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71 views

Can we consider a hypergeometric function as a closed-form?

Let's say a calculus problem like an integral or a series has a solution that inevitably involving a hypergeometric function. It turns out that hypergeometric function cannot be expressed in term of ...
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71 views

Math opportunities for a graduate

Are there any opportunities for young mathematicians who have finished their undergraduate education and are taking a year before going to graduate school, but want to do something math related? To ...
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127 views

Reference Request: Prereqs for Lecture Notes on “Abstract Linear Algebra”

I just found this set of lecture notes on linear algebra which seems to go over several things I've been wondering about as I study linear algebra. Unfortunately there are very few exercises in the ...
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54 views

Name for a body that can be completely described using its silhouettes

I'm shooting blind over here because I have no background in this field of mathematics. I assume that if you have a body (in $\mathbb{R}^3$), you can call it convex if any segment from one point ...
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207 views

Note-taking software which is capable of representing mathematical relation

After quite a few studying experiences (both alone and following a class, studying topology, algebra, analysis, measure theory, differential geometry) I have acquired a lot of notes that I have either ...
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129 views

Intuition about structures in Galois Theory.

Background Often in mathematics I find we can ask "why" something is true. Of course, this is not a well defined question. However, it usually prompts answers that includes words like ...
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67 views

Making modular representation theory and cohomology 'compelling' and 'accesible'

I'm currently putting together an application for a dissertation completion fellowship offered through my university. A part of the application includes 500-1000 words describing my dissertation. ...
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80 views

Is there a proper etiquette for asking an author for their (mathematical) software?

This may not be the correct place to ask such a question. I have read a mathematical paper on multiclass total variation clustering. I wish to use the algorithm in the contents to compare with another ...
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331 views

Mathematics felt by Srinivasa Ramanujan

At the moment I am reading the book Ramanujan's Papers by B.J. Venkatachala, V. Vinay and C.S. Yogananda; when clarifying some doubt with a professor, he told me that Srinivasa Ramanujan used Galois ...
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208 views

Difference between dynamic system and complex system

I know this might not be an easy question, I've already read the wikipedia page, and there is an interesting view: Therefore, the main difference between chaotic systems and complex systems is ...
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309 views

Paul Erdős Joke.

I was watching the great documentary "$N$ is a Number" and in it Erdős tells a joke where he writes: PGOM LD AD LD CD Which means poor great old man, living dead, archeological discovery, legally ...
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787 views

which branch of maths studies Standard Logical Matrices

In classical logic you have truthtables like: & | T | F ---|---|--- T | T | F F | F | F In many valued logic you have tables like: (this one is ...
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288 views

Logical consequence of Euclid's theorem

Are there any far reaching non-trivial consequences of Euclid's infinitude of primes where theorems make use of it? Wikipedia does not have the list of applications of this theorem, rather modern ...
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192 views

Recommendation textbooks on D-module

I am going to take part in a seminar on D-module and applications, the textbooks that will be used are : D-modules, Perverse Sheaves, and Representation Theory, and A Primer of Algebraic D-Modules ...
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204 views

Convex Hulls vs Shrink Wrap

I was recently explaining to a friend what the convex hull of a set of points is using the analogy of an elastic band around a set of nails hammered into a board. I was about to say that we can ...
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260 views

Have Changes in Applications Made Linear Algebra More Central/Urgent?

In the days when my father taught civil engineering (some decades ago), mathematical applications seemed to be mainly "scientific." (This was the "space age.) Hence the most important branch of ...
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282 views

logic lectures on youtube

Currently I am reading Logic an Structure by Dirk van Dalen (2008). As I am missing some basics I try to find related lectures on youtube. I frequently watch MIT, Stanford, and University of ...
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57 views

Proofs shorter than the statement of the theorem

In Postnikov's first book in his Lectures in Geometry Series, Analytic Geometry, he states and then proves the Desargues theorem. Then he writes (in my English translated copy) "The proof has turned ...
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37 views

What is the actual significance of the lambda calculus for the formalization of math?

The Simply Typed Lambda Calculus was proposed initially as a foundational system for the formalization of mathematics. As such, I would expect that soon there would be attempts to implement most of ...
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46 views

Books/“resources” for national math competitions.

I have started participating in math competitions an year ago. My target is to reach as far as I can in the future (USAMO and even IMO). I know that succeeding in these competitions requires a lot of ...
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50 views

Important question: Can do a very hard problem, 2 months after have no idea how to approach it. Is it Normal?

I have this problem like sometimes I can do a very hard problem (I usually pass hours thinking and then there's this insight and everything opens up and the solution comes up eventually after some ...
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55 views

Algorithm for finding “fact families”

My friend's 3rd grader encountered the following question regarding "fact families" on her math homework: I was in 3rd grade sometime in the 1980s, so I don't believe I ever encountered this term ...
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58 views

Unexpected applications of row rank = column rank

The fact that the row rank of a matrix is the same as the column rank is quite surprising (to me atleast, hopefully to you too!). I am looking for unexpected applications of this fundamental fact, ...
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47 views

Why not differentiable manifolds that are not of class $C^1$

In most, if not all (I cannot say for sure) references on manifolds, we seem to consider $C^k$-manifolds, including the case $k = 0$, which corresponds to topological manifolds. This means that we ...
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56 views

Are inequalities harder to prove than equalities?

