MAT 670 Foundations of Mathematics
This course is part of the Mathematics Teacher Transformation Institute, an NSF Math & Science Partnership program.
COURSE DESCRIPTION
What is mathematics? What are the objects of mathematics? How are mathematical statements proved, or disproved? This course will examine fundamental material and techniques in mathematics, with an emphasis on solving equations in number systems and related notions. Traditional foundational material, from set theory to number system constructions, will be developed while simultaneously charting a fast path from the quadratic formula towards Galois Theory.
Topics to be covered include: sets and operations on sets, infinite sets and cardinality, logic and axiomatic systems, the fundamental theorem of arithmetic, examination of proof techniques, construction of the real number system, other algebraic structures, the fundamental theorem of algebra, polynomial rings, extension fields, the fundamental theorem of Galois Theory.
Weekly meetings will consist of one hour lecture and two hours of guided student exploration. Students will work collaboratively on weekly problem sets, guided by material presented in interactive lectures.
Texts: Basic Concepts of Mathematics by Elias Zakon, The Trillia group
Field Theory and Its Classical Problems by Charles Robert Hadlock, Carus Mathematical Monographs; No. 19.
Instructor: Rob Schneiderman
Email: robert.schneiderman@lehman.cuny.edu
Office hours: Mondays 12:45-2:00pm, and Wednesdays 2:00-3:45pm, Gillet Hall room 137H.
Class meetings: Wednesdays 4-7pm Carmen Hall room 325
Enrolled students can access course documents via Blackboard at: http://lca.lehman.cuny.edu/lehman/itr/html/blackboard.asp