Questions tagged [applied-mathematics]

the branch of mathematics that deals with the mathematical aspects of problems from science and engineering: applied analysis, numerical mathematics, applied statistics etc. (For applications of mathematics in general, cf. also the [applications] tag.)

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144 votes
21 answers
20k views

How does one justify funding for mathematics research?

G. H. Hardy's A Mathematician's Apology provides an answer as to why one would do mathematics, but I'm unable to find an answer as to why mathematics deserves public funding. Mathematics can be ...
119 votes
33 answers
14k views

Examples of theorems misapplied to non-mathematical contexts

For something I'm writing -- I'm interested in examples of bad arguments which involve the application of mathematical theorems in non-mathematical contexts. E.G. folks who make theological arguments ...
92 votes
13 answers
14k views

Deep learning / Deep neural nets for mathematician

I am interested in finding out the math ideas behind the technologies that are under the umbrella of "Deep Learning" or "Deep neural nets". Most of the papers/books that are often quoted in papers/...
78 votes
9 answers
9k views

Mathematical conjectures on which applications depend

What are some examples of mathematical conjectures that applied mathematicians assume to be true in applications, despite it being unknown whether or not they are true?
60 votes
4 answers
5k views

Is there a mathematical and information theoretic explanation for this cube packing phenomenon?

I saw this unintuitive result on dice packing: A jumble of thousands of cubic dice, agitated by an oscillating rotation, can rapidly become completely ordered, a result that is hard to produce with ...
Turbo's user avatar
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58 votes
22 answers
12k views

Which high-degree derivatives play an essential role?

Q. Which high-degree derivatives play an essential role in applications, or in theorems? Of course the 1st derivative of distance w.r.t. time (velocity), the 2nd derivative (acceleration), and the ...
40 votes
17 answers
10k views

Interesting mathematical topics arising from biology

I've heard that there's a relatively new field of science called mathematical biology. It will certainly apply well known and less known mathematical techniques to the understanding of some biological ...
37 votes
17 answers
10k views

Listing applications of the SVD

The SVD (singular value decomposition) is taught in many linear algebra courses. It's taken for granted that it's important. I have helped teach a linear algebra course before, and I feel like I need ...
36 votes
11 answers
7k views

What "real life" problems can be solved using billiards?

Recently I gave an interview to local media where I explained some basic open problems in billiard dynamics. After a 45 min interview the reported asked me what "real life" problems can be ...
Ferran V.'s user avatar
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36 votes
3 answers
3k views

On Mathematical Analysis of MathSciNet & MathOverflow

This question has two original motivations: mathematical and social. The mathematical motivation is mainly based on what I have seen about Zipf's law here and there. The Zipf's law simply states ...
Morteza Azad's user avatar
35 votes
26 answers
5k views

Examples of mathematics motivated by technological considerations

I would like examples of technological advances that were made possible only by the creation of new mathematics. I'm talking about technology that was desired in some period of history but for which ...
35 votes
1 answer
3k views

Why is persistent cohomology so much faster than persistent homology

I refer to this paper: de Silva, Vin; Morozov, Dmitriy; Vejdemo-Johansson, Mikael. Dualities in persistent (co)homology. Inverse Problems 27 (2011), no. 12, 124003, 17 pp. (Journal link, arXiv link). ...
yoyostein's user avatar
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33 votes
8 answers
11k views

How is differential geometry used in immediate industrial applications and what are some sources to learn about it?

Intuitively it might be clear that differential geometry is a very applicable subject in engineering and industry. I'd like to know how some industries/companies use differential geometry. I'd guess ...
33 votes
3 answers
5k views

Do bubbles between plates approximate Voronoi diagrams?

For example, soap bubbles:                   Image from UPenn: "A 2-dimensional foam of wet soap bubbles squashed between glass plates, after 10 hours ...
Joseph O'Rourke's user avatar
32 votes
5 answers
11k views

Differentiable functions with discontinuous derivatives

For years I've taught my honors calculus students about functions like (the continuous extension of) $x^2 \sin 1/x$, and for just as many years I've told them that they won't encounter functions like ...
James Propp's user avatar
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31 votes
2 answers
2k views

Persistence barcodes and spectral sequences

Persistent homology is a well-developed tool which allows topological analysis of large data sets. From a topological perspective, the input is a filtered complex, and the output is a sequence of ...
Mark Grant's user avatar
29 votes
20 answers
7k views

Mathematics and cancer research

What are applications of mathematics in cancer research? Unfortunately, I heard quite little about applications of mathematics, but I heard something about applications of physics, and let me put this ...
28 votes
2 answers
3k views

Importance of integral equations

Differential equations are at the heart of applied mathematics - they are used to great success in fields from physics to economics. Certainly, they are very useful in modelling a wide range of ...
FusRoDah's user avatar
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28 votes
1 answer
2k views

Recent uses of applied mathematics in pure mathematics

In this answer Yves de Cornulier mentioned a talk about the possible uses of persistent homology in geometric topology and group theory. Persistent homology is a tool from the area of topological data ...
28 votes
1 answer
4k views

Is there any paper which summarizes the mathematical foundation of deep learning?

