Math 361: Real and Abstract Analysis
Fall 2012
Professor Levandosky
Contact Information
• Office: Swords Hall 325
• Email: spl@mathcs.holycross.edu
• Phone: (508) 793-3358
• Office Hours: Monday 4:00, Tuesday 10:00, 1:00 and 3:00, Wednesday 12:00, Friday 10:00
Text
• Real Analysis, by N.L. Carothers. This book is available at the Holy Cross bookstore. The material
in chapters 1 and 2 is a review of some of the topics covered in Principles of Analysis. We will spend
a day or two going over this material. The bulk of the course will involve chapters 3-8, which focus
on the general properties of metric spaces. We will then look at the material on function spaces in
chapters 10 and 11, and if time permits the material on Fourier series in chapter 15.
Course Description
The goal of this course is to extend several of the concepts studied in Principles of Analysis from the set
of real numbers to more general sets known as metric spaces. A metric space is a set in which there is a
notion of distance between elements of the set. In such a space, one can make sense of the familiar concepts
of limits, open and closed sets, connected and compact sets, and continuous functions. We will spend most
of the semester studying the basic properties of metric spaces. The remainder of the semester will be devoted
to studying an important class of metric spaces known as function spaces. Function spaces are sets of
functions of a particular type and arise frequently in the study of ordinary and partial differential equations.
Exams
There will be two in-class midterm exams and a final exam.
• Exam 1: Wednesday, October 3.
• Exam 2: Wednesday, November 14.
The final exam time and date will be determined by the registrar’s office, and could be as late as Saturday,
December 15. Please do not make any plans to leave campus before then.
Homework Assignments
There will be regular homework assignments. You may discuss the homework problems with each other.
However, anything you hand in should be written in your own words. You may not copy answers from each
other.
Rewrites. After each assignment has been graded and returned, you may rewrite any problem for which
you did not receive full credit, and resubmit them within one week. Your final homework score for that
assignment will be an average of the original score and the new score.
Grades
Your grade will be calculated using the following system: Midterm Exams 25% each, Final Exam 30%,
Homework 20%.