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2
votes
3answers
46 views

Is there any example of a set, together with the “sum” operation which is non conmutative?

I was wondering if there is any mathematical structure (Im not even sure this is the correct way to name what I have in mind) but basically, any set, together with the operation sum, (I don´t say just ...
2
votes
1answer
22 views

Sum of powers of eigenvalues

The sum of the eigenvalues $\lambda_k$ of an $n\times n$ matrix is equal to the trace of the matrix, i.e. $$\sum_{k=0}^{n-1}\lambda_k=\text{tr}(A).$$ Is there a "closed form" sum of positive integer ...
13
votes
5answers
318 views

Non-trivial “I know what number you're thinking of” [on hold]

Consider the following 'trick' (WARNING: very lame) Think of a number. Multiply this number by two. Add four. Divide the number by two. Subtract the number you were originally thinking of. I guess ...
10
votes
4answers
351 views

Examples for Hilbert's Quote

Hilbert once said, “The art of doing mathematics consists in finding that special case which contains all the germs of generality.” What would be (relatively) simple examples?
5
votes
3answers
139 views

How can a modern historian interpret historical mathematicians?

Interpreting historical mathematicians involves a recognition of the fact that most of them viewed the continuum as not being made out of points. Rather they viewed points as marking locations on a ...
1
vote
2answers
75 views

Is $(0.999999…9) \times (1.000000…001)$ smaller or greater than $1$? [duplicate]

Is $(0.999999...9) \times (1.000000...001)$ smaller or greater than $1$? The "..." mean there are "infinitely" many "$9$'s" respectively "$0$'s"
1
vote
1answer
59 views

How do I get good at calculus in specific, Mathematics in general? [on hold]

I understand that this question might look like a duplicate to some others asked before, but I assure you, read on, you'll find my case different (hopefully). I am a 12 grade student from the ISC ...
0
votes
0answers
34 views

Alternative view of matrix inversion (explanation required)

We were taught in linear algebra that in order to try to find the inverse of a matrix we can create an augmented matrix $[AI]$ where $A$ is the original matrix and $I$ is the identity matrix. Then we ...
0
votes
0answers
10 views

Statistics Topics Needed to Study Epidemiology [on hold]

I am wondering what topics in statistics epidemiologists must know for public health studies. I am trying to self-learn statistics. Is this endeavor possible?
3
votes
3answers
364 views

Do Gödel numbers have a practical use?

Is there any example of Gödel numbers being actually used in practice? If so for what purpose?
0
votes
0answers
9 views

Explicit heat kernels

For quite general domains, the Dirichlet heat kernel has a representation via the eigenfunctions of the corresponding Dirichlet problem. This form is usually not easy to analyse so I was wondering - ...
-5
votes
1answer
57 views

Why is there no maths nobel price? [duplicate]

I have been wondering for such a long time, anyone has an idea? Mabye it is because people didn't care for Maths enough?
3
votes
0answers
23 views

Hausdorff dimension via ergodic theory

This is definitely a soft question, but it was recently mentioned to me that one can study the dimension of fractals via ergodic methods. I'm familiar with ergodic theory on about the level of ...
1
vote
1answer
29 views

Good introduction to cohomology of spaces?

I'm trying to read chapter $3$ of Hatcher but I find it a bit difficult to read. I really only made it through the first two chapters because I had in-class lectures to go along with the reading. Does ...
16
votes
4answers
533 views

Gaining Mathematical Maturity [on hold]

I was redirected here by a kind fellow from math.overflow. This is not a typical math question, so I apologize if that is discourteous. I am currently a sophomore in my undergraduate mathematics ...
0
votes
0answers
12 views

Unsolved problems involving or concerning the unitary DFT

Does anyone know of any unsolved problems involving or concerning the unitary discrete Fourier transform matrix $F_n=n^{-1/2}(f_{j k})$ where $f_{jk }=e^{2\pi j k i}$ and $i=\sqrt{-1}$, or its ...
10
votes
1answer
142 views

Fake proofs using matrices

Having gone through the 16-page-list of questions using the tag (fake-proofs), and going though Best Fake Proofs? (A M.SE April Fools Day collection) and ...
0
votes
0answers
37 views

