Number Theory (Math 25 Fall 2013)

Instructor: Professor Dorothy Wallace
T-Th 2-3:50, W  4:15-5:30


Math 25  Number theory is possibly the oldest branch of mathematics. As such it serves as some of the inspiration for much of the mathematics we now consider "modern", such as abstract algebra (math 31, 71, 81), real and complex analysis  (math 63 and 43), as well as touching most other branches of mathematics.  As a course with few prerequisites, the goal of Math 25 is to give students practice in proving theorems and writing those proofs well.  This practice will serve you well when you take more advanced courses.  The small project is intended to give you a chance to learn independently by reading more technical literature and presenting it in your own words and on a poster.  You will be encouraged to present your work at the spring poster session hosted by the Math Department.

Grading: Grades (out of 500) are based on two midterms (100 each), the final exam (150), weekly homework (100 total, 20 each), and a small project (50) with write-up and poster.

Attendance: This quarter we meet T-Th 10-11:50 and Wed 3-4.  We spend class time on many examples and case studies not included in the text. We will frequently use the Wednesday time slot to participate in a research seminar in mathematical biology (timed this way just for you).  Students from Math 23 (Differential equations) may also attend and participate in the seminar, as well as students engaged in independent study in mathematical biology.  Attendance at the x-hour is required of Math 27 students when we use it, and of Math 4 students on certain days (to be announced).  Do not schedule other activities during this time.

Text: Elementary Number Theory by Gareth A. Jones and J. Mary Jones (Available at Wheelock Books)

Office hours: Wallace's office: Kemeny 204.  Office hours: 12-1 T,W, Th, and by appointment.

Syllabus: Will be sent via email.

Honor principle: (This prose was modified from Shemankse's 2010 course page)

On Homework and the project: Students are encouraged to work together to do homework problems. What is important is a student's eventual understanding of homework problems, and not how that is achieved. The honor principle applies to homework in the following way. What a student turns in as a homework solution is to be his or her own understanding of how to do the problem. Students must state what sources they have consulted, with whom they have collaborated, and from whom they have received help. Students are who rely on solutions to problems that are posted on the web must reference them with the URL. The solutions you submit must be written by you alone. Any copying (electronic or otherwise) of another person's solutions, in whole or in part, is a violation of the Honor Code.

Moreover, if in working with someone they have provided you with an important idea or approach, they should be explicitly given credit in your writeup. Hints I give in office hours need not be cited. Note: It is not sufficient to annotate your paper with a phrase like ``I worked with Joe on all the problems.'' Individual ideas are to be credited at each instance; they represent intellectual property.

On Exams: Students may not receive assistance of any kind from any source (living, published, electronic, etc), except the professor, and may not give assistance to anyone. Matters of clarification are to be left to the professor.

If you have any questions as to whether some action would be acceptable under the Academic Honor Code, please speak to me, and I will be glad to help clarify things. It is always easier to ask beforehand. S.

Disabilities, religious observances, other accomodation as needed:  (This prose was modified from Shemankse's 2010 course page)
I encourage any students with disabilities, including "invisible" disabilities such as chronic diseases and learning disabilities, to discuss appropriate accommodations with me, which might help you with this class, either after class or during office hours. Dartmouth College has an active program to help students with disabilities, and I am happy to do whatever I can to help out, as appropriate.

Any student with a documented disability requiring academic adjustments or accommodations is requested to speak with me by the end of the second week of the term. All discussions will remain confidential, although the Academic Skills Center may be consulted to verify the documentation of the disability and advise on an appropriate response to the need. It is important, however, that you talk to me soon, so that I can make whatever arrangements might be needed in a timely fashion.

Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with me before the end of the second week of the term to discuss appropriate accommodations.  The same goes for anything that might interfere with coming to class (e.g. sports trips).