MTH 1 Axioms, Theorems, and Proof in Geometry and Algebra.

Considers algebras and geometries defined by axiomatic systems, two very active fields in modern mathematics. Surprises are here: geometrics without parallel lines, geometrics with parallel lines and no rectangles, and new algebraic operations that can describe the structure of Rubik's cube and molecules. Develops the roles of definition, proof, and abstraction gradually until, at the 400 level, a full scale axiomatic treatment is given. At this level students provide many of the proofs. You rediscover results from the masters: Gauss, Hilbert, Galois, Abel, and others. Not an easy sequence, but you learn about how to read mathematics and solve problems on your own.

Prerequisite: MTH 151 (5) (MPF) or MTH 153 (4) (MPF) Calculus I.

1. MTH 222 Introduction to Linear Algebra (3); and

2. MTH 331 Discrete Mathematics (3); and

3. MTH 411 Foundations of Geometry (3), or
MTH 421 Introduction to Abstract Algebra (4)

Note: Not open to majors in the Department of Mathematics and Statistics.

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