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 11-12, Tuesday 10-11, Wednesday 10-12

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 ahve 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, 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. 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%.

Accommodations: Any student with a documented disability is welcome to contact me as early in the semester as possible so that we may arrange reasonable accommodations. As part of this process, please be in touch with Disability Services for Students Office at 330 Memorial Union, 401-874-2098 (http://www.uri.edu/disability/dss/).

Religious holidays: It is the policy of the University of Rhode Island to accord students, on an individual basis, the opportunity to observe their traditional religious holidays. Students desiring to observe a holiday of special importance must provide written notification to each instructor according to the procedure set forth in Sections 8.51.11 & 8.51.12 of the University Manual ( http://www.uri.edu/facsen/8.50-8.57.html )

Standards of behaviour: Students are responsible for being familiar with and adhering to the published "Community Standards of Behavior: University Policies and Regulations" which can be accessed in the University Student Handbook. If you must come in late, please do not disrupt the class. Please turn off all cell phones, pagers, or any electronic devices.

Academic Honesty: All submitted work must be your own. If you consult other sources (class readings, articles or books from the library, articles available through internet databases, or websites) these MUST be properly documented, or you will be charged with plagiarism and will receive an F for the paper. In some cases, this may result in a failure of the course as well. In addition, the charge of academic dishonesty will go on your record in the Office of Student Life. If you have any doubt about what constitutes plagiarism, visit the following websites: the URI Student Handbook, and Sections 8.27.10 – 8.27.21 of the University Manual.

Academic Enhancement Center: The work in this course is complex and intensive. To do the best you can, it’s a good idea to visit the Academic Enhancement Center (AEC) in Roosevelt Hall. The AEC offers a comfortable environment in which to study alone or together, with or without a tutor. AEC tutors can answer questions, clarify concepts, check understanding, and help you to study. You can make an appointment or walk in during office hours — Monday through Thursday from 9 am. to 9 pm, Friday from 9 am to 1 pm, and Sunday from 4 pm. to 8 pm. For a complete schedule For a complete schedule – including when tutors are available specifically for this class – go to web.uri.edu/aec, call (401) 874-2367, or stop by the fourth floor in Roosevelt Hall.