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

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1
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1answer
76 views

Book: Functional Calculus

Is there a good book that investigates in detail the various kinds of functional calculus? I'm having now some knowledge about unbounded operators and integration but I would like to understand ...
0
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1answer
19 views

About the convergence or divergence?

Whether the following integral converge or diverge by comparison test. \begin{align*} ...
0
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0answers
31 views

General Strategy for solving mathematical problems

Lately I noticed that I am good at solving only those problems, similar to which I have encountered before. I get stuck with problems which ask for new(at least to me) mathematical reasoning. When I ...
4
votes
1answer
173 views

Too “young” for advanced mathematics?

Is it harmful to try to learn an advanced topic that is way beyond your mathematical maturity, even if you're really interested in it? Should I focus only on standard material for undergraduates and ...
0
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1answer
50 views

Questions about the field Business Mathematics

What interests should one have to decide to pursue a master's degree in Business Mathematics? Which subjects are related with this field? What career opportunities are there having this master's ...
2
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1answer
97 views

Is it worth it? [closed]

I am studying pure mathematics at university, as well as minoring in physics. I am soon to finish to BSc degree, and I am considering continuing on with studying pure mathematics. However, I do have a ...
3
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3answers
130 views

Can a mathematician be a multi-discipline expert?

My professor says: If you be a mathematician then you can easily learn any discipline like physics, chemistry, engineering and even medical! Is he right? I am an enthusiast of all scientific ...
3
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3answers
47 views

Confusing -Probabilities.!!

Ok so far what i understand is this lets say...Having to draw a card from 52card-deck its probability is of course 1/52.Now the probability to say that i will keep drawing this same card 10 times of ...
3
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0answers
121 views

Which is the best transitional mathematics book for self-teaching among the ones listed?

What is Mathematics, An Elementary Approach to Ideas and Methods - Courant Robbins Stewart How to Solve It, A New Aspect of Mathematical Solving - Polya Introductory Mathematics, Algebra and Analysis ...
3
votes
1answer
108 views

How do high-achieving students in math study for their exams?

I'm taking a real analysis course that is a bit more advanced than usual in that it introduces you to the Lebesgue theory and has some deeper concepts in metric spaces. This is an honors and advanced ...
31
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9answers
4k views

When to give up on a hard math problem?

I practice olympiad problems from books like Putnam and Beyond. Often I come across a problem that I simply can't solve. After $\sim30$ minutes of deep thinking it feels like I'm ramming my head into ...
17
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2answers
349 views

Pure mathematics curriculum for self study with interests in foundational issues

I wonder if I want to make my own pure mathematics curriculum to study along the next 4 or 5 years. What topics should I include? I want it to be like one which an undergraduate student of pure ...
1
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2answers
106 views

A unique situation may prevent me from pursuing a science degree. Advice appreciated. [closed]

I'll try to keep this succinct. I'm enrolling in a second degree computer science program at my previous university. I graduated with a double major in Finance and Accounting about a year ago. Here's ...
4
votes
1answer
119 views

What should be in your graduate toolbox?

I've just finished my undergraduate degree at an average uni in the UK. Clearly the content will not be as in depth or rigorous as some of the higher ranked universities. I intend (well, hope!) to ...
-5
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1answer
81 views

Difficulty of coursework offsetting grades (graduate admissions) [closed]

Sorry to post another graduate admissions related question, but I hope a discussion on this would be helpful to people, in particular undergrads worrying about grades. I am an undergrad at a top 5 ...
1
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1answer
58 views

Graduate course selection for prospective probability student

I am about to begin my masters in applied mathematics, with the hopes of eventually researching probability theory and it's applications to physics. With that in mind, I was wondering which of the ...
2
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1answer
88 views

Questions about a computer science field

I would like to have some information about the computer science field, " Algorithmic and Systems Analysis ". Is this a field of theoretical computer science? What subjects are related with this ...
0
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0answers
172 views

Math Competitions such as Intel Science Talent Search for High School Freshmen

I am extremely interested in mathematical competitions. I was wondering if there was something like the Intel Science Talent Search, where one can present his/her research, for freshmen in high ...
2
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1answer
56 views

Post Baccalaureate Studying

So I'm currently finishing up my last quarter of undergrad, but unfortunately I have to take a year off before starting grad school. My degree is in physics, but I've been far more interested in ...
0
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1answer
33 views

Intuition or wisdom for stability and instability properties of locally linear system. Boyce, p513, Table 9.3.1

Our instructor requires us to memorize this table for our differential equations exam. So I wonder if anyone has some deeper intuition or observation to help with this? For example, I noticed ...
4
votes
3answers
352 views

I am failing at Analysis again. [closed]

I am stuck at this very hard course again. I don't want to put blames but if you were to ask me, what is going wrong I would say: The professor teaches too bluntly The book is too hard to ...
0
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1answer
77 views

Research Proposal help

Soft question, so I hope this is still in the right place. I have applied for a PhD position at the university I have just finished my undergrad degree at. I have to write a research proposal in the ...
38
votes
7answers
2k views

When working proof exercises from a textbook with no solutions manual, how do you know when your proof is sound/acceptable?

