Math 223: Introduction to Mathematical Reasoning
Winter '04

ANNOUNCEMENT (4/28/04): There will be a review session for the final exam for this class Friday from 3-5 PM. It'll be in 229 Hayes-Healy (our usual room)--this is official now.

I'll also hold some office hours Monday from 1-3 PM.

ANNOUNCEMENT (4/26/04): The final exam will be in our usual classroom (HH 229).

Instructor: Jeff Diller (click for contact info, office hours, etc.)

Time and place: MWF 9:35-10:25, Hayes-Healy 229.

Textbook: Mathematical Thinking (Problem Solving and Proofs) 2nd Edition, by John D'Angelo and Douglas West.

Why this course: Up til now, most of your mathematics courses have likely emphasized examples, computation, and intuitive understanding of mathematics. This course will emphasize careful mathematical arguments. By addressing questions about familiar things like numbers (Are there finite or infinitely many prime numbers? Do all rational numbers have rational square roots?) and sets (What does it mean for a set to have ``infinitely many'' elements? Do all sets with infinitely many elements have the same size?), we will see how it is that one justifies statements in mathematics. In a nutshell, the subject of this course is numbers, and its goal is to help you understand, invent, and present proofs.

What we'll cover: The material covered falls into roughly three categories (with a fair amount of overlap).

• Basic material concerning sets, logic, and methods of proof. Chapters one through four of the textbook.
• Algebra & Number Theory (i.e. things relating to integers). Chapters five through eight.
• Analysis (i.e. things relating to real numbers). Chapters thirteen through fifteen.

How you will be evaluated:

• Homework: assigned and collected (more or less) every Wednesday, worth 30% of your final grade. I encourage you to collaborate with each other on homework problems. In fact for each assignment, you may join forces with one or two other students to turn in a single, jointly written set of solutions.
• Two Midterm Exams: given in class, each worth 20% of your final grade. The first will take place on Friday February 20 and the second on Friday April 2.
• Final Exam: Tuesday, May 4 at 8 AM. Room TBA. Worth 30% of your final grade.