This class introduces the fundamental and unifying concepts of contemporary mathematics. Topics covered divide into four categories: 1) fundamental concepts of mathematics: definitions, proofs, sets, functions, elementary number theory; 2) discrete structures: graphs, counting; 3) discrete probability theory; 4) elements of analysis and topology. The underlying goal is to teach students about careful mathematics: precisely stating assertions about well-defined mathematical objects and verifying these assertions using mathematically sound proofs. Prerequisite: MTH 3007 or MTH 3010.
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