MATH 2080

Introduction to Analysis

(Lab required) The course is intended for students in mathematically rich disciplines. Fundamental properties of the real number system as a complete ordered field, Archimedean property, existence of square roots, density of rational numbers, uncountability of real numbers. Sequences, subsequences, limit theorems, monotonicity, Bolzano-Weierstrass theorem, Cauchy sequences. Rigorous treatment of limits and continuity of functions of one and several variables. Uniform continuity. Applications. May not be held with MATH 2081 or the former MATH 2202. Prerequisites: [MATH 1232 (C) or MATH 1690 (C) or MATH 1700 (B) or MATH 1701 (B) or MATH 1710 (B)] and [MATH 1220 (C) or MATH 1300 (B) or MATH 1301 (B)] and [MATH 1240 (C) or MATH 1241 (C)].

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course_MATH_2080 cluster_equiv_1 cluster_equiv_2 cluster_equiv_3 MATH 2080 MATH 2080 MATH 2150 MATH 2150 requires C or better MATH 2080->MATH 2150 MATH 2180 MATH 2180 requires C or better MATH 2080->MATH 2180 MATH 4330 MATH 4330 requires C or better MATH 2080->MATH 4330 MATH 1232 MATH 1232 C or better MATH 1232->MATH 2080 MATH 1220 MATH 1220 C or better MATH 1700 MATH 1700 B or better MATH 1700->MATH 1232 or MATH 1701 MATH 1701 B or better MATH 1701->MATH 1700 or MATH 1220->MATH 2080 MATH 1240 MATH 1240 C or better MATH 1300 MATH 1300 B or better MATH 1300->MATH 1220 or MATH 1301 MATH 1301 B or better MATH 1301->MATH 1300 or MATH 1240->MATH 2080 MATH 1241 MATH 1241 C or better MATH 1241->MATH 1240 or