INSTRUCTOR: Stephen D. Smith
OFFICE: 536 SEO; (312) 413-2165, smiths@math.uic.edu
OFFICE HOURS: 1 - 2 PM, MWF, or by appointment

This course is designed to develop the student's ability to think mathematically and to create and understand valid mathematical proofs. In addition to learning techniques and concepts of rigorous proof, this course will help develop the writing and analytic abilities of students. Reading and writing assignments of various lengths will occur throughout the course.

Upon completion of this course, each student will be able to:

1. Prove statements using: mathematical induction, direct proofs and proofs by contradiction; regarding each of the following objectives:
2. Build and apply truth tables in examining statements, propositions and other logical entities.
3. Understand intuitive set theory and build proofs using set-theoretic arguments.
4. Do direct proofs and proofs by contradiction.
5. Understand what a complete rigorous mathematical proof is.
6. Do proofs using relations and congruence.
7. Apply induction to simple number theory.

There are many books giving an introduction to mathematical reasoning (the Bibliography lists a selection of these; thanks to Prof. Steven Hurder for this and various other course supplements on the web).

The textbook was chosen because its topics and style match the goals of this course most closely.

An Introduction to Mathematical Reasoning Numbers, Sets and Functions
by Peter Eccles, Department of Mathematics, University of Manchester
Published by Cambridge University Press, Paperback 0-521-59718-8, $27.95.

This book introduces students to the rigors of university mathematics. The emphasis is on understanding and constructing proofs, and writing clear mathematics. The author achieves this by exploring set theory, combinatorics, and number theory, topics that include many fundamental ideas and may not be a part of a young mathematician's toolkit. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all-time-great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.

The UIC Bookstore should have the book by the start of term.

Barnes & Noble lists the book as currently available.

amazon.com lists used copies for sale.

It is extremely important to attend classes, to do the assignments on time, to participate in discussions in class, and---equally important---to go over your notes after each class and to ask questions, either in class or during my office hours, about any difficulties you are having. It is also extremely important to work with other students in the class, to collaborate with them on homework assignments and to discuss the material with them.

Each Friday there will be a homework assignment due to be handed in the following class period - either a Monday or Wednesday. Problems may also be assigned on other class days, and be due in the next class. Students in the class will often be asked to show their solutions at the blackboard, in lieu of having them handed in. The homework, and possibly occasional quizzes, will be worth 100 points total.

There will be two Midterm Exams, each worth 100 points.

The Final Exam will be worth 200 points.

Your class ranking will be the sum of these scores, out of a possible 500 points total.