Mathematical Structures and Proofs

This course provides students with a transition from mathematics courses at the first-year level to rigorous, theoretical courses at the upper-division in which mathematical proof is emphasized. The nature and purpose of mathematical proof are examined. Many common techniques of proofs are studied and applied in analyzing a large number of elementary proofs. Students spend a considerable amount of time analyzing sample proofs and constructing their own proofs. No single area of mathematics will be emphasized; examples may be chosen from abstract algebra, number theory, analysis and combinatorics.