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1
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3answers
440 views

Is it mathematically wrong to prove the Intermediate Value Theorem informally?

I have been looking at various proofs of the IVT, and, perhaps the simplest I have encountered makes use of the Completeness Axiom for real numbers and Bolzano's Theorem, which, honestly, I find a bit ...
3
votes
1answer
62 views

How long before the prey can escape?

I've (sort of) come across the following problem in my research. The actual scenario is a little abstract to explain, so I'm rephrasing the problem in terms of a predator/prey scenario. I'm tagging ...
0
votes
1answer
47 views

Probability as a function of time

I was really wondering when I have to select any one out of the n options available - the probability of selecting A (let's say) is 1/n. But then I'm confused. When I (or anyone/anything else) bring ...
1
vote
1answer
57 views

what is significant about closed sets? [on hold]

Looking at this, what is the Significance / usefulness of a set being closed? what more can be deduced when a set is proved to be closed ? l am sure it activates number of short cuts in proving ...
2
votes
3answers
60 views

How do set theory, and formal logic fit in together?

Im at that stage in my mathematical understanding where I kinda understand what set theory is and what first order logic is but dont really understand how they fit together to create Mathematics. I ...
0
votes
0answers
61 views

Engelking or Munkres for General Topology? [on hold]

I am a last-year Bachelors student and when I finish my Bachelors, I will have one year free time just before I start Masters in Pure Mathematics. I like to be better in General Topology before ...
1
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0answers
39 views

Possible Connections between Harmonic Analysis, Potential Theory and Analytic Capacity for a Fourier Analyst

So, Folks, here's the deal: After looking at this question, posted a little earlier on this site, and getting quite inspired by the beauty of this kind of result, I have got quite interested on this ...
2
votes
2answers
84 views

Is $\frac00=\infty$? And what is $\frac10$? Are they same? Does it hold true for any constant $a$ in $\frac{a}0$ [duplicate]

I know that $\lim_{x\to0}\frac{x}{x}=$ 1. But in my text book, it is written that it is $\infty$ and even $\frac10=\infty$. But how is it possible? And are they both same? What is the difference ...
2
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0answers
26 views

Proofs by analysing games

I recently read the following article giving a novel proof of the uncountability of $\mathbb{R}$ by analysing a particular game, amongst other results. ...
0
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0answers
28 views

What properties could a spectra of derivatives have?

Imagine that we have a function $f(x)$. Now imagine that we have access to all orders of its derivatives at any point x, denote this by $F(n)={{df^n} \over {dx^n}}$. So we have a function that's ...
3
votes
3answers
79 views

How to discover other fields of mathematics? [on hold]

I am currently an undergraduate and thinking about applying to graduate school for math. The problem is that I don't know what field I want to go. Taking graduate classes even more confuse me because ...
1
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0answers
25 views

How Kriging, Bochner theorem and Positive definite (PD) function are related?

This question referes to the link: https://en.wikipedia.org/wiki/Kriging I can understand the relation between Bochner's theorem and PD function. But could not properly understand and connect all ...
3
votes
0answers
77 views

Opportunities to learn algebraic geometry outside of PhD education [on hold]

After a lot of deliberation, I decided to go to professional school instead of pursue academic mathematics. I don't have research aspirations, but I do have an obsession with "getting" esoteric ...
1
vote
0answers
21 views

How can I determine if I should major in math? [closed]

I am an undergrad computer science student thinking about switching to pure mathematics. I enjoyed all the math courses I took but I found really hard to keep up with some of them and did poorly this ...
1
vote
1answer
35 views

Applications of statistics to pure mathematics [closed]

Are there any "applications" of statistical methods to pure mathematics?
7
votes
2answers
96 views

Finding math research problems [closed]

What is an efficient strategy to find fruitful research problems. So far the best advice I have heard about choosing a problem is to "talk to as many people as possible and go to as many talks as ...
4
votes
0answers
44 views

Estimate what percentage of math articles on Arxiv are eventually published. [closed]

I was looking through arxiv and was curious about what percentage of the math articles on there get published. Does anyone know or care to take a guess?
2
votes
0answers
51 views

(Theoretical) Complex Analysis Textbooks

Most books I've seen on complex analysis do not develop it theoretically, which can be somewhat infuriating for the budding pure mathematician. What I am looking for are some comprehensive, rigorous ...
6
votes
2answers
84 views

What Topics of Mathematics to study to go into Big Data

I am interested in Big Data and related jobs after graduation from Math PhD/Masters, what topics and fields of Mathematics should a student learn that are most relevant to Big Data? Currently, I know ...
3
votes
0answers
72 views

Exam question: Are zero points justified for this answer?

