University of Rhode Island MTH307: Introduction to Mathematical Rigor
Spring 2017

General Information

Instructor: Tom Sharland
email: tsharland "at" uri "dot" edu
Office: Lippitt Hall 202F
Lectures: TTH 12.30-1.45, Bliss Hall 211
Office hours:3-4 on Monday, 11-12 Wednesday and 3-4 Thursday 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: Book of Proof by Richard Hammack. The author has very kindly put a free version of the book on his webpage, but a hard copy can also be bought. 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. I also have recently come across "Tools of Mathematical Reasoning" by Lakins, which is at a similar level to the course textbook and contains a lot of worked out examples of proofs.

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

Homework and Quizzes: Homework will be assigned weekly and will contain two components. Each week I will highlight in bold font three questions which should be carefully solved and handed in at the start of class on the following Thursday, one of which will be graded for credit - this is the first component. You are expected to produce legible, well argued answers with full explanations. The second component will be weekly quizzes (no notes allowed) which will be based on (but not necessarily exactly the same as) the questions in the homework. Some leeway will be given on these answers due to time constraints. Each component will contribute half-weight to the total homework score, thus each is worth 10% of the total grade.

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 03/09 in class.
  • Midterm II: 25% - on 04/20 in class.
  • Final: 35% - 11.30am on 05/04.
The final will be cumulative. There are no plans for extra credit.

Useful notes:
  • Ryan, a student from this class last semester, is available in the Academic Enhancement Center on Mondays and Wednesdays, 4.30-7.