Instructor: Jonathan Sands, Room 404, 16 Colchester Ave. (Henry Marcus Lord House)
656-4339
email: sands@cems.uvm.edu homepage:
http://www.cems.uvm.edu/~sands/m52f09/index.html
My office hours are M, W, F 11-12, Tu 12-1
and
by appointment. I am often available mid-afternoons. 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 team project, described below.
Goals: At the end of this course, students will be able to
1) Write sound logical proofs on various topics, with correct terminology, notation, and grammar.
2) Think like a mathematician: analyze how conlusions are arrived at, distinuishing definitions from theorems.
3) Use foundational material in various settings.
4) Collaborate on research and presentation of a mathematical topic.
5) Make connections between various areas of mathematics.
Topics: The integers, sets, logic, relations, functions, induction, recursion, and modular arithmetic. (Chapters 1,2 and 3 in the text). Additional topics will be presented by you and your fellow students!
Text: Introduction to Discrete Mathematics, by James Burgmeier and Larry Kost, is our primary text. Photocopies of the relevant pages of these notes are available for $10 from the Math/Stat Office in Henry Marcus Lord House at 16 Colchester Ave.. The supplementary text Mathematical Proofs by Chartand, Polimeni and Zhang is recommended, but not required. We will use it for some additional material, explanations, examples, and exercises.
Homework:
Assignments are designed to
reinforce important habits and skills as well as concepts, addressing
the goals listed above. Your
objective
on homework assignments should be to create a polished, complete,
crystal-clear
presentation of solutions. To help you achieve this objective,
your fellow students will provide feedback on the first draft of
your
solutions before you
turn in the finished product. 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 should normally be ready
for class on Monday. Final drafts are then due on Wednesday.
Writing Assignments: Several times during the semester, you will have an assignment requiring you to write an explanation of a concept that was demonstrated in class by the Great Sandzini. Such an assignment is designed to improve your understanding and retention of the concept, as well as your ability to communicate mathematics effectively.
Class Participation: Active participation in classroom activities will contribute to your success and enjoyment in this course. These activities will include asking questions, journaling, and providing feedback to your fellow students.
Journals: You should bring a small journal to class. Each day of class, you will outline in your journal the main topics we have covered and write down any questions that occur to you. You will have an opportunity to raise these questions at the next class, and you may be called on to remind the class what was discussed last time. This will count as part of your class participation.
Tests: There will be a test in class on Wednesday, October 14, covering chapter 1 and supplementary material on sets. A second test will be held in class on Wednesday, November 11 covering chapter 2 and 3. Please inform me at least one week in advance if you must miss a test.
Projects: As part of a team with 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: complex numbers, 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, puzzles (e.g. Rubik's cube), games, and introductory group theory. The deadline for a choice of topic and mentor is Friday, October 23.
Final Exam: Comprehensive 3-hour exam in 207 Terrill on Thursday, December 17, at 3:30pm.
Course Grade: Homework assignments will be worth 25% of your grade, and written assignments will be worth 10%. 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 10% and your class participation will be worth 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.