I just recently had an exam and had to answer the following question: Find the solution to the initial value problem $$x'(t)=\frac{1}{x(t)}; \space x(0)=1$$ and specify the maximum interval off ...
2
votes
2answers
63 views

Do “small” and “large” numbers actually exist in an absolute sense?

Numbers like $(10)^{-10^{10^{10}}}$ are generally regarded as small, whereas numbers like, for example, Graham's Number, are regarded as extremely large. My question is, are these numbers simply ...
4
votes
0answers
72 views

Fruitful advice to get back to study Mathematics again? [closed]

I have completed masters in Pure Mathematics a year back.I was preparing for an exam for pursuing a PhD program in the same .The results came out in this year in the month of April and found that I ...
0
votes
0answers
53 views

Which kind of jobs allow time and energy for one to pursue their mathematical interests? [closed]

I would like to give some perspective on why I am asking this. I'm a undergraduate who heard the siren calling for mathematics about a year ago after struggle of finding what I wanted to do with my ...
3
votes
1answer
67 views

Differential geometry in the context of manifolds

I am an undergraduate student of mathematics. I have a solid background on calculus, linear algebra, real analysis and point set topology, but I have never studied differential geometry. I am very ...
4
votes
1answer
38 views

Mathematics of Magic Squares

I have seen many popular accounts of simple magic squares but I would like to find a proper mathematical background to understanding magic squares. What background knowledge do I need. I am a retired ...
4
votes
2answers
95 views

Advantages to learning Sage?

I'm wondering if anyone can let me know advantages to installing/setting up Sage on my computer for doing computational math (work in groups, finite fields, and combinatorics, along with some search ...
2
votes
1answer
70 views

What's a good book on geometry to read after Kiselev?

I have finished reading both books on geometry by Kiselev and now look to move on but can't find any book to let me do so. Which book would you suggest that one may read after finishing Kiselev?
2
votes
0answers
69 views

Student working with a researcher [closed]

I was wondering if it is possible for a student to "work with" a researcher on a regular basis. That is, the researcher would give him articles to read, as well as small problems he feels might be ...
-4
votes
0answers
84 views

Comments about “Topics in Algebra” by I.N. Herstein and “Abstract Algebra” by Dummit/Foote? [closed]

Today, I got two gifts from my research mentor: "Topics in Algebra" by I.N. Herstein and "Abstract Algebra" by Dummit/Foote. I am very happy and grateful for his gifts, but I already have been ...
11
votes
1answer
208 views
+50

Is there a profitable way to read mathematical proofs

Mathematical proofs are often presented in a sequential way, i.e., presenting definitions, building lemmas based on these definitions, building further results on these lemmas and finally invoking a ...
1
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0answers
53 views

Does a mathematical construct exists which explains all theories?

If I am not wrong quantum mechanics is about measurements of different physical properties and probabilities of getting different outcomes. We have a mathematical construct to explain it, that is how ...
5
votes
2answers
141 views

How to understand mathematics on a deep level? [closed]

I've been focusing on self studying mathematics for the past couple months, and I'm currently working on discrete mathematics. Here's my attempt at a metaphor to describe my issue. Imagine you have a ...
2
votes
1answer
27 views

Intuition about Blumenthal's 0-1 law

I'm studying Brownian motion from Durrett. I'm trying to understand what Blumenthal's 0-1 law really says about what Durrett calls the germ field, $\mathcal{F}_0^+$. Let $\mathcal{F}_t^+ = \cap_{s ...
1
vote
1answer
53 views

What are the topics that must be covered in a beginning graph theory course? [closed]

Good day to everyone. It will be my first time to make a syllabus on elementary graph theory. My question will be: What are the topics that must be covered in a beginning graph theory course? Also ...
1
vote
0answers
27 views

Applications of Pure Mathematics in Computational/Algorithmic Geometry

I am a student having Pure Mathematics background currently doing M.Tech in Computer Science and want to do PhD in the area of Combinatorial Computational Geometry. I was wondering if there are areas ...
0
votes
0answers
28 views

How to study numerical analysis?

