What type of math is used in physics

The future of interdisciplinary research will depend a lot on the next generation, but Penn is well positioned to continue leading these efforts thanks to the proximity of the two departments, shared grants, cross-listed courses, and students and postdocs that actively work on problems across fields. It is not something you see every day. He earned a Ph. She also has a secondary appointment in the Department of Mathematics and was recently named as a Principal Investigator of a Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics.

He also has a secondary appointment in the Department of Physics and Astronomy. He also has a secondary appointment in the Department of Mathematics. He most recently worked as a post-doctoral research fellow in the in the School of Arts and Sciences at the University of Pennsylvania.

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Speakers include physicists James Batteas, the D. Penn is home to an active and flourishing collaboration between physicists and mathematicians. A tale of two disciplines Math and physics are two closely connected fields. Where math meets physics An example of mathematical thinking Mathematicians look for patterns and ask if that pattern is just a special case or indicative of something deeper.

Kamien works on physics problems in that have a strong connection to geometry and topology and encourages his students to understand problems as mathematicians do. Where math meets physics, part two String theory String theory is a quantum gravity theory which seeks to find a unified description of both gravity and quantum mechanics.

Calabi-Yau manifolds, conjectured in the s by emeritus professor Eugenio Calabi, is a fundamental component of research in both particle physics, including fields such as string theory, and cutting-edge mathematics research on homological mirror symmetry Image: Simons Foundation.

Where math meets physics, part three String theory definitions F- theory: A branch of string theory developed in the mids. Get Free Membership. Remember me. Forgot your login? Ask the Experts. University Departments. Discussion Forums. Online Chat. Einstein eGreetings. Science eStore. Question What is the most useful type of mathematics for physics? Asked by: Don Answer This is the first time I am answering such a 'highly subjective' question.

So, parts of my answer will probably range from 'educated advice' to 'wild speculation'. Physics is probably the one area of science where many areas of mathematics have been directly applied. The reason is simple; nature seems to obey 'mathematical rules' rather than acting whimsically. In other words, it seems that natural laws can be expressed in terms of mathematics. Why this should be so, nobody knows.

If I were asked to single out one area of mathematics that is of absolutely maximum use in the study of physics, I would probably pick calculus. All of classical mechanics, thermodynamics, fluid dynamics, classical electromagnetism, statistical mechanics, and many other fields of physics make extensive and sometimes exclusive use of calculus. Is this sufficient? Probably not for all areas of physics you might work in.

The very next requirement would probably be differential equations, and can be thought of as part of calculus although it is a vast area of study within itself. In addition, you may need probability theory and statistics, linear algebra, numerical methods and the like depending on the field you choose.

It pops up now and again as a basis for book clubs , and you occasionally find it adapted into other fields. If I were to take a stab at a physics version of "Humiliation," my play would likely be this: To the best of my knowledge, I have never used Noether's theorem to calculate anything.

This, despite it regularly being hailed in terms like " the backbone on which all of modern physics is built ," and " as important a theorem in our understanding of the world as the Pythagorean theorem ," and " possibly the most profound idea in science. How did I manage to get a Ph. Mostly because I'm an experimentalist in low-energy physics. I took the required classes in graduate school, and a few courses beyond that some subject-specific electives and some stuff that I expected I might someday need to teach , but once I passed the qualifying exam, I moved into the lab, and was concerned more with technical details of vacuum pumps and lasers and electronic circuits and computer data acquisition and analysis.

While you probably could start from first principles and describe our experiments in terms of a Lagrangian with identifiable translation symmetries and the like, it's really not remotely necessary. The conserved quantities we worry about are garden-variety energy, momentum and angular momentum, and don't require all that much justification. There's rarely any need for calculus of variations in analyzing atomic physics data, and on those occasions when some bit of advanced math proves necessary, we were generally happy to pass that off to professional theorists.

I was thinking about this because I had dinner last week at a conference where I sat with a colleague and some students from my undergrad alma mater. One of the students was fretting that he hadn't been able to take enough math to be fully prepared for graduate school--I think the course he was regretting not being able to fit into his schedule was Complex Analysis.

My colleague and I both tried to reassure him that he would be just fine, as neither of us could recall ever using that material outside of a "Mathematical Methods for Physics" course.

But then, my colleague is also an experimentalist, working in a similar low-energy regime, so he had a similar graduate school experience.

Had we been sitting with a high-energy theorist, things might've been different. I get asked sometimes "What math do I need to take to study physics? But it is true, as the above illustrates--if your goal is to work in a lab with lasers and atoms, you don't need nearly as much math as if you plan to discover a Theory of Everything.

You need to understand gradient and curl and related operations on vector fields, and have a solid conceptual understanding of what it means to integrate along a path, over a surface, or through a full volume.