Over the course of the year, there will also be assigned 2 Projects and 3 Computer Explorations. The due dates are again by 11PM on Sunday evening, three days from the date of the assignment. These probems are much more substantial than the Exercises (so no paper limit). In addition, the use of MATHEMATICA (Mma) will be helpful for the former and essential for the latter. You are encouraged to submit a Mma Notebook (instead of a hand-written solution) for the Projects; and you are required to do so for the Explorations. See the Mathematica page for the policy on collaboration. See the Grading Policy below for point allocations.
Grading Policy
The maximum possible number of points you can score in this course is 650. Your final grade will depend upon the total points you score on the: KW Exercises; KW Projects; KW Computer Explorations (using MATHEMATICA), three hourly exams, and the final exam, distributed as follows:
Category | Total Points |
---|---|
Projects | 20 |
Computer Explorations | 30 |
Exercises | 100 |
Three Hourly Exams | 300 |
Final Exam | 200 |
There will be no make-up exams for any of the three in-class exams. If you miss ONE in-class exam (due to an excused absence), then your score for that exam will be one half of your final exam score. In all other cases if you miss one or more in-class exams, then no final grade will be issued for the course.
Finally, there will be several additional Projects and Explorations (likely five in total) listed as optional assignments. You may earn up to an additional 50 points for these; points that will count in the numerator, but not the denominator in computing your course score.
Class Schedule
The class meets on Thursdays,
3:00PM -- 4:00PM in room 38 at Poolesville High School.
Consultation Hours
Because of the unusual nature of the course, there is no opportunity to schedule office hours wherein students could ask questions or discuss course work outside of class with Dr. Lipsman. However, Dr. Lipsman welcomes phone calls, texts or emails from students at any time with relevant questions, comments or suggestions. Please feel free to avail yourself of this opportunity. Also, Dr. Lipsman tends to arrive early on Thursday and hang around a bit after class. If your class and transportation schedules permit, feel free to engage him at those times.
Nature of the Course
Since Number Theory is largely about the discovery of the remarkable properties of numbers (esp. integers, primes, rational numbers), its study typically involves proofs and the development of abstract methods. This differs from the study of Calculus or Ordinary Differential Equations (ODE) wherein the subject leads investigators towards symbolic and numeric algorithms for carrying out concrete processes. Thus this course will be much less formulaic than what you ecountered in calculus or -- if you participated last year -- differential equations. In the latter, the student learns many formulas and techniques that can serve as a foundation in more advanced courses in math and science. In this course, you will learn more about the kind of abstract reasoning that will also serve you well in those courses.
One consequence of this difference will be the role of mathematical software -- in our case, MATHEMATICA -- in the course. Mma is ideally suited to Calculus and ODE because it implements and automates the algorithmic processes that one encounters there. It is less ideally suited to proof construction and abstract reasoning. Nevertheless, Mma does have a rich set of number theory commands. Unfortunately, there is no analog of the Mma instruction book for differential equations that we used last year in ODE. Thus it will be largely left to the student to discover the relevant commands and how to use them. To get you started, go to the Help tab in a Mma Notebook, open the Documentation Center and search for "guide/NumberTheory".
Office: Mathematics Building, Room 4301
Phone: (301) 405-7061
Cell Phone: (301) 538-8381
Email: rlipsman@math.umd.edu
Backup Email: rlipsman@umd.edu