Mathematics Topics in String Theory

[idrach55]

Hello all,

I am currently a Junior in High School with a deep interest in Physics/Mathematics, specifically in the area of theoretical Physics and String Theory. I was accepted to a summer course on String Theory and am quite excited. The course stated that the only prerequisite is Single Variable Calculus, which I am quite comfortable with. They mentioned that a physics background is helpful, yet not necessary as the course is mostly Math. I expect it to move quickly and cover a lot of curriculum in a short amount of time, and I wish to be prepared. Besides Single Variable Calculus, I have dabbled in Multivariable Calc, and have some experience with complex numbers and other higher level mathematics. I was wondering if there were any resources/books/websites/etc. that would be helpful to prepare me for material in this course. These resources should cover the individual topics or String Theory as a whole, either way it would be helpful. Thank you for your help in advance.

- Isaac

 

[marcus]

Hello all,

I am currently a Junior in High School with a deep interest in Physics/Mathematics, specifically in the area of theoretical Physics and String Theory. I was accepted to a summer course on String Theory and am quite excited. The course stated that the only prerequisite is Single Variable Calculus,...

Isaac, I'm curious to know more about the summer course. Where is it being held? Is there a website that would let us find out a little more about the summerschool program?

 

[idrach55]

The course is being held at Columbia University as part of their program for High School students. Here is the link to this particular class: http://ce.columbia.edu/Summer-Progr...thematical-Boot-Camp-Budding-String-Theorists

 

[marcus]

Isaac, I read the course description. Thanks for indulging my curiosity. It sounds like it could be ideal, a wonderful introduction to the multipurpose math toolbox of physics at just the right time in one's life. The range of applied examples is exciting. Of course I can't tell all that much really just from the description, but it sounds great!

==quote from the webpage==
Course Description
This course is intended for highly motivated students familiar with the basic elements of calculus but who are eager to further expand their mathematical toolboxes in preparation for serious future work in the natural sciences. Prior exposure to calculus is assumed and will be built upon.

Rich examples drawn from classical and quantum wave phenomena, statistical physics, astrophysics, cosmology, engineering physics, chaos and nonlinear dynamics are used to introduce and develop crucial mathematical concepts during the morning lectures. Afternoons are devoted to hands-on experiments and computer simulations to test the physics concepts presented. There will be science-based NYC field trip, as well as a visit to one of the Columbia research labs.

This course is mainly math, but with plenty of physics mixed in, whereas Investigations in Theoretical and Experimental Physics focuses more on introductory physics material. Because there is significant overlap between the two courses, it is not recommended that students take both.

Instructor(s)
Timothy Halpin-Healy
Tim Halpin-Healy received his doctorate in physics from Harvard University in 1987, following an A.B. from Princeton University in 1981. He’s been a research fellow at the Isaac Newton Institute for Mathematical Sciences; Cambridge University, England; as well as the Departement de Physique, Ecole Normale Superieure, Paris. He is currently Ann Whitney Olin Professor of Physics at Barnard College, Columbia University. His scientific research concerns the dynamics of complexity, where the competing effects of order and disorder delicately balance, producing some of nature’s most beautiful pattern formation phenomena. The technical tools of his trade involve quantum field theory, the renormalization group, fractals and chaos.
==endquote==
http://ce.columbia.edu/Summer-Progr...thematical-Boot-Camp-Budding-String-Theorists

 

[bapowell]

Maybe gaining a bit of an introductory background in some of the physics would be beneficial, like cosmology and statistical physics. Mastering a few of the basic concepts (if you haven't already) could go a long way to making the mathematics "spring to life", and make the experiments and computer simulations much more interesting and valuable.