Is there any paper which summarizes the mathematical foundation of deep learning? Now, I am studying about the mathematical background of deep learning. However, unfortunately I cannot know to what ...
almnagako's user avatar
  • 341
24 votes
5 answers
6k views

Is the field of q-series 'dead'? [closed]

I had a discussion with my advisor about what am I interested as my future research direction and I said it is special functions and q-series. He laughed and said that the topic is essentially dead ...
20 votes
5 answers
2k views

Examples of research on how people perceive mathematical objects

What examples are there on research related to human perception and mathematical objects? For example, the shape of a beer glass influences drinking habits, since people are bad at integrating. ...
Per Alexandersson's user avatar
17 votes
4 answers
2k views

Differential geometry applied to biology

This was originally a question posted here on MathSE. But I'll ask again here to see if I can get some different answers. I'm looking for current areas of research which apply techniques from ...
Argent's user avatar
  • 171
16 votes
2 answers
1k views

Physical interpretation of the Manifold Hypothesis

Motivation: Most dimensionality reduction algorithms assume that the input data are sampled from a manifold $\mathcal{M}$ whose intrinsic dimension $d$ is much smaller than the ambient dimension $D$. ...
Aidan Rocke's user avatar
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16 votes
2 answers
781 views

What tools should I use for this problem?

Suppose we have $d$ cylindrical metal bars, with radius $l$, attached orthogonal to a support in random places: Now we have to attach bars with radius $k$ EVENLY SPACED, with distance $p$ between ...
Diego Santos's user avatar
15 votes
4 answers
6k views

Mathematicians learning from applications to other fields

Once upon a time a speaker at the weekly Applied Mathematics Colloquium at MIT (one of two weekly colloquia in the math department (but the other one is not called "pure")) said researchers ...
15 votes
4 answers
4k views

Robotics, Cryptography, and Genetics applications of Grothendieck's work? [closed]

I was reading about the passing of Alexander Grothendieck, and something caught my interest: Mr. Grothendieck was able to answer concrete questions about these relationships by finding universal ...
Tring Vu's user avatar
  • 311
14 votes
8 answers
3k views

Relevant mathematics to the recent coronavirus outbreak

I would like to ask about (old* and new) reliable mathematical literature relevant to various mathematical aspects of the recent coronavirus outbreak: In particular, standard statistical/mathematical ...
14 votes
1 answer
2k views

On the non-rigorous calculations of the trajectories in the moon landings

In a paragraph written by a person emphasizing that rigour is not everything in mathematics (I wish I had written down the details), it was stated that the moon landings would have been impossible ...
teil's user avatar
  • 4,261
13 votes
6 answers
7k views

Applications of commutative algebra

Hi. I'm preparing a thesis in commutative algebra, and when I say this to my friends they always ask me what are the applications to "real-world", and I don't know what to answer. This let me think ...
13 votes
3 answers
2k views

Models for graphs representing real-life networks

I am interested in basic models of graphs (stochastic or deterministic) that are offered for real-life networks (like social networks, the Internet, neuron networks). I will be thankful for answers ...
Gil Kalai's user avatar
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13 votes
1 answer
1k views

How is Ricci flow related to computer graphics?

I recently came across the book Ricci Flow for Shape Analysis and Surface Registration: Theories, Algorithms and Applications by Wei Zeng and Xianfeng David Gu. Because, I just saw the book on the ...
terett's user avatar
  • 1,069
13 votes
1 answer
807 views

2/3 power law in the plane

I've recently come across a particular problem whose solution turns out to be a probability distribution given by $f(x) = \alpha \|x\|^{-2/3}$ in the unit disk in $\mathbb{R}^2$ and zero elsewhere (I ...
John Gunnar Carlsson's user avatar
12 votes
0 answers
802 views

Malaysia Airlines Flight 370? [closed]

News reports about Flight 370's disappearance have given a sketchy idea of how hourly pings to a satellite have helped build up a picture of where it went. From a naive intuitive point of view, if ...
Charles Matthews's user avatar
11 votes
3 answers
812 views

Are there any books/articles that apply abstract coordinate free differential geometry to basic thermodynamics?