Starting an REU late because of quarter system? [on hold]

So I am really looking forward to participating in REUs after sophomore and junior years in college, but I just noticed that since I am on a quarter system I will only be done with finals at around ...
0
votes
0answers
49 views

Rigorous Approach to Precalculus

I've made the mistake of looking at more advanced texts that deal with precalculus-level mathematics in a more formal, rigorous way than usual. Perhaps this isn't a mistake, but now that I've glimpsed ...
2
votes
1answer
50 views

Mori cone and birational geometry

Let $X$ be a projective and smooth algebraic variety (maybe here the hypotheses may be relaxed). If I understand correctly, Mori cone is defined as the closure of the cone in $N_1(X)$ of effective ...
1
vote
0answers
22 views

Math jobs in visualization? [closed]

What kinds of jobs can mathematics graduates (with an undergrad or grad degree) acquire in fields such as modelling, graphics, etc.? Links would be very helpful too. Thanks!
0
votes
1answer
43 views

What computer science skills would be beneficial for a maths major? [closed]

I'm currently entering my third year of my general science/maths undergrad degree (somewhat like a combined honours in life sciences and maths), and I'm a little wary of what I'm going to be doing ...
1
vote
0answers
72 views

Cat and a mouse on a circle

I hope this is the right plcae to post it as I'm not sure if the solution is mathematical. I saw this riddle on a board at the university and it seems that there's something I'm missing. It goes as ...
1
vote
3answers
63 views

I don't get it, does “augmented chain complex” actually mean anything?

If I understand correctly, chain complexes make sense in any category enriched in the world of pointed sets. In practice, there's also a notion of an augmented chain complex, where we have an extra ...
0
votes
1answer
25 views

Recommendations for tutorials specifically devoted to real integration using contour integral techniques.

Complex analysis, and in particular contour integrals and the residue theory have proved a very powerful tool in computing a large class of real function integrals which would be quite troublesome to ...
4
votes
3answers
53 views

Vectors sometimes used in math just as arrays/lists of numbers, sometimes as concept of “change”

As a freshman in a small town college. Ive been getting mixed signals to what vectors (and matrices/tensors) are. Sometimes I get the feeling they are used just as containers/arrays for multiple ...
0
votes
1answer
35 views

Complex Roots of Unity?

I just had a question about complex roots of unity. It's not a computation thing; I know how to find them and I know what they mean. In my class last semester, my professor mentioned that they are ...
0
votes
0answers
17 views

What is the point of solving a system of linear equations using back-substitution (as opposed to reduced echelon form)

In lecture the other day, my professor offhandedly mentioned the existence of a process called back-substitution a way in which a computer program would solve a system of linear equations rather ...
2
votes
1answer
72 views

Pure mathematics research [closed]

What can a first year mathematics undergraduate, who wants to pursue research in pure mathematics, learn in 67 days that will help him in the future?
0
votes
2answers
31 views

Why are Optional Stochastic Processes Important?

I understand to some degree why adapted processes, progressive processes, and predictable processes are important. EDIT: I am referring only to the continuous time case, NOT discrete time. But why do ...
-1
votes
4answers
541 views

Why do they call it base 10?

Now, I know intuitively why it's called base 10: because there's 10 numbers. But see here's the thing, if we're working with numbers 0-9 (and of course we are), we use up our numerical artillery at ...
2
votes
0answers
13 views

Describe the position of $w_0=\frac{(|z_0|+r)+R}{2}\cdot\frac{z_0}{|z_0|}$ w.r.t. $B_R(0)$ and $B_r(z_0)$

I am working with two circles $B_R(0)$ and $B_r(z_0)$ and want to describe the position of the point given by $$w_0=\frac{(|z_0|+r)+R}{2}\cdot\frac{z_0}{|z_0|}.$$ First I would like to know whether my ...
1
vote
2answers
36 views

What is Convex about Locally Convex Spaces?

