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-3
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0answers
10 views

Math Study Advice Needed - How to “Get Into It” / Need Motivation

Sorry if this question is a little too general for this forum, but I've seen some really useful stuff on here in the past so I thought I'd give it a shot. So I'm a first year student at university in ...
0
votes
0answers
21 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 ...
0
votes
1answer
39 views

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

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 ...
0
votes
1answer
388 views

Prove that the function is of exponential order and proving in mathematics

I'm currently learning about the Laplace transform and in my textbook in college and I have this definiton: Function $f$ is of exponential order if there exist constants $M>0$ and $a$ such that ...
1
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0answers
18 views

Math jobs in visualization? [on hold]

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!
-2
votes
4answers
530 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 ...
8
votes
1answer
280 views

When is a function a dimension?

The concept of dimension is used in many different contexts. Generally a dimension is a function that has as domain some family of sets ad has value on a set that, in the most common situations, is ...
31
votes
7answers
2k views

Do the axioms of set theory actually define the notion of a set?

In Henning Makholm's answer to the question, When does the set enter set theory?, he states: In axiomatic set theory, the axioms themselves are the definition of the notion of a set: A set is ...
3
votes
1answer
118 views

Is there some kind of deep relationship between substitution and recursion?

Define $\mathbb{N}$ as the initial object in the following category: Objects. Sets $X$ equipped with a function $S : X \rightarrow X$ and an element $0:X$. Morphisms. Functions that preserves ...
1
vote
0answers
62 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
57 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 ...
4
votes
3answers
46 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
19 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
166 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 ...
1
vote
1answer
37 views

What does “loss of regularity” mean?

I have seen a lot the phrase "loss of regularity" in references regarding PDE. (For instance, there are questions like "do solutions of 3D Navier-Stokes equations lose regularity or not?") Could ...
0
votes
1answer
31 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
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 ...
6
votes
1answer
235 views

A book on advanced math for a “novice” mathematician, but “mature” thinker

I enjoy giving interesting problems to my peers who have not seen a lot of mathematics. It is a constant conversation I have with many friends who would interchange "mathematical thinking" with ...
0
votes
0answers
16 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
69 views

Pure mathematics research [on hold]

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?
11
votes
3answers
180 views

Why are we interested in cohomology?

I've been studying algebraic topology for over half a year now and came across alot of different topics of it (fundamental groups, Van Kampen, singular homology, homology theory, Mayer Vietoris, ...
3
votes
0answers
60 views

Reference request for Grothendieck's work on “Integration with values in a topological group”

Recently I was reading the available part of the second part of W. Scharlau's book on Alexandre Grothendieck (see here). There I found, An anecdote survives about Grothendieck's arrival in Nancy: ...
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 ...
-3
votes
0answers
99 views

Number system where $e^x$ is identically zero [on hold]

In a previous post I tried to come up with an interesting example of a finite dimensional real algebra in which $e^x$ can be $0$. My attempt was not successful. I think part of the problem is that ...
1
vote
2answers
35 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 ...
4
votes
1answer
1k views

Preferable Order of Mathematics Study

I was just wondering if someone would be kind enough to tell me in what order (I know that there is no real "best order") one would most profitably study these subjects/books: (edited to conform with ...
1
vote
1answer
54 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
0answers
12 views

Used memory in Singular software [on hold]

Is there any command in Singular to Evaluate the amount of used memory?
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
30 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 ...
1
vote
0answers
33 views

Reference Quest: Measure Theoretic and Functional Analytic Intro to Stochastic Processes

Does anyone have any recommendations for a good book which introduces and cleanly and rigorously explains the measure theory and functional analysis implicit in and relevant to stochastic processes, ...
2
votes
1answer
35 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
12 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 ...
1
vote
1answer
32 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 ...
0
votes
1answer
56 views

Non-traditional student and undergraduate admission [on hold]

If you'd told me at 17 that I would find a passion for math later in life, I'd have told you you're crazy. But, here I am, loving math and chomping at the bit to pursue a B.Sc. in math. My problem is ...
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
50 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 = ...
26
votes
4answers
1k views

How much time is too much (to put into a single problem)?

As a self-studier, I have no due dates and no time pressure. This is partly a good thing since I do have a life outside of my pursuit of mathematics. However, the lack of pressure is also a bad ...
42
votes
12answers
3k views

Refuting the Anti-Cantor Cranks

I occasionally have the opportunity to argue with anti-Cantor cranks, people who for some reason or the other attack the validity of Cantor's diagonalization proof of the uncountability of the real ...
1
vote
4answers
412 views

Why do transcendental numbers exist?

(This is a revision of the below question, which was not clear. If I have used incorrect terminology, please offer corrections.) Given the sets $A$ and $B$, $B$ contains transcendental elements ...
2
votes
0answers
83 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, ...
76
votes
25answers
12k views

Mathematicians ahead of their time?

In every field there's always that person who's just years ahead of their time. For instance, Paul Morphy (born 1837) is said to have retired from chess because he found no one to match his technique ...
1
vote
1answer
33 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 ...
2
votes
0answers
64 views

Is Leibnizian calculus embeddable in first order logic?

We just published an article making what we feel is a plausible case in favor of an affirmative answer in Foundations of Science, see preprint here. The basic argument is that while such a requirement ...
0
votes
1answer
13 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 ...
10
votes
3answers
576 views

Why do people care about principal bundles?

I've started to learn a little about principal bundles (in the smooth category) and while I see how notions like connections and curvature are abstracted from the setting of vector bundles and brought ...
3
votes
0answers
29 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 ...
3
votes
1answer
33 views

Recommend of English video about math

My mother tongue is not English, but sometime there are some math reports or conference using English .Because my English is poor, I can't understand it well and can't suitably describe my question. ...
3
votes
2answers
66 views

Dissertation on Integrals

I'm considering doing a dissertation on Integrals: Riemann, Henstock-Kurzweil, Lebesgue and more I'm wondering if I can do it. This is usually a masters level dissertation (while I'm an undergraduate ...