Instructor: Jeffrey Diller (click for contact info, general policies, etc.)
Time and place: MWF 8:30-9:20 AM, DeBartolo 119
Office Hours: Help session Mondays 6-7 PM in 125 Hayes-Healy. I'll also be available in my office Tuesday afternoons 2:30-4 PM for last minute homework questions. However, I assign homework a week before it's due and expect you to take advantage of all that time. It would definitely not be a good idea to wait til Tuesday to start your homework or to ask me questions about it.
Textbook: An Introduction to Mathematical Thinking. by William Gilbert and Scott Vanston. We'll also rely heavily on notes that I provide for download on the schedule page.
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: Course content falls roughly into four categories. We'll definitely cover the first three, though the first will be somewhat dispersed among the other two. The fourth category is a sort of grab bag that we'll reach into as much as we can.
Basic material concerning sets and proofs: methods of proof, relations, functions, cardinality.
The integers: ring axioms, order and induction, divisibility and factorization, Euclidean algorithm, congruences, rational numbers.
Analysis: least upper bound property, sequences, convergence, decimal expansions.
Other topics, time permitting: RSA encryption scheme, complex numbers, fundamental theorem of algebra.
In terms of the textbook, we will cover the following in more or less the order listed: chapter 2, sections 4.1 and 4.3, chapter 3, chapter 5 (we'll definitely need notes here, since this one is far to brief for our purposes), and sections 6.1-6.6. It'd be nice to spend time on chapters 7 and 8, too.
How you will be evaluated:
Homework: assigned and collected every Wednesday, worth 30% of your final grade. I encourage you to collaborate with each other on homework assignments. In fact, on each assignment, you may collaborate with up to one other person and turn in a single, jointly prepared set of solutions. Since I assign only a small fraction of the number of problems that you face in classes such as Calculus, I expect you to take special care in writing up your solutions well. If the grader takes off points for sloppy presentation, he's only doing his job. On a similar note, if you want feedback from the grader, you should allow space for this to happen. As a general rule of thumb, you should alot at least half a page for short solutions and at least a page for longer ones.
Midterm Exams: given in class on Monday 10/5 and Monday 11/23, each worth 20% of your final grade.
Final Exam: Friday, December 18 from 8-10 AM in 119 DeBartolo (i.e. same as lecture room), comprehensive and worth 30% of your final grade.