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0
votes
2answers
25 views

A numerical scheme for finding radical matrices.

If the goal would be to solve the (matrix) equation: $${\bf P}^2 = {\bf A}$$ Do you think a numerical scheme alternatingly minimizing for $\bf P_1, P_2$ would be stable: $$\|{\bf P_1P_2-A}\|_2,\hspace{...
0
votes
3answers
35 views

How to denote 4th level of nested parentheses?

When dealing with equation that contains nested parentheses, they are usually denoted using the {[()]} system, with 'regular' parentheses being the innermost member, square brackets middle member and ...
13
votes
2answers
331 views
+50

Can Path Connectedness be Defined without Using the Unit Interval?

Can path connectedness be defined without using the unit interval or more generally the real numbers? I.e., do we need Dedekind cuts or Cauchy convergence equivalence classes of the rational ...
19
votes
2answers
2k views

So can anybody indicate whether it is worthwhile trying to understand what Mochizuki did?

So I am looking at some math stuff and I start looking at the abc-conjecture. Naturally I run into the name Mochizuki and so start trying to see what he did. Well, he is starting look like another ...
729
votes
55answers
426k views

Visually stunning math concepts which are easy to explain

Since I'm not that good at (as I like to call it) 'die-hard-mathematics', I've always liked concepts like the golden ratio or the dragon curve, which are easy to understand and explain, but are ...
4
votes
1answer
107 views

Are there any proofs that only exist by induction? [duplicate]

I've come to learn more about induction recently for proving things, and one thing stands out to me. It seems like you could just data-mine patterns and guess a relationship you think might be ...
1
vote
2answers
46 views

What is the meaning of 'regression' in 'linear regression'?

I can see why linear regression is linear, i.e., because it is represented by a line, but what does regression have to do with the term as a whole? What is the meaning this word contributes to the ...
4
votes
1answer
41 views

(Self) learning for adults.

Let me begin by saying English is not my fist language (i.e. I did not learn maths in English) and I'm not familiar with the US/UK school system. So if what I ask is blatantly obvious that might be ...
1
vote
2answers
50 views

Should one always perform logical reasoning intuitively and contentually?

I have been studying mathematics for more than a year now. In general, it's relatively easy for me to solve the exercises and to find proofs for certain propositions myself. In this sense, I would say ...
4
votes
3answers
17k views

How to calculate Maximum or Minimum of two numbers without using if?

How to to calculate the maximim or minimum of two numbers without using "if" ( or something equivalant to that manner)? The above question is often asked in introductory computer science courses and ...
6
votes
4answers
507 views

What should “The Fundamental Theorem of Linear Algebra” assert? [closed]

Unlike some other basic fields of mathematics, linear algebra does not seem to have a universally agreed-upon fundamental theorem. This I imagine might be because the subject usually admits a lot of ...
-5
votes
1answer
33 views

Can one extend the analogy between mathematics and art beyond a just “pleasing” result? [on hold]

This is a soft question. It's extremely commonplace for mathematician's to refer to work as "elegant," "beautiful," and I've seen many compare the process of doing mathematics to painting, or playing ...
2
votes
0answers
30 views

Geometry Of Unitary Transformations

Ever since I first took Linear Algebra, I have over time realized how concepts like determinants, eigenvalues, diagonalization, orthogonal transformations and so on have very intuitive geometric ...
3
votes
1answer
88 views

Ham Sandwich Theorem - intuitive proof

Ham Sandwich Theorem. Given 3 measurable "objects" in $\mathbb{R}^3$, it is possible to divide all of them in half (with respect to their measure, i.e. volume) with a single 2-dimensional plane. Can ...
16
votes
4answers
6k views

Why do we need to learn Set Theory?

I was planning to write some article for the Mathematics magazine of our college and it occurred to me that it will be a good idea to write about the impact and importance of Set Theory. I plan ...
0
votes
0answers
32 views

Do you need to understand measure theory to learn Lebesgue integration?

