| Description | Syllabus | Documents |
|---|
| Kyle Petersen | François Dorais | |
|---|---|---|
| Office | 1847 East Hall | 3848 East Hall |
| Phone | 936-2879 | 936-9938 |
| tkpeters@umich.edu | dorais@umich.edu | |
| Office Hours |
Mon 12pm–1pm Wed 1pm–2pm Thu 12pm–1pm |
Mon 2pm–3pm Tue 2pm–3pm Wed 2pm–3pm |
| Monday | Tuesday | Wednesday | Thursday |
| 10am–11am | 10am–11am | 10am–11am | 10am–11am |
| 4096 East Hall | 4096 East Hall | 4096 East Hall | B745 East Hall |
| Monday | Tuesday | Wednesday | Thursday |
| 11am–12pm | 11am–12pm | 11am–12pm | 11am–12pm |
| 325 Dennison | 325 Dennison | 325 Dennison | B745 East Hall |
This course gives a historical introduction to cryptology and introduces a number of mathematical ideas and results involved in the development and analysis of secret codes. While the mathematical subjects treated include enumeration, probability, and some statistics, the bulk of the course is devoted to elementary number theory, with the goal of understanding public key encryption.
The course has two components, the classroom component and the computer component. The classroom component meets Monday to Wednesday, and will be driven by worksheets that we give you to do in class. We will introduce each worksheet with some background material (definitions, motivation), and then you will complete the worksheets in groups of 2 or 3. Each worksheet will consist of a list of problems that you will attempt to solve together during class over the course of a few class periods. As you solve problems from the worksheet, you will be asked to explain your solutions to the rest of the class. In particular, we want you to share the strategies you used to solve the problem, rather than simply giving the final answer. During the first few weeks we will help with these explanations, but our hope is that you will soon explain your own methods and solutions. Effective communication is a skill everyone should develop.
On Thursdays we will meet in the computer lab. There we will have various discovery-based projects designed to allow you to explore the ideas developed in the classroom.
This is not a traditional lecture-style course. You don't learn how to swim by watching a swim meet, and you don't learn how to play the violin by going to a recital. Why should you learn how to do mathematics by watching a professor do mathematics? In this course, we will help you learn how to solve problems and create your own mathematics through experimentation, critical thinking, and discussion with one another. THIS IS VERY EXCITING!! It can also be a little scary if you've never been asked to do it before. Don't worry, though, this is how mathematics has been done since ancient times... It works!
But why should you want to learn how to solve problems and create the mathematics when we could just tell you the answers and show you how to work the problems? The answer is because good problem solving skills are essential to success in all walks of life. Throughout your time at the University, you will be faced with all sorts of different and challenging problems, both inside and out of the Math department. Being relaxed and confident when confronted with a different situation is the hallmark of a good problem solver, and having that skill will serve you well in your time in Ann Arbor and beyond. Employers aren't looking to hire people who mindlessly plug numbers into formulas that are given — they want people who are comfortable when faced with new challenges and possess good analytic skills.
People often graduate from college saying, "I didn't learn anything in college that I actually used later on in the real world." Well, chances are you won't have much specific need for the mathematics of cryptology in your future career, either. Nevertheless, no matter what you go on to do, knowing how to use logical reasoning to solve problems will always be a useful skill.
As you may have gathered from the structure and philosophy of the course, attendance and participation are very important. We will keep track of how much effort you've put into each day's work, and how often you volunteer your thoughts in the explanation portion of class. Clearly, when you skip a class, you miss out on both counts — don't skip class!
Serial absenteeism clause: You are allowed up to three (3) unexcused absences from class. The instructors decide what constitutes an excused absence on a case-by-case basis. For each absence beyond those three, your final grade for the class will drop by one letter grade. For example, if you would have otherwise earned a B+ for the course but you have 4 unexcused absences, your final grade will be a C+.
There will be regular homework assignments. Homework is due at the beginning of class on the given due date.
You are encouraged to discuss the homework assignments with other students in the class; however, if you do, you should write on your homework submission the students with whom you discussed the assignment. You may not copy the written work of another student or allow another student to copy your written work. What you submit should be your own work: written by yourself and in your own words.
Late homework will not be accepted in the absence of divine intervention or matters of similar weight. Unexcused late or missing papers count zero.
There will be two midterm exams and one final exam. These are scheduled as follows:
Exam dates are absolutely firm. All enrolled students must plan to take exams at the scheduled times. Travel plans will not be considered an excuse to take an examination on a different date.
Your final grade will be based on your two midterm exams, final exam, homework, and participation according to the following distribution: