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0
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0answers
3 views

Cycloidal coincidence?

For the cycloid $$x=a(t-\sin t)\ ,\quad y=a(1-\cos t)$$ we have, as is easily seen, $$\frac{dx}{dt}=y\ .$$ Does this have any geometrical or physical significance? Or is it just a meaningless ...
2
votes
1answer
36 views

Does memorizing a proof help to provide the intuition behind it?

To be clear, I'm $\bf{\text{not}}$ talking about rote memorization. If I can follow a proof, follow each step on its own, but still have trouble believing that the result is true. I usually try to ...
7
votes
1answer
82 views

Create a Huge Problem

I am wondering if any problems have been designed that test a wide range of mathematical skills. For example, I remember doing the integral $$\int \sqrt{\tan x}\;\mathrm{d}x$$ and being impressed at ...
7
votes
4answers
222 views

Application of computers in higher mathematics

Currently the main application of computers in mathematics seems to be to compute things, i.e. to solve equations, evaluate integrals, etc. It is at all possible to delegate the thinking of a ...
2
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0answers
42 views

Changing research area in grad school

I'm a PhD student about to close out my third year. My current research area is operator algebras. At the beginning of this semester I completed my qualifying exams (this was accomplished a semester ...
3
votes
4answers
447 views

Topological groups, why need them?

I'm reading through Munkres and Armstrong's books on topology. However, I find topological groups to be really complicated objects! I feel they are twice as hard to deal with then just groups and ...
1
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3answers
28 views

Which discrete mathematics book to read for a software engineer?

I'm a computer science student, but I lack a good mathematics background. So I decided to start working on that. I was searching in the topic and I found that for computer science a good knowledge of ...
0
votes
1answer
31 views

In which course one learns Lie Group&Algebra and to which category of mathematics this subject belongs?

I'm a junior and i have never leanred this subject. I think "Lie Group&Algebra" is really deep and massive theory since the wikipedia page for it is quite long. Nevertheless, i'm not sure ...
1
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0answers
26 views

What courses require multivariable analysis?

For which undergraduate and introductory graduate mathematics courses is a rigorous course in multivariable analysis an essential prerequisite?
1
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0answers
30 views

Analogy between linear basis and prime factoring

I recall learning that we can define linear systems such that any vector in the system can be represented as a weighted sum of basis vectors, as long as we have 'suitable' definitions for addition and ...
1
vote
0answers
35 views

Applications of PDEs

I teach an undergrad ODE course. As I have completed basically all the material, I thought it would be nice to give the students a brief introduction to PDEs. At the end of the lecture, I said that ...
4
votes
1answer
84 views

Forgetting mathematics. Memory problem [duplicate]

I got an A from Game Theory. But after that i forgot almost all the formulas and theorems. What should i do to prevent that? Do you forget math like i do?
0
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0answers
52 views

Choosing between Universities for Mathematics

I am trying to advise a younger friend looking into colleges and I was wondering what others would think: Is it better to go for a prestigious university where the focus would be almost exclusively ...
1
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1answer
65 views

Uncertainty of Graduate Mathematics

I will be starting my graduate studies next semester right out of my undergrad and I am uncertain about courses that I am ready to take. The main courses of concern are algebra, analysis and applied ...
0
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0answers
24 views

Proving Maths Skills for MSc Data Science Degree

In September I'll be applying for a Master's degree in Data Science (2015 intake). With the degree I hold (BSc Psychology), I will forfil the entry requirements provided I have a "demonstrable ...
2
votes
0answers
56 views

Calculus book advice

I'm reading Thomas Calculus now but I don't think it includes Mellin transform or Riemann-Stieltjes integration... Can you recommend an advanced calculus book which includes all of this stuff?
2
votes
0answers
21 views

Pure Math or Stats undegrad for Stats Grad School

Hello I'm currently a first year undergrad double majoring in physics and math. My school offers both a pure math and a statistics concentration and I'm wondering which one would be better for ...
0
votes
0answers
23 views

A nowhere zero point in a linear mapping and Research Resources

Conjecture: If $\mathbb{F}$ is a finite field with at least 4 elements and $A$ is an invertible $n\times n$ matrix with entries in $\mathbb{F}$, then there are column vectors $x,y \in \mathbb{F^n}$ ...
17
votes
8answers
5k views

Are there contradictions in math?

