| MTH307: Introduction to Mathematical Rigor |
Instructor: Tom Sharland
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.
Grade breakdown: The grading scheme will be as follows: