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0answers
4 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 ...
3
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0answers
19 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 ...
1
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0answers
27 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
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0answers
55 views

Student working with a researcher [on hold]

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 ...
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0answers
72 views

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

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 ...
5
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0answers
73 views

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 ...
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0answers
50 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
118 views

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

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
26 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
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1answer
48 views

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

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
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0answers
20 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
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0answers
22 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
180 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
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3answers
166 views

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

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
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0answers
36 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
30 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
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0answers
54 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.
-1
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0answers
57 views

How can I make math joyful to learn? [on hold]

As a kid I had a strong interest in games, especially competitive-type games. Chess for example was and still is fun for me, it can be described as being competitive, addicting, beautiful and filled ...
0
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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
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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
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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
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0answers
55 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
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0answers
7 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
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1answer
23 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 ...
0
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0answers
61 views

When to use $\Delta$ or $\delta$ in formulas? [on hold]

I use this symbol to denote the interval of created packets (variable, not constant) in the field of computer science. In formulas, which symbols should I use, $\Delta$ or $\delta$? Or other symbols? ...
0
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0answers
52 views

What is the most practical field in Pure Mathematics? [closed]

What is the most practical field in Mathematics? I am a student of Pure Mathematics.I have covered various courses like algebra (abstract and linear),analysis(real,complex,functional),measure ...
2
votes
1answer
51 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
37 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
72 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 ...
8
votes
4answers
333 views

How To Develop A Higher Mathematical Aptitude? [closed]

First off I must say I'm pretty blown away by the vast majority of the people in this forum. I do aspire to reach the knowledge of mathematics as shown on the site, but honestly it's a little daunting ...
-1
votes
0answers
70 views

why is $3704554$ a magic number? [closed]

Someone told me $3704554$ is a magic number, but I am unable to see why. I've tried factoring it: $2\cdot7\cdot107\cdot2473$, binary: $1110001000011011101010_2$, but nothing seems to explain it.
0
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1answer
43 views

Books on multivariable calculus

I'm looking for a book that covers the following subjects: multivariable functions, extremes of multivariable functions, integration, implicit function theorems, functions defined by integrals, vector ...
5
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3answers
656 views

Which background is more suitable to study “Cryptography”

I am a student of Pure Mathematics and also interested in programming .I have learnt C++,SAGE . Recently I have started learning "Cryptography" .But there are many definitions involved here like ...
-1
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0answers
23 views

What is the correct way to give an online source in a bibliography of Bachelor's or Master's Thesis by Bibtex? [closed]

Recently, I am creating the bibliography for my master's thesis with bibtex. For books and articles, I use MathSciNet to get the right Bibtex-data. But I am not sure how to write down online sources ...
1
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0answers
19 views

General Topology on Complex field?

While Real Analysis is based on spaces of real numbers so we have also Complex Analysis uses complex numbers in its spaces also. General Topology has commons with Real Analysis and whatever I see in ...
0
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0answers
34 views

Chaos theory in stock market

I am doing an IB Extended Essay on chaos theory and fractals in the consumer stock market. It is a high school level essay (4000 words) and should be understandable for a calculus student. I'm having ...
0
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0answers
40 views

Interested in Math Olympaids [closed]

I study Advanced Mathematics in University and am interested in Math Olympaids. Where can I start to build the fundamental skills to solve some questions?
2
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0answers
11 views

What kind of subject/book(s) should I get if I'm interested in random motions hitting a barrier and being added to the barrier?

I'll explain in more detail. I'm interested in learning more about diffusion limited aggregation and the fractals that result from that process, however it'd probably be best to know more about ...
7
votes
1answer
142 views

Reading mathematics at the graduate level - does every single proof matter?

I would be interested in hearing from PhD students (and upwards) specializing in pure maths (in particular, the more algebraic aspects). My question is this: When reading to learn mathematics at ...
1
vote
2answers
65 views

Any “DIY Analysis” books?

Are there any good "analysis through problems" type books? I've tried reading analysis books but I literally get bored to death, and, until I manage to concoct a way of transforming a normal textbook ...
1
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0answers
33 views

Vector calculus vs Vector analysis?

I was just wondering, is vector analysis the same as vector calculus? What about multivariable calculus? Because my multivariable calculus book (which I assume is the same as vector calculus?) covers ...
46
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11answers
7k views

Why there is no sign of logic symbols in mathematical texts?

Either in undergraduate or graduate textbooks on Mathematics (Real/Complex Analysis, General Topology, Differential Geometry, ...), I never saw symbols $\Rightarrow$, $\iff$, $\forall$, $\exists$, ... ...
0
votes
2answers
61 views

Meaning of symbols like $\inf\limits_{\epsilon>0}$

I am very confused at the precise definition of the following symbols. A reference or explanation would be great. $$\Large\inf\limits_{\epsilon>0}\qquad \sup\limits_{\epsilon>0}$$
2
votes
1answer
19 views

what is a spectral function?

My knowledge in spectral theory is very limited, but lately I heard talking about the spectral function of an operator and how it's important. By curiosity I tried to look for a definition and a ...
-1
votes
0answers
45 views

Guidance required [closed]

I know the question you are going to read WILL sound unconstructive and surely 'll get slammed but a good guidance instead in the matter concerned might prove very useful to me. As I'm into my 3rd ...
3
votes
2answers
79 views

Interesting facts and problems to motivate high school combinatorics students

I will give some classes in combinatorics to high school students and I would like to know some facts (and proof) I can show to my students to motivate them to study this beautiful subject. I'm ...
8
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0answers
96 views

What was the original motivation for matrix multiplication? [duplicate]

When I took linear algebra class in my freshman year, the multiplication operation for matrices was defined without any apparent motivation. Given an $m$-times-$n$ matrix $A$ and an $n$-times-$p$ ...
0
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1answer
45 views

How do you memorize theorems and techniques for long? [closed]

I have a very serious problem with memorizing things. After I concentrate on one suject for some months, I hardly remember other subjects. For example, when I study topology, I get familiar with ...
0
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2answers
27 views

Interpreting a Quotient Group ($D_8/\langle r^2\rangle$) in 2 Distinct Ways

I seem to have a misunderstanding about quotient groups. Let $D_{2n}$ denote the group of symmetries of an $n$-gon and let $V_4$ denote the Klein-4 group. On one hand, if we identify $r^2$ with $1$, ...
2
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0answers
61 views

Generalizing beyond proper classes

I noted that issues such as Russell's Paradox involving the set of all sets that don't contain themselves can be resolved by stating that the object that is all set that don't contain themselves is a ...