Instructor: Jonathan Sands, Room 404, 16 Colchester Ave.
656-4339
email: sands@cems.uvm.edu homepage:
http://www.cems.uvm.edu/~sands/m52s09/index.html
My office hours are M, Tu, W, F 1-2
and
by appointment. Or send me your question by email. No question is too
small!
I urge you to drop by or make an appointment in the beginning of the
semester
to get acquainted, discuss personal goals and consider topics for your
independent study project, described below.
Goals: My main goal is to help you develop certain habits of the mind that will serve you well in your mathematical career and beyond: posing questions, thinking logically and creatively, assimilating new concepts, using a variety of resources, solving problems, reflecting on what you have learned, and trusting in your conclusions.You will also gain important experience in teamwork, communicating precisely, composing mathematical proofs, and using computers as a tool to discover and test mathematical principles, . The concepts of central importance in higher mathematics which we study will often be familiar; this allows us the luxury of examining them more closely, investigating the fascinating relationships between them, and focusing on the art of doing mathematics. You will also get to know members of the mathematics department faculty and gain some experience in working independently while pursuing a topic of special interest to you in a mentored project.
Topics: The integers, sets, logic, relations, functions, using a computer algebra system, induction, recursion, modular arithmetic, and complex numbers. (Chapters 1,2,3 and 5 in the text). Additional topics will be presented by you and your fellow students.
Text: Introduction to Discrete Mathematics and Computing, by James Burgmeier and Larry Kost. Photocopies of the relevant pages of these notes by two UVM mathematicians will be made available to you at cost. It can be helpful to find other books that suit your individual taste or just provide you with other explanations, examples, and exercises.
Homework: These assignments are designed to reinforce important habits and skills as well as concepts. Your objective on homework assignments should be to create a polished, complete, crystal-clear presentation of solutions. To help you achieve this objective, I will provide feedback on the first draft of your solutions before you turn in the finished product. Also, you may choose to work as a team with up to three other students. Teams should submit one assignment, and all team members will receive the same grade for that assignment. As a team member, you should contribute to the finished product and understand the whole of it before adding your signature to it. Academic honesty demands that you indicate clearly if you have obtained help from other people, books, or sources of any kind. Responsible work habits and consideration for the grader dictate that late homework cannot be accepted without special prior arrangement. First drafts of weekly homework assignments will normally be due on Friday at the beginning of class. They will be returned with feedback on Monday, but without grades. Final drafts are then due on Wednesday. You must submit a timely first draft in order to have your final draft graded.
Computer Work: There will be a weekly computer assignment using Mathematica, due at class time on Monday. You can work on these assignments wherever and whenever you want. The same principles apply as for homework: think of yourself as a professional! To facilitate grading, your submissions must be organized and clear, and the Mathematica functions you define should produce output when tested. Additional help with Mathematica can be found on the UVM Math web pages, and in person at the Help Sessions for all classes using Mathematica .
Tests: There will be a test in class on Friday, February 27 covering chapter 1. A second test will be in class on Friday, April 10 covering chapters 2 and 3. Computer and programming expertise will not be tested on these. They will focus on the mathematical concepts which you should have mastered, including concepts stressed in computer assignments. Please inform me at least one week in advance if you must miss a test.
Projects: As part of a team with two or three other students, you will participate in an independent study project mentored by a Mathematics/Statistics faculty member. The result of this project will be a 40 minute presentation to the class by the team at some time during the last two weeks of the semester. Although you are encouraged to come up with your own project topic, some suggestions are: cryptography (e.g. knapsack ciphers, RSA ciphers, or discrete logarithm ciphers), fractals, chaos, cardinality, the Cantor set, combinatorics (e.g. tournaments, combinatorial designs, finite geometries, graph theory),coding theory, elementary number theory (Fermat and Mersenne primes, primitive roots, quadratic reciprocity, distribution of primes, factoring and primality), data compression, and introductory group theory. The deadline for a choice of topic and mentor is Friday, March 13.
Classwork: You are responsible for informing me when something is unclear, or when you are struggling with a new concept or problem, so that I can help you out. I will ask questions in order to get feedback, and simply expect honest efforts to answer my questions as completely as possible. Also, various classroom activites will strengthen our grasp of the subject matter, and require your full engagement. Of course your class participation will suffer if you are not present.
Final Exam: Comprehensive 3-hour exam in 220 Votey on Friday, May 8, at 8am.
Course Grade: Homework assignments will be worth 25% of your grade, and computer assignments will be worth 15%. Each of the two tests will be worth 15% of your grade, and the final exam will be worth 20% of your grade. The project will be worth 7.5% and your class participation will be worth 2.5%. Letter grades will be assigned in accordance with the traditional standards for this course. In particular, a numerical grade of 90% will translate into at least an A-, 80% will translate into at least a B-, 70% will translate into at least a C-, etc.
Academic Honesty: The UVM classroom code of conduct and academic honesty policy are in effect, as always. In particular, always be sure to give proper attribution for work or ideas that are not your own.
Special Needs: If you need an accomodation for which you are
eligible,
please inform me at the beginning of the semester (during the first two
weeks of class) so that this can be implemented.