I want to learn the topic of Lebesgue integration but I know no measure theory yet. Would I be correct in assuming that I first need to learn measure theory (or at least get a feel for it) before ...
1
vote
1answer
59 views

Is $\mathbb{Q}P^{n}$ less studied/less useful than $\mathbb{R}P^{n}, \mathbb{C}P^{n}$?

I was wondering why we hardly ever talk about the rational projective spaces. We frequently use the real, complex, finite or even quaternionic ones, but for instance there is apparently only one ...
5
votes
6answers
642 views

How to Axiomize the Notion of “Continuous Space”?

EDIT (to clear up controversy and misunderstandings caused by my poor wording): Historically, Riesz's efforts to try and make rigorous a notion of a "continuous space" (as opposed to "discrete ones") ...
2
votes
1answer
29 views

Probabilistic Method/Model for Traffic Flow

Context: Given a network system or a traffic system with some value related to the system. Question: Which probabilistic methods, model, distributions are used frequently to predict a event (for ...
-1
votes
0answers
20 views

Bayesian Theory: Is it doable from $0$? [on hold]

How hard is Bayesian Theory? It is listed as a postgraduate course (I'm an undergrad), I haven't done much stats (only a bit of likelihood and liner regression). Is it possible to learn and do it as ...
10
votes
5answers
3k views

Mathematics, Philosophy and writing.

Do you know of any famous mathematicians who were also philosophers? I have heard of Descartes, Plato and Leibniz. Are there other good examples, especially more modern examples? Also welcome are ...
25
votes
2answers
278 views

Origins of Differential Geometry and the Notion of Manifold

The title can potentially lend itself to a very broad discussion, so I'll try to narrow this post down to a few specific questions. I've been studying differential geometry and manifold theory a ...
3
votes
1answer
126 views

Are there any modern mathematicians whose research interest is in “Probability Theory”? [closed]

I have seen professors in universities list "stochastic calculus", "stochastic analysis", "stochastic processes", "stochastic geometry" and "applied probability" as research interests, but are there ...
31
votes
6answers
5k views

What are some interpretations of Von Neumann's quote?

John Von Neumann once said to Felix Smith, "Young man, in mathematics you don't understand things. You just get used to them." This was a response to Smith's fear about the method of characteristics. ...
4
votes
0answers
108 views

On comparing two different notions of compactly generated space

I have encountered, in different circumstances, the following two slightly different categories: The full category of $\mathsf{Top}$ consisting of all objects that are: a) topological spaces ...
11
votes
4answers
2k views

Topics on Number theory for undergraduate to do a project [closed]

Im an undergraduate in the mathematics field ..So i wanna be alittle more productive and wanted to do an essay or project mostly on number theory or Algebra(Rings or Groups) and i want to ask if you ...
4
votes
6answers
3k views

Applications of Complex Numbers

For my Complex Analysis course, we are to look up applications of Complex Numbers in the real world. The semester has just started and I am still new to the complex field. I want to get a head start ...
14
votes
3answers
2k 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 ...
2
votes
1answer
97 views

How do you use reference books?

Reference books at the research levels often does not include any problem or exercise. While you can't read these books like novels(you normally need to work on other sheet of paper), I'm just ...
6
votes
1answer
317 views

Recommended research topics for high school student

I am a high school senior and I am interested in doing a math research. I hope someone can recommend areas or topics of research that are challenging, rewarding, and yet do not exceed my capability. (...
23
votes
11answers
3k views

Gap year to study math

This is a plan in its earliest and thus least concise stage, so either bear with me or don't read the following babble (I bolded some of the important stuff): I am a high school graduate who is about ...
48
votes
6answers
11k views

What is mathematical research like?

