University of Rhode Island MTH435: Mathematical Analysis and Topology I
Fall 2017

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:M 10.30-11.30, W 9.30-10.30, Th 2-3 or by appointment

Course description: This course is an introduction to real analysis, as well as giving a brief insight into the notions of a metric space and topology. We will start by examining the notion of limits of sequences and series in R. After this, we will consider limits in metric spaces, and then move on to a study of real functions. This course will be continued as MTH436 in the Spring.

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.

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

Prerequisites: MTH215, MTH243 and MTH307 (or permission of the instructor).

Homework: 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.

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

Knowledge Check: Each week there will be a reading assignment. To check this is being done, a weekly knowledge check will take place. This will be a quick check that you know a definition or statement from this (or previous) weeks reading. For example, you may be asked to give the definition of a convergent sequence or the statement of the monotonic sequence theorem.

Grade breakdown: The grading scheme will be as follows:

  • Knowledge Check: 5%
  • Quizzes: 10%
  • Homework: 10%
  • Midterm I: 20% - Midterm I will take place in class on 10/23.
  • Midterm II: 25%
  • Final: 30%
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.