Someone told me that math has a lot of contradictions. He said that a lot of things are not well defined. He told me two things that I do not know. $1+2+3+4+...=-1/12$ what is infinity $\infty$? ...
0
votes
1answer
13 views

what are some typical systems of equations generating from practical problems?

I want to know some typical forms of system of equations generating from practical problems in engineering/economics/physics,etc. Some examples or research articles would be good. Specifically, I am ...
0
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0answers
25 views

Do those red cubes aligned circulary next to MATHEMATICS have any mathematical significance? [migrated]

Or they just look fancy and that's why it was put there ?
0
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0answers
30 views

The term $rank$ in methematics

Reading wikipedia's disambiguation page about the "rank" word I see many concept of rank of many different matematical object. I only know about the rank of a graded poset and the rank of a set that ...
4
votes
0answers
68 views

Is it easier to publish in certain areas of mathematics?

I was wondering whether there are areas of mathematics that it is easier to publish in than in others. The reason I'm asking this question is not because I would then want to do research there, but ...
4
votes
1answer
27 views

Surprising constructions in algebraic topology that facilitate one's understanding of underlying theory

I am recently come into the world of algebraic topology and find it a fascinating place with lots of beautiful constructions that challenge one's intuition. Also, understanding these constructions are ...
0
votes
3answers
31 views

Question about variable and constant notation in some properties

I am just starting to think about mathematical notation a lot more and some parts of it do not make as much sense to me as I would like. I am operating under the convention that beginning alphabet ...
0
votes
1answer
42 views

Is there a significance to a matrix having an eigenvector equal to a column vector within a matrix?

Consider matrix $A$: $\begin{bmatrix} 2 & -2\\ 3 & -3\\ \end{bmatrix}$ After little computing, we find the eigenvectors (and their corresponding eigenvalues) to be equal to $E_{\lambda=0}= ...
0
votes
1answer
56 views

Is it bad for a potential grad schooler to take Abstract Algebra and Real Analysis my last year?

I'm taking Abstract Algebra and Real Analysis my last year. I've already taken the following: Calc 1-3 DiffEQ Complex Analysis Operations Research Linear Algebra Mathematics Foundations Theory of ...
2
votes
2answers
68 views

Does attempting numerous questions in Mathematics textbooks actually help?

Specifically for high school/college maths where the textbook contains numerous exercises with similar trivial examples - would attempting all of the questions actually be more beneficial than (lets ...
1
vote
1answer
84 views

Foundations book using category theory?

I'm about to embark on a PhD in mathematical biology. My major is in computer science. I would like to acquire a more rigorous understanding of math, which I am going to need to tackle some research ...
0
votes
0answers
14 views

Help disabling press-to-test [on hold]

I've got a TI Nspire CAS (not the newest CX edition) and I accidentally put degrees instead of radians on Press To Test. Now it's stuck in this mode and the information at ...
3
votes
5answers
341 views

Jumping back into Calculus III

At the age of 30 I am going back to school for Electrical Engineering. Because of the way higher education works, all of my previous college coursework is being transferred, which does not allow you ...
3
votes
1answer
46 views

Gain confidence in maths.

I am a maths student and I really want to stand out in maths, to be good at it because I like it. But the transition from high school's computation-based maths to uni's concept-based maths made me ...
0
votes
2answers
54 views

Is 1 rad important?

Of course radians generally come in ratios of π. So is 1 rad important/useful/special? Or, for that matter, is any integer radian measure important? Besides being approximately 57°, I can't seem to ...
8
votes
3answers
632 views

Does writing a bachelor thesis make sense?