I'm planning on applying for a math research program over the summer, but I'm slightly nervous about it just because the name math research sounds strange to me. What does math research entail exactly?...
-3
votes
2answers
55 views

Redundant proof in Math paper [on hold]

Recently, I read a published math paper and I found that in the excessive argument in the proof of one of its theorem. In fact, in my opinion, the redundant part is not even correct, because it ...
2
votes
1answer
110 views

Undergraduate Project Suggestions

A student of mine has expressed interest in doing an independent project next quarter with me. This would not be for credit and it is purely for her own educational stimulation. She wants to study ...
1
vote
0answers
45 views

Error Correcting Code and Graph Theory

I am currently in an introductory graph theory class, and we are supposed to give a short presentation by the end of the semester. Recently, I've learned (a very small amount) about error correcting ...
18
votes
4answers
620 views

Problems from the Kourovka Notebook that undergraduate students can fully appreciate

The Kourovka Notebook is a collection of open problems in Group Theory. My question is: could you point out some (a "big-list" of) problems [by referencing them] presented in this book that are, ...
0
votes
0answers
23 views

Calculus for Proving Properties of Discrete Objects

I posted a question earlier about a proof in graph theory I was trying to figure out. In my attempt I used Calculus to prove a part of the theorem. In the comments people kept saying how you shouldn't ...
-1
votes
0answers
38 views

Advice on Research topics in Linear Algebra [on hold]

I am a rising senior undergraduate student. I have taken following courses and I have an opportunity to do a project in Applied Linear Algebra at a fairly good Mathematics department. I am trying to ...
9
votes
0answers
186 views

How can I begin reading journals and papers?

I am an undergraduate CS student but I love Math and spend most of my time doing and reading Maths books. I realise that it's important to get into the habit of reading papers and journals so it will ...
1
vote
1answer
95 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?
6
votes
3answers
1k views

How to stay academically active during a Mathematics Gap Year? [closed]

This year I started at the University of Cambridge to study Maths. I was very unfortunate to contract a serious infection early on in the term, and as a reult it has been mutually decided between ...
1
vote
5answers
2k views

What really is an indeterminate form?

We can apply l’Hôpital’s Rule to the indeterminate quotients $ \dfrac{0}{0} $ and $ \dfrac{\infty}{\infty} $, but why can’t we directly apply it to the indeterminate difference $ \infty - \infty $ or ...
1
vote
0answers
21 views

Style guide/typeface for handwritten mathematics

When writing math on graph paper, it's a small struggle to make my work as legible as possible and also use the page as efficiently as possible. I've read a little online about how latex typesets, ...
1
vote
1answer
36 views

Suggest books on Combinatorial Graph Theory

I am going to start self-studying Combinatorial Graph Theory. Kindly suggest books or study materials available online. I have been told that it is basically application of linear algebra, mainly ...
-3
votes
1answer
59 views

Simple examples for motivation of topology [closed]

It is easy to see motivation for groups and fields, as abstractions of operations defined on integers, rationals, reals etc. and how the results from those abstractions apply to integers, reals etc. ...
3
votes
3answers
45 views

What is the proper usage of $f: X \to Y$ and $f: \mathcal{P}(X) \to \mathcal{P}(Y)$ in proof writing.

I have read somewhere that suppose we are given a $$f: X \to Y$$ then $f$ is further associated with $$f: \mathcal{P}(X) \to \mathcal{P}(Y)$$ Does "associated" here means extended to a set valued ...
0
votes
0answers
26 views

What are interesting functions in 2D that vary visually as compositionality increases?

I wanted to create a function that its shape was a function of the depth of the compositionality (on a fixed interval). For example consider some compositional function $$f(x_1, x_2) = g( g( g( h_1(...
3
votes
1answer
72 views

Writing Math: Is using both $e^x$ and $\exp(x)$ ok for longer works?

I wanted to know what you guys think about mixing both notations for the exponential function $e^x$(for simple argument and to save space for larger equations) and $\exp(x)$ (for more complicated ...
1
vote
1answer
80 views

Does anyone know a no-nonsense intro to “logic for mathematics” that I can give to a Year 11 student?

I'm looking for material on propositional and first-order logic to give to a Year 11 student that explains how they're used "in practice." For example, I want to be able to write the null-factor law ...
8
votes
2answers
258 views

Explaining Mathematical Modelling to a nonmathematician

Due to the interdisciplinary nature of my project, I find myself collaborating a lot with nonmathematicians especially biologists, medical doctors, etc. I work mostly on mathematical models as applied ...