Natural Science 0213 - Introduction to Group Theory

Motivated by geometric symmetries found in nature, such as rotational symmetry of snowflakes and bilateral symmetry of some animals, this course will introduce the mathematical foundations of the branch of mathematics known as group theory. Group theory, among other things, allows us to describe symmetries of an object in terms of operations, such as rotations, which leave the object unchanged. The course is divided into three parts. In the first part we introduce the basic definition of a group by considering symmetries observed in nature. In the second part we will study the formal structure of some special groups, such as rotations and inversion in three-dimensional Euclidean space, the distinction between abelian and non-abelian groups, the notion of a subgroup, etc. The third part is reserved for special topics on applications of group theory to physics (crystallography, particle physics, relativity, etc.) in the form of group projects. The course is best suited for students with concentrations in math and physical sciences, but will be accessible to anyone with a general interest in the subject. Knowledge of linear algebra will be useful but is not required. Readings and written work will be assigned for each class.

Independent Work Quantitative Skills Writing and Research In this course students are generally expected to spend at least 6 to 8 hours a week of work and preparation outside of class time.