Syllabus for Junction 2009
Linear Algebra and Quantum Mechanics
Instructor:
Shaunak Kishore and Kenan Diab bio
Class Description:
This class is a brisk introduction to the theory of linear algebra and non-relativistic quantum mechanics, two jewels of modern science whose applications extend far beyond their respective fields. The theory of linear algebra is developed abstractly using the language of linear transformations, and this level of abstraction is used to develop quantum mechanics mostly using operator methods. Famous results in both subjects are covered: in linear algebra, results include the dimension theorem, the rank-nullity theorem, and a special case of the spectral theorem. In quantum mechanics, the theory of the simple harmonic oscillator, the two-state system (and its applications to neutrino physics and magnetic resonance), and an extensive treatment of the hydrogen atom and angular momentum is developed. This class will emphasize mathematical rigor and physical reasoning throughout - by the conclusion of the course, students will not only understand the basic facts about these subjects, but also develop the problem solving skills and reasoning abilities necessary for serious study in higher math and modern physics.
Lecture Schedule
Is available as a PDF here (not completely set in stone).
Prerequisites:
AP Calculus (either AB or BC) and AP Physics C Mechanics (or equivalent self-study.)
Application Question:
Prove that there are infinitely many prime numbers of the form 4n+3.
The 2009 Junction Application: APPLY! due by April 30th