Spring 2008

MTHS 644
Foundations of Analysis

Reid,James D.

01/28/2008 - 05/10/2008
Tuesday 06:00 PM - 08:30 PM

Science Tower 109

A classical trichotomy splits mathematics into three parts -- Algebra, Analysis, and Geometry -- and this classical view still has a certain validity. Broadly speaking most people might view Algebra as the art of symbolic manipulations and Geometry as the study of spatial shapes and relationships. That leaves Analysis.

For purposes of discussion, we view Analysis as having to do with the study of infinitesimal processes as codified in the concept of a limit. The gateway to Analysis, the basic ideas, form the content of what is called Calculus. This course will study the foundations of Calculus, the motivation for its existence, and the structure of the resulting theory.

The basic idea is that of "limits." This appears notably in discussing continuity of functions, in the idea of the derivative, and in the definition of the integral. We will make a careful study of this fundamental concept and examine some of its most important applications. Participants in the course should come away with a solid understanding of the fundamental ideas of Calculus, and through many examples, a deep appreciation of its power.

Weekly problem sets will be assigned to help in the assimilation of ideas. Grades will be based on these assignments together with participation in class.

As prerequisites we cite familiarity with the idea of notation of functions and the representation of functional relationships by means of graphs, though these will be reviewed and every effort will be made to make the course accessible to those in attendance. Most important is the willingness to think hard and the patience to let things sink in.

A syllabus for this course is available at:

James Reid (B.S., M.A. Fordham University; Ph.D. University of Washington) is professor of mathematics, emeritus. He has published extensively in the field of Abelian Groups, including recent papers "Quotient divisible groups, omega-groups, and an example of Fuchs. Abelian groups, rings, modules, and homological algebra", 265-273, Lect. Notes Pure Appl. Math., 249, Chapman & Hall/CRC, Boca Raton, FL, 2006; "Endomorphism Rings of Free Modules," Rocky Mtn. J. Math., 2002; and "Some Matrix Rings Associated with ACD Groups," Proc. International Conference on Abelian Groups and Modules, Dublin, 1998.


Consent of Instructor Required: No

Format: Seminar

Level: GLSP Credits: 3 Enrollment Limit: 18

Texts to purchase for this course:
Maxwell Rosenlicht, INTRODUCTION TO ANALYSIS (Dover Publications), Paperback


PLEASE NOTE: Copious notes will be provided to augment the discussion in the text.

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