As the title says, I'm curious about what methods can be used when trying to study numerical analysis (or numerical methods ). I have no problem studying abstract algebra or real analysis, since that ...
8
votes
1answer
193 views

Objects Too Big To Care About?

I was wondering if in certain fields of math (denoted by some set of axioms describing some class of objects), that there is a cap on size beyond which the existence of larger objects is "irrelevant" ...
3
votes
3answers
182 views

How to overcome the temptation to read many books covering the same topics [closed]

S.E advisers, I am a college sophomore in US with a major in mathematics and an aspiring mathematician in the computational complexity theory. I have been reading some math books on different topics, ...
1
vote
0answers
37 views

“Successful applications in engineering outpace mathematical rigor” - other way 'round?

I saw the above quote on Jeremy Kun's and it really hit a note with me. This was in the context of the Fourier transform, in that physicists were using it to discover elegant identities before there ...
2
votes
1answer
33 views

Space between $L^1$ and $BV$?

I am looking for a function space $X_s$ such that this space has following properties: $X_s$ is a Banach space, and has lower semi-continuous properties with respect to $L^p$ strong convergence. I ...
1
vote
0answers
55 views

Operator form $L^2$ space to$L^1$

Can we have an operator such that it transforms an element of $L^2$ to $L^1$? Is this a valid question or this is incorrect? We can consider the measure space as finite.
0
votes
1answer
49 views

Functions with real domain but complex range, do they have any use?

For example if we define the square root function like this: $$\text{Sqrt}({x})= \begin{cases} \sqrt{x} & x\geq 0 \\ i\sqrt{-x} & x<0 \end{cases}$$ Or we could have an exponential ...
0
votes
0answers
21 views

Is there one to one relation Positive definite(PD) matrix and PD function?

Is it correct to say that a PD matrix can be built from a PD function? For example circulant matrix or Toeplitz seems to be built from a positive definite function. Positive definite function is ...
0
votes
0answers
29 views

Final year dissertation/project ideas for numerical methods

In my final year, I have to submit a project/dissertation on Numerical Methods. I have done a course on it, which included some proofs and programming. Just eager to get ideas that I can look at. PS ...
0
votes
0answers
59 views

Examples of mathematicians getting started on a PhD 'late' in life.

I am interested in notable mathematicians who contributed deeply to mathematics but who earned their PhD 'late' in life. For our purposes I will define 'late' as near age 40 or later. Most graduate ...
1
vote
0answers
9 views

Is self-similarity a form of symmetry, is it the other way around, or is it something else?

I'm aware that self-similarity is a form of symmetry, however I'm interested in getting a more in depth explanation of the relationship. Could you consider symmetry to be a form of self-similarity? ...
1
vote
1answer
26 views

Geometric interpretation of the derivative of a Bezier curve

For a given set of control points $b_0, b_1, \ldots, b_n$, the Bezier curve is defined as $$b^n(t) := \sum_{j=0}^n b_j B_j^n(t),$$ where $B_j^n(t):=\binom{n}{j}t^i(1-t)^{n-i}$ are Bernstein ...
2
votes
1answer
53 views

Intuition on the Representable Functor

Given a locally small category C, and an object $C$, the functor: \begin{equation} \mbox{Hom}_\textbf{C}(C,-):\textbf{C} \longrightarrow \textbf{Sets} \end{equation} that sends objects to hom-sets ...
5
votes
1answer
39 views

Why “singular” in “singular homology/cohomology”?

As the title suggests, I'm curious to know whether there is any reason why the word "singular" appears in "singular homology/cohomology".
2
votes
4answers
75 views

Are there relations between elements of $L^p$ spaces?

I have read about dual spaces and the relation $1/p+1/q=1$ as mentioned in the Wikipedia page. Are there any more theorems or relations that connect elements between the $L^p$ spaces for different ...