When working proof exercises from a textbook with no solutions manual, how do you know when your proof is sound/acceptable? Often times I "feel" as if I can write a proof to an exercise but most ...
1
vote
2answers
66 views

Should the theory be studied thoroughly before solving exercises?

Most of the books claim in the preface that the important part of the book is in the exercises, which makes sense considering that solving problems improves in great depth the understanding of the ...
0
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0answers
73 views

math student looking to do better in math competitions.

I am currently in my summer vacations. Next year I will star my undergraduate studies in mathematics. I used to be in mathematics competitions. Last year I got a silver medal in my countries national ...
4
votes
1answer
143 views

How should one go about obtaining “mathematical maturity”?

tl;dr: Is mathematical maturity better obtained by doing hard subjects slightly out of your reach, or by doing more simple subjects to gain experience? The end of the semester is close, and I ...
0
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3answers
218 views

I have a proof of the Collatz conjecture . Where should I submit my proof?

I have been working on the Collatz conjecture starting around 10 years ago. I would like to submit my proof for analysis. I would like advice on where to submit my proof.
2
votes
1answer
118 views

What should a student (with algebraic-geometry minded) study in differential geometry?

One of my friend who is an undergraduate student, has known something about algebraic geometry (equivalent to chapter 1 and a little bit chapter 2 in GTM 52 by Hartshorne). He is now has to study a ...
28
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27answers
2k views

Gift advice: present for high school graduate interested in math

I am a PhD student in mathematics who recently found out that I will be attending my girlfriend's cousin's high school graduation party. I have never met the cousin, but hear that he is very ...
4
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0answers
136 views

How to balance learning and researching as a new PhD student?

As a new PhD student, how to balance learning and researching? I am in Australia and here we don't have any course in PhD period. I know I need to learn something about my programme, but sometimes ...
8
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3answers
1k views

What Maths are the most important for Artificial Intelligence?

I am just curious about this. Please don't include anything about programming.
3
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1answer
241 views

Ultimate GRE Prep

I'm planning on taking the math GRE Subject Exam in April (~11 months from today). I want to start preparing now in the hopes of scoring in the 95+ percentile. I have already taken a number of ...
3
votes
2answers
95 views

How many times should students repeat reviews? Frequency of repetitions? [closed]

The usual advice is that a math student has to read or study something "a couple of times" to appreciate it. But is there a narrow range of the optimal number? Any research on this? And what's the ...
1
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0answers
81 views

Exam Advice or Tips, specific for Undergraduate Math or Higher [closed]

What are some noteworthy, even rare suggestions for exams in undergraduate math or higher? I'm not interested in general advice that can apply to many different subjects, like ...
1
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0answers
99 views

Is it worth it to start over in math?

Alright, so I wasn't sure where to ask this question but this website seemed the most relevant. I wasn't too good of a math student in middleschool and highschool, I got through my classes, sure, but ...
2
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3answers
80 views

Intuition - Linear Congruence Theorem

Let a and b be integers (not both 0) with greatest common divisor d. Then an integer $c = ax + by$ for some $x, y \in Z$ $\iff d|c$. In particular, d is the least positive integer of the ...
3
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0answers
140 views

Isolation and self-study

A little background: I am currently a sophomore (studying mathematics) at an unknown university in the Middle East. My mother is European so it does not make sense to study mathematics in the Middle ...
1
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1answer
86 views

How to remember modular arithmetic and divisibility results?

I tried reviewing the same material $\ge 5$ times, once every 2 weeks or whatnot. Withal, I query intuition like this. But I forget these results quickly or don't remember them 100% perfectly. But ...
0
votes
2answers
89 views

Career advice: Mathematical neuroscience

I need some advice about my career. Currently, I'm an undergraduate student of math. Since I can remember, I wanted to be a scientist, so I decided to go for applied math. The field that I'm ...
2
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1answer
81 views

Learning Advanced Mathematics

I'm a 12th grade student and I've recently developed a passion for mathematics . Currently my knowledge in this particular area is comprised by : single-variable calculus , trigonometry , geometry , ...
3
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2answers
63 views

In what order does mathematics build upon itself?

I have many times come across mathematical proofs, theorems, conjectures, and generally interesting things. For example: Twin primes conjecture Millennium problems Ramsey theory Fermat's last ...
0
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0answers
113 views

Which math courses should I take to prepare myself for Masters in Financial Mathematics?

I am an Applied Mathematics (BSc.) student that is graduating soon. Apparently, I need to take one more elective course (but I can also fit in two more electives if I want to) before I can graduate. I ...
0
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0answers
24 views

What is the standard notation for Neuman Boundary Condition.

I would like some one to help me to explain how one can represent the Neuman Boundary condition in a standard way. What I wrote was like the following, $\frac{\partial \phi_{st}}{\partial n}=0$ but ...
32
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10answers
3k views

Becoming Better at Math

How can I become excellent at math? It really interests me but when I fail I become demotivated and begin to give up. EDIT: Could anyone suggest books for someone with a math education that just ...
3
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0answers
52 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 ...
11
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6answers
1k 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 ...
3
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3answers
148 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 ...
2
votes
5answers
342 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 ...
5
votes
1answer
124 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 ...
2
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1answer
50 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 ...