General Information

Instructor: Tom Sharland
email: tsharland "at" uri "dot" edu
Office: Lippitt Hall 202F
Lectures: TTH 11.00-12.15, Swan Hall 207
Office hours:Monday 11-12, Tuesday 3-4 and Thursday 2-3 or by appointment

Course description: This is an introductory course on the concept of rigour in mathematics. We will move away from the viewpoint of mathematics as a computational subject and begin seeing it as a subject requiring airtight logic and, surprisingly, a fair amount of creativity. Particular topics we will investigate include set theory, methods of proof and applications of these to relations and functions. This is a 3 credit course.

This course is very different to the previous mathematics courses you have taken. You should expect to work hard both inside and out of class to keep up with the course material and make you sure you understand the concepts being covered.

Textbook: Tools of Mathematical Reasoning by Tamara J. Lakins. This is a new choice of textbook for the course (see the following paragraph). It very quickly gets into proving mathematical statements, which is the aim of the course; hopefully we will start proving statements within the first two weeks of classes.

Other recommended reading (but no means necessary) is "How to Prove It" by Velleman and (for the more advanced/curious) "Foundations of Mathematics" by Stewart and Tall. "What is Mathematics?" by Courant, though not really a course textbook, is a wonderful survey (if a bit dated) of general mathematics, but does not require any advanced mathematical knowledge. All these books would be good reading for anyone considering further (e.g postgraduate) studies in mathematics. Previously I have used Book of Proof by Richard Hammack for this course. Following this link will lead you to a free version of this book on his webpage.

Prerequisites: MTH 142 (purely to ensure a level of mathematical maturity).

Homework and Quizzes:

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. To check for this (and to prevent plagiarism), I may on occasion set a quiz question that was on the submitted homework. I am more than happy to discuss the homework in office hours, but will at most provide very small advice on the submitted questions.

Grade breakdown: The grading scheme will be as follows:

• Quizzes/Homework: 20%.
• Midterm I: 20% - on 10/18 in class.
• Midterm II: 25% - on 11/20 in class.
• Final: 35%.
- on December 18th at 11.30am in Swan 207.

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.