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Math 101 Spring 2016
Course: Math 101
Freshman Seminar: The Hadwiger-Nelson Problem
Title: Freshman Seminar
Textbook: There is no required textbook for this course. Throughout the course, I will make reference to various materials that can be used for further reading if desired. One excellent resource on the Hadwiger-Nelson problem and related ideas is Alexander Soifer's book The Mathematical Coloring Book. Other references and lecture notes will be provided as needed.
Subject Material: The goal of this course is to use the Hadwiger-Nelson problem as a tool for thinking about how mathematicians approach problems. We will study various approaches to the problem, and by doing so, discuss the ways that mathematicians think about research and work towards solutions of unsolved problems. Along the way, we will have the opportunity to play with and discuss some wonderful, beautiful mathematical concepts, such as density, measurability, the Axiom of Choice, and others. The overall goal is not just to understand the Hadwiger-Nelson problem, but to use this problem as a springboard for understanding a little more of what research in mathematics is all about.
A note on course structure: Unlike most of your math classes, there is no syllabus of material we need to cover here. The course structure is a little more free for us to explore as we choose. If you want more of a particular topic, or there's something you're interested in covering, please let me know! I'd by super happy to try and accommodate any requests as we go along. In addition, you should expect that there may be more writing and less problem-solving than you're used to in this course. It's a great time to sharpen your LaTeX skills, without piles of equations to deal with!
Lecture: Attending the lecture is a fundamental part of the course. Your attendance and participation will be a substantial part of your course grade. Should you need to miss lecture, I suggest talking to a classmate to get a rundown of what happened, so that you are prepared for the next class. Attendance and participation grades will be calculated as follows: For each lecture, attending, and actively participating/listening earns 5 points. The total will be taken out of 100 points. There are 21 lectures total.
Classroom Conduct: In the classroom, a certain level of respect and attentiveness is expected. Please do not use phones or computers, play games, or talk to friends during lecture. This can be distracting to other students and the instructor.
Calculators: A calculator is not required for this course. A calculator would never help you understand these concepts anyway.
Homework: Homework problems will be assigned on the course homework page, and should be completed and turned in by the beginning of class on the indicated due date. Some homework problems may be assigned during the lecture, and added to the course homework page immediately following lecture. Please be attentive as this page will be updated very frequently, and I'd hate for you to miss something.
Exams: There will be no exams in this course! Hurray!
Final Essay: In lieu of a final exam, students will write a final essay. More information about this can be found here.
Grading: Your final course grade will be based on the following weighted average:
A curve may be applied to final scores or individual examinations at the instructor's discretion. Regardless of the curve, the following basic rubric will be in place:
- 50% Attendance/Participation
- 35% Homework
- 15% Final Essay
- Scores above 90%: A
- Scores above 80%: At least B
- Scores above 70%: At least C
- Scores above 60%: At least D
Academic Honesty: Academic dishonesty is a serious offense, carrying serious administrative sanctions. Any instance of dishonesty will be pursued by the instructor. It is in your best interest to follow all policies laid out here and elsewhere on the website, and familiarize yourself with the university guidelines for academic honesty. Please help maintain both your own integrity and the integrity of Carnegie Mellon University.
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