Introduction to Mathematical Proof

MTH

206

Introduction to Mathematical Proof

This course is designed to provide students in the mathematical sciences degree program with a general introduction to the formal language and methods of proof and argument that are universally applied in the mathematical sciences. The close relationship between language (both natural and symbolic) and mathematical abstractions will be discussed in detail. The roles of undefined terms and defined terms in mathematics as well as the distinctions between them will be presented and illustrated. The basic mathematical terminology and standard notational systems will be presented, and students will be shown how to devise acceptable and efficient descriptive notation and symbols that may be required for specific mathematical tasks. The concepts of logical truth and consistency, along with the qualifiers and their use will be analyzed in detail. The construction method, the choose method, and the first and second principles of mathematical induction will be discussed in detail as will the indirect methods of proof by contradiction and proof by contrapositives. Proofs based on arguments by the method of exhaustion along with arguments based on the exhibition o

Fall, Spring

Undergraduate

No

027912