University of Rhode Island MTH436: Mathematical Analysis and Topology II
Spring 2018

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: Monday 10.30-11.30, Tuesday 11-12 and Wednesday 9.30-10.30 or by appointment

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 Riemann Integral. 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 and the generalised Riemann Integral. 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.

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

Prerequisites: MTH435.

Homework: The homework will be as in MTH435, unless stated otherwise. 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: This may or may not be continued in MTH436. 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% or 0%
  • Quizzes: 10%
  • Homework: 10%
  • Midterm I: 20% -in class on 03/07.
  • Midterm II: 25% - in class on 04/23.
  • Final: 30% or 35% - 05/09, 3-6pm in Lippitt 204.
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.