This might be a silly question, but what motivates the name "locally convex" for locally convex spaces? The definition in terms of semi-norms seems to have nothing to do with convexity or with the ...
0
votes
0answers
12 views

Used memory in Singular software [closed]

Is there any command in Singular to Evaluate the amount of used memory?
1
vote
1answer
57 views

Review of Differential and Integral Calculus in 60 hours

Hopefully this question isn't too narrow. It is similar yet distinct from this: Calculus Review On The Web and this: What are some good resources to review basic university calculus, years later? I ...
0
votes
1answer
31 views

The definition of random sequence

Suppose that I ask you to tell me four integers between $0$ and $10$ randomly. You tell your numbers, for example $\{3,7,2, 5\}$. However I don't trust you about your numbers being random, hence I ...
1
vote
2answers
33 views

What is the difference between Mapping and Morphism

I wonder if there's differences between Mapping and Morphism. Although the terms are used in different context i.e. mapping for set theory and morphism for category theory, from my understanding they ...
4
votes
3answers
175 views

Learning differential calculus through infinitesimals

In class, we've studied differential calculus and integral calculus through limits. We reconstructed the concepts from scratch beginning by the definition of limits, licit operations, derivatives and ...
2
votes
1answer
36 views

What is the difference between an adapted process and a predictable process?

As the footnote on page 1 of this document mentions, even most experts in the field of stochastic processes don't seem to know rigorously what the difference is. However, since I don't have any idea ...
0
votes
0answers
15 views

An empirical correspondence in algebra

In the article Simplicity of Jordan superalgebras and relations with Lie structures by C. Martinez, the author states: "What is know about Jordan superalgebras with non-semisimple even part? Here the ...
0
votes
0answers
16 views

Continuous indicator-like functions

Let $\Omega$ be a compact subset of $\mathbb{R}^n$. Let $g:x\in\mathbb{R}^n\to\mathbb{R}$ be a continuously differentiable function such that $$ \begin{cases} g(x)>0 & x\in\text{int}\Omega,\\ ...
3
votes
1answer
51 views

Alternate Definition of Infinite Series Summation?

Question I was wondering if one could define the sum of conditional convergence without using the notion of before or after (time)? My Understanding We define the following partial sum: $$ S_n = ...
0
votes
1answer
39 views

Is there a list of recommended problems to do in each chapter of Spivak's Calculus anywhere?

I've recently been self-studying Spivak's Calculus, and since I don't have the time to do every problem from every chapter at a and finish at reasonable rate, I've looked for a course syllabus or ...
2
votes
0answers
102 views

Isothermal coordinates

Is there an application or interest in studying the isothermal surfaces where the metric is $ds^2=E*(du^2+dv^2)$ and where $E>0$ is an harmonic function? I know that this metric is a special kind ...
1
vote
1answer
67 views

Examples of the use of $(p \vee q) \wedge (\neg p \vee r) \Rightarrow (q \vee r)$ in “real” mathematics?

Here, a proof is requested for the following tautology: $$(p \vee q) \wedge (\neg p \vee r) \Rightarrow (q \vee r)$$ Its pretty easy to prove; nonetheless, I don't find the formula at all intuitive, ...
1
vote
1answer
35 views

Eulers identity history

When Euler discovered/invented $e^{ix} = \cos(x)+i\sin(x)$. Did he doubt his calculations for a length of time? Was it Readily accepted by the mathematical community quickly or did they object at ...
0
votes
1answer
14 views

Is there a Relationship Between Multi-Valued Logic and n-Satisfiability?

Is binary (Boolean) logic related at all to the two-satisfiability problem? And is ternary logic related in some way to the three-satisfiability problem? Would it follow then that if one were to ...
3
votes
0answers
31 views

Why does (h,k) generally represent the center of a circle?

Why are h and k generally used to denote the coordinates of the center of a circle? After a bit of research, we found that h may represent "horizontal shift" or "horizontal translation", but we're ...
1
vote
0answers
63 views

Bringing Up Weak Derivatives on Calc I Quiz

Ok so I realize that I was being a bit of a smart ass but we had a quiz in my honors Calc I class the other day and one of the questions was: "Is the following function $f:[-2,2] \to [0,1]$ ...
3
votes
2answers
88 views

Is Wikipedia a reputable source for Mathematics? [closed]

I am currently in High School, possibly interested in pursuing a career in Mathematics or the Philosophy/Logic behind Mathematics. I don't have a lot of money for books or videos about Higher ...