

I have taken a course on complex analysis in university, at that time the instructor chose the book "Complex Analysis" by Serge Lang. Now I am participating a cemina on Riemann Surfaces which truly ...
4
votes
1answer
40 views

Proving that $Hom_G (V,W)$ is 1-dimensional when $V,W$ are irreducible

Question: Let $G$ be a group. For any two representations $V,V'$ of $G$ over $\mathbb C$, let $Hom_G (V,V')$ denote the space of all linear maps $h: V\rightarrow V'$ such that $h\rho'_g = \rho_g ...
1
vote
1answer
42 views

Show that there can be no trail in $G$ that contains all edges.

Let $G=(V,E)$ be a graph. Assume that $G$ contains at least three vertices with an odd degree. Show that there can be no trail in $G$ that contains all edges. First I checked the definition of a ...
6
votes
4answers
1k views

Two Different Approaches to Self-learn Calculus

Here's my situation: I'm a computer science student who has taken Calculus I twice. Not less than a week ago, I finished a second semester of the class and felt entirely defeated finishing the final. ...
2
votes
1answer
119 views

Rudin: Problem Chp3.11 and need advice.

I am working on the following problems and I have a couple of questions. Suppose $a_n>0, s_n = \sum_{i = 1}^{n}$ and $\Sigma a_n$ diverges. RTP (a) $\Sigma \frac{a_n}{1+a_n}$ ...
3
votes
0answers
96 views

A partial ordering on textbooks

After college, it has been very difficult to continue learning math as a hobby, I have the time for it, but I get incredibly frustrated when I run into something that it feels like I will never ever ...
3
votes
1answer
150 views

Advices on learning SDE/PDE for junior undergrad

Everyone. I am about to take an ODE Course in the summer. I wonder if it will help my understanding in stochastic differential equation and partial differential differential equation. My future plan ...
21
votes
4answers
857 views

Understanding mathematics imprecisely

For a long time, it has been a complete mystery to me how any of my peers understood any math at all with anything short of filling in every detail, being careful about every set theoretic detail down ...
10
votes
4answers
259 views

Communicating mathematics

As a TA, my ratings have been fairly mediocre. There's nothing to suggest I'm a problem, but I have room to improve. What's more disturbing to me is that I even struggle to communicate math with ...
5
votes
7answers
814 views

What should I learn next for pure math?

I can do basic single variable calculus which is essentially all you do at A Level in the UK. I also just read "What is mathematics?" by Richard Courant which I found very good. I would like to know ...
18
votes
6answers
2k views

Submit papers: arxiv or vixra? [closed]

If I submit a paper at other place (for example vixra) first, can I (modify it and) submit it to arxiv again? Is it valuable to publish a paper at the vixra? Except arxiv and vixra, does any other ...
1
vote
1answer
198 views

Which topics of real-analysis should be studied if you have already done calculus

Which parts of real-analysis are worth studying if you have already taken several calculus courses? I know that real-analysis is more 'rigurous', but still I wonder whether it is worth to again go ...
7
votes
6answers
711 views

Which topics of mathematics should I study? [closed]

I'm a first year econometrics student with a great interest in mathematics. I very much enjoy my study, but still I am interested to learn about more topics in mathematics which are not part of my ...
6
votes
3answers
744 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 ...
7
votes
2answers
254 views

Applications of information geometry to the natural sciences

I am contemplating undergraduate thesis topics, and am searching for a topic that combines my favorite areas of analysis, differential geometry, graph theory, and probability, and that also has ...
5
votes
2answers
347 views

What are some reasonable things to prove about the Collatz Conjecture?

I am writing an undergraduate paper on the $3n+1$ problem, and I am looking for some theorems related to the problem that would be reasonable for someone with my mathematical background to prove. I'm ...
1
vote
0answers
54 views

Improving my Mathematics [duplicate]

This isn't a regular maths question. So I'm currently in my first year at Uni doing a Mathematics major. I would like to know what things I can do to help me improve in Mathematics? I would say I am ...
11
votes
1answer
463 views

Practical Tips: Mathematical research and discoveries [closed]

How to be when you are working on something innovative? What to do if there is a chance (even the $1\%$) that your work is leading you to something original? For example what have I do if I ...
5
votes
3answers
257 views

Does Differential Topology or Differential Geometry play a larger role in Chaos Theory?

I'm an undergraduate on somewhat of a time constraint in school. I have room in my remaining schedule for a semester of either Differential Geometry or Differential Topology. I understand the ...
20
votes
2answers
483 views

Advice: Difficult Situation

I'm in need of advice with my life/studies. This will probably turn out to be a long post so here goes. My background I did very well in high school mathematics achieving an average 97.5% over 6 ...
5
votes
2answers
327 views

Advice: Modern vs. Classics

First of all, my apologies if (well, I know I am but I don't know where to put it) I am posting this in the wrong place. So please feel free to move it to someplace else or to tag it differently if ...
2
votes
2answers
270 views

The maths required for an economics degree

I have a degree in computer science and I wanted to do another degree in economics. However, my maths have been weak since high school always scoring slightly above passing rate. During my course of ...
19
votes
3answers
642 views

Why should “graph theory be part of the education of every student of mathematics”?

Until recently, I thought that graph theory is a topic which is well-suited for math olympiads, but which is a very small field of current mathematical research with not so many connections to ...
85
votes
9answers
6k views

How do I sell out with abstract algebra?

My plan as an undergraduate was unequivocally to be a pure mathematician, working as an algebraist as a bigshot professor at a bigshot university. I'm graduating this month, and I didn't get into ...
1
vote
1answer
187 views

Will I have learned the prerequisites for self learning stochastic calculus and monte carlo method?

I'm an undergraduate econ major, and my main focus is in actuarial sciences, which as you may or may not know it's pretty mathematical. Some of the topics I will have to learn at some point on my own ...
9
votes
3answers
2k views

Choosing a PhD topic

My supervisor and I recently had a long chat about PhD related stuff. He said something to the extent that your chances of employment after finishing your PhD among other factors depends on the topic ...
33
votes
6answers
2k views

Should I be worried that I am doing well in Analysis and not well in Algebra?

I attend a mostly liberal arts focused university, in which I was able to test out of an "Introduction to Proofs" class and directly into "Advanced Calculus 1" (Introductory Analysis I) and I loved ...
1
vote
0answers
43 views

What's the interested topic or applications about random graph, probabilistic method or combination?

I want to pick some topics or applications to do a project of a current course. Those topics should be related to graph theory, combinatorics, random graph, probabilistic method etc. Such as social ...
10
votes
7answers
539 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 ...
29
votes
8answers
2k views

How to use math textbooks

I'm a higher schooler who was recently gifted a book by my teacher (Schaum's outline of advanced calculus) which is really awesome and I've started working my way through it. I have run into a ...
16
votes
3answers
626 views

What's next for me?

I'm in my last year of undergrad, and I would like to do original research for my senior thesis. I am already published in finite group theory and am looking for a new topic to study. I have taken ...
3
votes
1answer
308 views

Taking an exam in math analysis course.

So I'm taking my first midterm exam in math analysis soon and I'm confused on how to study for it. I mean in calculus one would be able to just go into the book and take derivatives and integrals ...