University of Rhode Island MTH307: Introduction to Mathematical Rigor
Spring 2018

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.
The final will be cumulative. There are no plans for extra credit.

Useful notes: