All Questions
Tagged with applied-mathematics applications
20 questions
1
vote
1
answer
280
views
Application of Yamabe and Liouville type equation
Let $\Omega$ be a domain in $\mathbb{R}^n$. I am interested in the following critical elliptic partial differential equations (PDEs):
The Yamabe Type Equation (for $n>2$):
\begin{equation}
-\...
- 914
7
votes
1
answer
433
views
Do the exceptional root systems arise in the real world?
I am looking for a list of real world examples where the exceptional roots systems $E_6, E_7, E_8, F_4$, and $G_2$, and their associated Lie algebras and Lie groups, arise. To make this question a ...
2
votes
1
answer
631
views
Does there exist a Python package that samples random special unitary matrices such that the matrices are parameterized
For reference, the linked paper is Composite parameterization and Haar measure for all unitary and special unitary groups by Christoph Spengler, Marcus Huber and Beatrix C. Hiesmayr (J. Math. Phys. 53,...
- 123
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 ...
37
votes
17
answers
13k
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 ...
0
votes
0
answers
241
views
How to measure perceived note similarity in music / simplicity of ratios?
I have discovered a method to measure the similarity of two successive musical notes which I wanted to share with a question:
It is known in music theory that two successive pitches $a,b$ which sound “...
- 3,064
1
vote
0
answers
107
views
Plethora of variant neural networks?
Since a decade ago when new life was breathed in to neural networks in the form of deep learning a plethora of different architectures have come about. Is there a reference that gives compendium of ...
- 13.9k
1
vote
0
answers
259
views
Industrial research projects on "mathematical modeling and PDEs" [closed]
Apparently there are several companies in a great variety of fields (medical, biological, engineering, etc.) that need "consulting on mathematical modeling and PDEs" from applied mathematicians.
I'...
user89890
8
votes
2
answers
955
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 ...
- 283
33
votes
8
answers
12k
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 ...
95
votes
14
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/...
37
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 ...
- 637
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 ...
- 311
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.
...
- 15.8k
2
votes
0
answers
47
views
Where to read about this kind of "measure of irredundancy" of a set from a family of sets?
Studying a very practical problem from psychometrics, I encountered the following construction.
Let $(X,\mu)$ be a measure space; if preferred, you can presume $\mu$ is a probability measure. In any ...
- 18.4k
3
votes
2
answers
478
views
Physical and real life interpretation of the concept of regularity used in differential equations?
I guess the title kind of speaks for my questions: I'm curious to know what could be the physical interpretation or real life application of the concept of regularity that arises in PDE: take for ...
- 1,467
29
votes
20
answers
8k
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 ...
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 ...
5
votes
2
answers
3k
views
Rotationally-Invariant 2D Discrete Transforms
I'm interested in 2D discrete transforms (such as discrete wavelet transforms, Curvelets, Ridgelets, Beamlets etc.) that operate on a discrete unit disk and:
Are invariant to rotations only
Output a ...
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 ...