I am a math student in my fourth semester. At my university, it is common to write a bachelor-thesis in the end of the bachelor program in almost all subjects while in the math undergraduate program ...
1
vote
1answer
54 views

How to study analytic number theory?

Should i study many books at the same time? Or should i go one by one? I started with Apostol's book... But for example if i don't understand a proof, i check another book for a different proof of the ...
3
votes
3answers
58 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 ...
8
votes
3answers
160 views

$1^3 + \dotsb + n^3 = (1 + \dotsb + n)^2$: reason? [duplicate]

We have $$ 1^3 + \dotsb + n^3 = (1 + \dotsb + n)^2 $$ as we can establish by induction. But why does this hold? Can we connect it to something else?
20
votes
3answers
630 views

Totally lost and frustrated [closed]

I love maths. Rather I think I love maths. I am not sure. Whenever I study maths, I like it but there are times that i get really frustrated and stop studying it. I am preparing for an entrance exam ...
0
votes
1answer
49 views

Working towards Abel's proof of unsolvability of quintics

I am currently doing a course in Abstract Algebra. I have been told that while some of the basic theory is laid down, we will not get as far as actually proving the unsolvability of quintics. ...
2
votes
0answers
32 views

Can the chaotic motion of a double,triple,… pendulum be used as a source of randomness?

I've been playing with this animation, and I was curious whether the chaotic motion could be used as a source of randomness. It seems that if the motion is unpredictable (i.e. nondeterministic), then ...
0
votes
0answers
62 views

Copying and Pasting $\LaTeX$ [closed]

Is there any way to copy and paste $\LaTeX$ directly out of someone's question into the answer or comments? This would save a lot of time answering certain questions it seems like... Also, can this ...
0
votes
0answers
21 views

Translation of Théorie des distributions?

Does anyone know why there is no English translation of Laurent Schwartz's Théorie des distributions? Also, is it then worth attempting a translation?
0
votes
1answer
30 views

Changing the subject of formula to calculate data transfer speed

I am looking into buying a fast card reader, and concluded that to transfer $8 GB$ of data $(8\cdot 1024 MB)$ to my computer at a data transfer speed of $130 MB/s$ would take me $1.024$ minutes. ...
0
votes
2answers
70 views

Which do you prefer sine or cosine? [closed]

A soft question. Which do you prefer between sine function or cosine function? While I feel the sine funciton more clear and comfortable, but I prefer cosine, since $\Re{e^{ix}} = \cos{x}$, The ...
56
votes
14answers
4k views

A good way to retain mathematical understanding?

What is a good way to remember math concepts/definitions and commit them to long term memory? Background: In my current situation, I'm at an undergraduate institution where I have to take a lot of ...
3
votes
3answers
57 views

How to tell if algebraic set is a variety?

I've been reading some basic classical algebraic geometry, and some authors choose to define the more general algebraic sets as the locus of points in affine/projective space satisfying a finite ...
5
votes
1answer
62 views

What's the trick to re-focusing on your math studies?

If you check my history on MSE, you'll see that I was very active about 1/2 a year ago. Right now I'm working and socializing a lot, which is important, but I also have spare time to devote to my ...
1
vote
0answers
66 views

Is Modeling the Future of Mathematics [closed]

So my Differential Equations professor today said one sentence then left the room. It was the weirdest moment of my college career but I felt like he really tried to say something. He walked in 1 ...
3
votes
1answer
76 views

Examples of the Mathematical Red Herring principle

I read the Mathematical Red Herring principle the other day on SE and wondered what some other good examples of this are? Also anyone know who came up with this term? The mathematical red herring ...
3
votes
1answer
70 views

Where to begin my Math journey

I apologize if this is not the correct forum for this, but I felt it appropriate. I want to start getting into more mathematics and learning all I can to step up my programming career. I know plenty ...