Math History/Foundations (MHF)

Introduction to axiomatic systems and techniques of proof, in preparation for upper-level study in mathematics. Topics include: symbolic logic, boolean algebra, set theory, countable and uncountable sets, techniques of proof, functions and relations, mathematical induction, group axioms. Emphasis is on preparing the student to read and write mathematical proofs, and to work with abstract definition and axioms.

Introduction to symbolic logic and logical proof methods.

The evolution of mathematical thought and methods from antiquity through the Renaissance. Topics include development of the concepts of number, quantity, and magnitude, algebraic techniques and symbolic notation, solution of polynomial equations, the evolution of the concept of proof, development of numeration systems, history of number theory and congruences, and notions of infinity and infinitesimals. Mathematical ideas and practice in European, African, Mesoamerican, and Asian cultures will be considered.

Introduction to modern set theory. Topics include the Zermelo-Fraenkel axiom system, cardinal and ordinal numbers, the Axiom of Choice, and related topics.

Introduction to Logic & Language, Arguments with Compound Statements, Method of Deduction, Propositional Functions and Quantifiers, The Logic of Relations, and Deductive Systems.