Browsing through the inequalities tag, I see a lot of straightforward-looking arithmetic statements that I nevertheless have no idea how to prove (and apparently I'm not alone). With equalities it's ...
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73 views

Methods of constructing rapidly convergent series

It's fairly easy to see that the series $$1-\tfrac{1}{3}+\tfrac{1}{5}-\cdots=\tfrac{1}{4}\pi$$ is : 1. Convergent to the value given, and - 2. Very slowly converging, which can be seen just by ...
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62 views

Quantifying infinitely large sums such as $\sum_{x\in\mathbb{R}^+} x$

I thought of this as a student in calculus years ago, and it may be a silly kind of question. I wondered if there were notions of different sizes of infinity a series might sum to, which then lead me ...
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88 views

From algebraic master degree to algebraic geomery Phd

I am a foreign master student in algebra at the final year. I'm familar with categorical algebra and have interesting in algebraic geomery and number theory. I have learned some knowledge about scheme ...
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50 views

Numbers Made From Concatenating Prime Factorizations

I came across the following curious problem while playing around with my calculator. Take any positive integer $n$; for this example we'll use $216$. Create a sequence as follows: Factor $n$ into ...
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88 views

How can I retain the mathematics that I've supposedly learnt?

So my question simply is "What is the best method to make sure you retain what you have learnt?" Okay so I've tried learning mathematics up to where I should be at in the past. Every time though I ...
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83 views

How to select good exercises?

I'm studying on Rudin "Principles of of Mathematical Analysis" which I begin to find as a good and complete reference. I wonder how many exercises shall I do at the end of each chapter ? In case of ...
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76 views

Do Natural transformations make 'God given' precise?

Often in mathematics, one encounters certain structures in which there are natural choices to be made. For example, there could be a 'god given' map relating two mathematical objects, in the sense ...
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97 views

Have any authors suggested mathematics-wide prefixes for “missing a quotient” and/or “missing an identity”?

The prefixes in the following terms both mean: "missing the obvious quotient by the obvious equivalence relation." seminorm pseudometric Similarly, the prefixes in the following terms both mean: ...
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88 views

Why not defining a measure as a function on functions?

A measure $\mu$ is a function to $\left[0,\infty\right]$ on the sets belonging to a $\sigma$-algebra. Then for integrable functions $f$ the integral $\int fd\mu$ comes in, having nice properties ...
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130 views

Category of metric spaces versus category of non-empty spaces

Denote by $\mathbf{Met}$ the category of metric spaces with metric maps as morphisms. A function $(X,d)\xrightarrow{\ f\ }(X',d')$ is called metric if for every pair of points $x,y\in X$ we have ...
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108 views

Sufficient conditions for closed infinite pasting lemma

It's well known that the pasting lemma for infinitely many closed sets is false. It's reasonably easy to cook up examples such that for $X = \bigcup X_i$ with $X_i$ closed in $X$ such that $\left. ...
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58 views

Let $\Phi$ denote the statement that $\mathrm{GCH}$ holds, and that no inaccessible cardinals exist. Is $\Phi$ limiting?

By an "inner model," let us mean a transitive subclass of the universe satisfying $\mathrm{ZFC}.$ Given that, here's an (intentionally) vague definition. Definition. Call a set of axioms $\Phi$ in ...
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185 views

How to balance learning and researching as a new PhD student?

As a new PhD student, how to balance learning and researching? I am in Australia and here we don't have any course in PhD period. I know I need to learn something about my programme, but sometimes ...
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246 views

Isolation and self-study

A little background: I am currently a sophomore (studying mathematics) at an unknown university in the Middle East. My mother is European so it does not make sense to study mathematics in the Middle ...
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83 views

Is there a way to figure out the minimum number of participants or maximum number of rounds in my tournament style?

I just finished hosting a Euchre tournament at work that was meant to get people to meet other people in the company. This is the third time I've hosted this type of tournament. The first two times, ...
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90 views

Was the Weierstrass function constructed or discovered?

Reading Halmos' I want to be a mathematician, he mentions a continuous function without a tangent. Naturally, I was curious to see how such a function could possibly exist, and I imagined it to be ...
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114 views

Earliest precursor to category theory

In the Historical notes section of the Wikipedia article on category theory, it is mentioned that in 1942-1945, Samuel Eilenberg and Saunders Mac Lane, in the course of their work in algebraic ...
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256 views

start studying advanced topics in number theory

I am a first year undergrad and have had elementary course in Number Theory which includes only basic introductory topics like: divisibility,gcd-lcm,primes,congruences, number theoretic functions etc. ...
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900 views

Is there any English version of Récoltes et Semailles?

I felt like my question isn't appropriate for MO, so I though maybe I should post it here. I want to read Alexander Grothendieck's "Récoltes et Semailles", but I don't know any French. I can easily ...
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117 views

definition of determinant in Artin

In Artin, the discussion on determinant starts from the standard recursive expansion by minors. Artin defines determinant as a function $\delta$ from a square matrix to a real number. Then Artin lists ...
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631 views

Soft question : First year student and confused

I hope I won't tire the fellow mathematicians with this question but I am very, very confused... I am a first year undergraduate student of Mathematics. I can't say I am a prodigy, maybe having an ...
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0answers
161 views

Examples of good phone interview quetions.

My school asked me to prepare some students for maths questions in a phone interview. But this is my first time doing this kind of job and I never had this kind of interview myself so I am a little ...
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120 views

Generic Points to the Italians

When I first learned algebraic geometry, I naturally wiki-ed the subject and there was a line there that said the old school Italians used the notion "generic points without any precise definition." ...
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117 views

Why are 'Groups' and 'Rings' in Algebra called so ? and other nomenclature questions

I have always wondered why are the following concepts/objects in Mathematics named so : 1.) Group 2.) Ring 3.) Exterior derivative (in differential geometry) 4.) Interior multiplication (in ...
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122 views

How does the fundamental theorem of algebra follow from Weierstrass’s theorem.

Could anyone please explain to me how the fundamental theorem of algebra follows from Weierstrass’s theorem (Bolzano Weierstrass)?