University of Rhode Island MTH436: Mathematical Analysis and Topology II
Spring 2020

General Information

Instructor: Tom Sharland
email: tsharland "at" uri "dot" edu
Lectures: MW 3.00-4.45, Lippitt 204
Office: Lippitt Hall 202F
Office hours: TBA

Course description: This course is a continuation of MTH435. This semester we will study continuity of functions of one real variable and in metric spaces. We will then look at derivatives of real valued functions, followed by studying the Darboux Integral. For the integral, I will prepare worksheets to replace Chapter 7 in the book. If there is time, we will choose from a collection of optional topics; these include looking at properties like compactness and connectivity in metric and topological spaces, functions of several real variables or something else. Which topics we cover will be a decision made as a class.

This course will be relatively fast-paced, so in order to keep up with the material, you should be prepared to spend sufficient time outside of class attempting practice problems and reading and understanding your notes and textbook. You should certainly make sure you are comfortable with the material from MTH435 - we will be making use of much of it throughout this semester. There is insufficient class time to teach everything you need to know from this class, and so a fair amount of learning will have to take place away from the class room. You are more than welcome to come to office hours to discuss any issues you have with concepts, theorems and so on. The earlier you sort these problems out, the better.

Textbook: Introduction to Real Analysis by Bartle and Sherbet (4th Ed.).

Prerequisites: MTH435.

Homework: The homework will be as in MTH435. Homework will be assigned weekly. Each assignment will be split into (up to) 3 parts. Part A will be simpler questions, which you may find useful with solving the later questions and may also appear on the weekly quiz (more later). Part B will consist of the questions to be submitted for credit. Part C are harder questions and may go beyond the scope of the course. Tackle these if you want a challenge or are interested in learning more.

You are positively encouraged to work together on the homework assignments. However, you should write up your submitted solutions on your own - this will ensure you understand the answer. Though I cannot prevent you looking for help in books or online resources, you should make sure that you understand anything you read, and not just copy it down verbatim. Indeed, you should cite any resource you use if your answer heavily relies on it.

Quizzes: These will take place weekly and will be based on the homework.

Grade breakdown: The grading scheme will be as follows:

  • Quizzes: 10%
  • Homework: 10%
  • Midterm I: 20%.
  • Midterm II: 25%.
  • Final: 35%.
The final will be cumulative, and for this reason a strong performance on the final will be taken into account when calculating the final letter grade. There are no plans for extra credit. A few problems in the exams may cover standard material from MTH435.