The mathematical structure of thermodynamics by Peter Salamon (pdf) would be an example, but i would like a more abstract natural formulation of application of differential geometry or even geometric ...
Tyson's user avatar
  • 309
11 votes
5 answers
492 views

What are efficient pooling designs for RT-PCR tests?

I realize this is long, but hopefully I think it may be worth the reading for people interested in combinatorics and it might prove important to Covid-19 testing. Slightly reduced in edit. The ...
Benoît Kloeckner's user avatar
11 votes
2 answers
2k views

random category theory

This question is in some sense dual to the one asked in Is there an introduction to probability theory from a structuralist/categorical perspective? since contrary to the OP who asks for references ...
Sylvain JULIEN's user avatar
11 votes
1 answer
4k views

Is fuzzy mathematics useful in pure mathematics ?

Fuzzy sets and logic seem to be mostly used for applying to real-world situations, control-theory, game-theory, economics, statistics, data management, artificial intelligence, automated reasoning etc ...
user12269's user avatar
  • 111
11 votes
2 answers
3k views

Is it fine to inquire about a paper that's been under review for around 9 months?

I have submitted a paper on applied probability in one of SIAM journals. The paper is under review for 9 months. I asked the editor 1 month ago about it, I was told that one review report has come and ...
11 votes
2 answers
564 views

Orthogonal polynomial under linear transformation

Let $M_n(x) = x^n$ be the standard monomials. The binomial formula allows one to expand $M_n(ax+b)$ as a linear combination of $M_k(x)$, for $k \leq n$, giving $$ M_n(ax+b) = (ax+b)^n = \sum_{k=0}^n \...
ANSI C Mastah's user avatar
10 votes
2 answers
3k views

How difficult will it be for me to switch fields (details below) after my Ph.D. in pure mathematics?

I'm a first year postdoctoral researcher, working in pure areas of Riemann surfaces and differential geometry, after just finishing my Ph.D. in 2013. Recently I've also started taking interest in ...
10 votes
4 answers
980 views

Moduli spaces in applied mathematics and condensed matter physics?

In this MO question it is stated that there is a relation between some aspects of condensed matter physics (namely the fractional quantum Hall effect) and the algebraic geometry of Hilbert schemes. ...
10 votes
1 answer
1k views

positions of a methane molecule with carbon atom at the origin

Let $\text{CH}_4$ be the molecule of Methane: The four hydrogen atoms form vertices of a regular tetrahedron with the carbon atom in the center of the regular tetrahedron. Here we regard all atoms to ...
QSR's user avatar
  • 2,213
9 votes
0 answers
442 views

Useful applications of applied category theory

Led by John Baez, applied category theory (e.g. [1]) seems to accumulate much popularity. As someone who has noticed the importance of category theory in pure mathematics (e.g. homotopy theory, tqfts, ...
Student's user avatar
  • 5,008
8 votes
3 answers
613 views

Explain seemingly non-random figures which arise from random Poisson points with normalization

Context Working with some biological datasets it was puzzling to see the patterns like Figure 2 (right) below. The first feeling was, that it corresponds to some biological effects like correlations ...
Alexander Chervov's user avatar
8 votes
2 answers
921 views

Applications of Topological Complexity of configuration space

I'm starting to work on topological complexity of configuration spaces. Articles say that this field has applications in robotic and control theory. One of the important articles belongs to Michael ...
Mojtaba's user avatar
  • 283
8 votes
2 answers
4k views

What are the top journals in applied mathematics and what are the differences between them? [closed]

This question is essentially an applied mathematics version of Which are the best mathematics journals, and what are the differences between them? Unfortunately, unlike the above question I was not ...
just-someone's user avatar
8 votes
1 answer
702 views

Question on pure mathematics helping climate change research

While I am a pure mathematics tenured professor, still at a relatively young age, and fairly passionate about my area of research, I cannot help but feel that it may be more useful to humanity if I ...
Dr. Pi's user avatar
  • 2,939
8 votes
0 answers
682 views

The function space defined by deep neural nets

Given a deep net graph and the activation functions on the hidden vertices do we have a description of the function space spanned by it? (even if for some specific architectures and activation ...
gradstudent's user avatar
  • 2,136
7 votes
3 answers
3k views

Is there a way to define a Lie derivative of a connection?

I've been reading a little bit about the definition of symmetries on General Relativity, and they are related with the concept of Killing vector, i.e., vectors along which the Lie derivative of the ...
Dox's user avatar
  • 690