Abstract Algebra and Number Theory (MAT4343.01)

Andrew McIntyre

The goal of this class is to introduce the standard topics and theorems of a first abstract algebra course (groups, rings, modules, and fields), in a historically motivated context, primarily through number theory. Number theory asks questions about whole numbers: for example, are there infinitely many fundamentally different “Pythagorean triples”, where two whole number perfect squares add to a third, such as 3^2 + 4^2 = 5^2 ? Which other whole numbers can be written as a sum of two perfect squares? These questions have a rich history. Natural questions lead to surprising answers and clever techniques, introducing new ideas which then take on their own life.

The class will be taught with a number of optional topics, so that students taking it directly after Logic and Proof can concentrate on the core material, while more senior students can go into more depth in topics of interest. Note that Calculus is not a prerequisite for this class.

Learning Outcomes:
- Develop capacity to reason mathematically at a higher and more abstract level
- Further develop skills at writing mathematical proofs
- Integrate and consolidate mathematical concepts from various other courses
- Learn some history of mathematics

Delivery Method: Fully in-person
Prerequisites: Logic and Proof, or permission of instructor. Linear Algebra would also be helpful, but is not required. Contact Andrew McIntyre by email (amcintyre@bennington.edu), before 4000 registration opens, to be added to the class.
Course Level: 4000-level
Credits: 4
T/F 10:30AM - 12:20PM (Full-term)
Maximum Enrollment: 20
Course Frequency: Every 2-3 years

Categories: 4000 , All courses , Four Credit , Fully In-Person , Mathematics