Home  MyESC  Site Index 
REAL ANALYSIS: THE THEORY OF CALCULUS (SMT274344)
Course Description: This advanced course is an introduction to the theory of calculus of functions of a single real variable. In the usual introductory calculus sequence (Calculus I, II and III), students learn how to perform routine calculations with little attention to the theory that makes these calculations possible and meaningful. In this course, students will learn how to establish calculus on a rigorous foundation: familiar concepts will be revisited in the context of mathematical proof. This advanced course is an indepth, behindthescenes look into the theory of calculus of functions of a single real variable. Topics covered in this course include: the real numbers, limits of sequences, completeness, the Monotone Convergence Theorem, the BolzanoWeierstrass Theorem, the Cauchy Criterion, the Cantor Set, open and closed sets, sequential compactness, limits of functions, continuity, the Intermediate Value Theorem, the derivative, the Mean Value Theorem, the Riemann Integral, and the Fundamental Theorem of Calculus. The primary audience for this course is students who wish to concentrate in either mathematics or applied mathematics. Students concentrating in a tangentially related field, such as physics, may also be interested in this course. Prior to enrolling in this course, students should be fluent in differential and integral Calculus, as would be acquired in a three or four course sequence of Calculus. Also, students should be comfortable with mathematical proof (both reading and writing of proofs). Such knowledge may be obtained from courses such as Logic & Proof, Discrete Mathematics, or Linear Algebra, for example. This online course is offered through Online Learning. You can take this as an individual course or as part of an online degree program, with term starts in March, May, September, November and January. View current term offerings and all online courses. Click here to register for online courses.
Other Areas: The Arts  Business, Management & Economics  Community & Human Services  Communications, Humanities & Cultural Studies  Educational Studies  Historical Studies  Human Development  Labor Studies  Nursing  Science, Math & Technology  Social Science Liberal Study Upper Level Credits: 4 Term(s) Offered (Subject to Change) : Spring 1. Fall 1. For Books and Materials List Go to the Online Bookstore

Copyright © 1999  2018 Empire State College.  Contact the webmaster 