CDL COURSE ENTRY FORM


Author: Laura Wait/SUNY
Last modified by: Laura Wait/SUNY
Composed: 06/25/2010 10:29 AM
Curriculum Committee Approval Date: 06/03/2010
Modified: 04/26/2018
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Course Number: (prefix) SMT (number) 274344 ESC 2.0 Course number: MATH-4030 MATH-4030Real Analysis

Name: Real Analysis: The Theory of Calculus
Datatel Title: (30char) Real Analysis: Theory of Calc

Area Coordinator: Jennifer Blue Department Code: 10SM Team: SMT

Liberal Study? YES Level: UPPER Credits: 4 Prerequisite? YES
General Education Course? NO GenEd Approval Term/Year:

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Pre-registration Information?
Course will be offered (for online course descriptions, proposed offerings for by term views and web views)
Spring 1, Fall 1		Course will be offered (for final term listings, online registration, online bookordering, web views)
Spring 1, Fall 1
First Term Offered: 2011FA (Required Format: YearTerm - i.e., 2005SP)
Last Term Offered in Print Version:
Title Changes:
AC Changes: EFFECTIVE 4/23/18 CHANGED BACK TO JEN BLUE 10SM. GAVE LYNAE 10AR. CATALOG UPDATED 4/26/18. LWAIT
EFFECTIVE SP1 2018 CHANGED FROM JEN BLUE TO LYNAE WARREN; SHE TOOK OVER THE 10SM DEPT CODE. CATALOG UPDATED 1/4/18. LWAIT
EFFECTIVE SEPT '13 TERM CHANGED FROM SARAH MCALLISTER TO JEN BLUE. CATALOG UPDATED 7/23/13 LWAIT
BK Number:

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 in-depth, behind-the-scenes 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 Bolzano-Weierstrass 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.

Generic:



Major Course Area
Science Math & Technology		Minor Course Area
Math and Quantitative Studies		SLN Disciplines
Mathematics
Additional Course Requirements
 Undergrad Certificate Association:


0




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