This course is a natural continuation of Linear Algebra, but the material is much more proof-driven and abstract. We will study groups, rings, and fields, which are standard objects in mathematics and are used in subjects as varied as quantum mechanics and digital communications. The subject originates with the study of symmetry and we will keep returning to this unifying theme throughout the course.

The more general objective of this course is to continue providing you with a deeper understanding and working knowledge of mathematics, while in the process strengthening your analytical skills, increasing your ability to communicate mathematics symbolically and orally, making you comfortable with reading and understanding mathematics on your own, and continuing to develop your appreciation for abstract mathematics.