MAT 3610 - INTRODUCTION TO REAL ANALYSIS

credits: 3.0
Students are introduced to the analytical techniques of mathematics that depend upon the topology of the real numbers. Will cover: set theory, including cardinality; the axioms of the real number system and their consequences; the concept of the limit and its applications in calculus, including integration theory; the convergence of sequences and series of functions of a real variable; and an introduction to metric spaces as a generalization of real analysis. Objectives: A) Identified key concepts in set theory, and stated and proved many theorems about set theory, including intersections and unions, functions, images, inverse images, and cardinality; B) Identified the axioms of the real numbers, and stated and proved many theorems about basic properties of the real number system, including basic properties of algebra, order, and completeness; C) Identified the concept of a limit, both of functions and of sequences, stated and proved many theorems about limits, including techniques for their computation, and applied limits in the proof of many of the basic concepts in calculus, including derivatives, integrals, and the convergence of series; D) Identified sequences and series of functions, stated and proved many theorems concerning the way in which sequences and series of functions converge; E) Identified metric spaces, and stated and proved many basic facts about them, generalizing the relevant concepts in objectives B-D. Method of Instruction: Lecture and classroom discussion; regular assigned and graded homework that is discussed in class. Method of Evaluation: Homework: 3/5 of grade, Midterm exam: 1/5 of grade, and Final exam: 1/5 of grade.

Prerequisite(s): MAT 2100 - DISCRETE MATHEMATICS and MAT 3010 - CALCULUS III