General Information

Instructor and Scheduled Lectures

Instructor Samantha Allen
Lecture (11) MWF 11:30 - 12:35
x-Hour Tu 12:15 - 1:05
Classroom Kemeny 201
Email samantha.g.allen AT
Office Hours Tu 1:30-3:30, Th 11-12,
or by appointment.
Office Kemeny 311
Canvas We will use Canvas for the gradebook.

Course Description

The great mathematician C. F. Gauss once wrote "Mathematics is the queen of sciences and number theory is the queen of mathematics." Number theory is that part of mathematics dealing with the integers and certain natural generalizations. Topics include modular arithmetic, unique factorization into primes, linear Diophantine equations, and Fermat's Little Theorem. Discretionary topics may include cryptography, primality testing, partition functions, multiplicative functions, the law of quadratic reciprocity, historically interesting problems.
Prerequisites: MATH 8


Elementary Number Theory by Gareth A. Jones and J. Mary Jones


There will be two midterm exams and a cumulative final exam. The exams are scheduled as follows:

Exam 1 In-class portion: Wednesday, October 9 Take-home portion: Due Friday, October 11
Exam 2 In-class portion: Wednesday, October 30 Take-home portion: Due Friday, November 1
Final Exam Sunday, November 24, 3:00-6:00 pm Kemeny 007

If you have a conflict with an exam because of a religious observance, scheduled extracurricular activity such as a game or performance [not practice], or similar commitment, please see your instructor as soon as possible.

Homework Policy 

  • Written homework assignments will be assigned weekly. They are due each Wednesday at the start of class (11:30am). Homework assignments will typically cover the material up through the previous Friday. So the first written assignment (available on the Homework page) covers the first three classes worth of material and is due on Wednesday of week 2.
  • If you must miss a class, it is your responsibility to submit all homework on time, and to arrange to get notes from a classmate.
  • Late homework will be accepted only in case of serious, unpredictable events such as documented illness or family emergency. Unexcused late and missing papers count zero.


The course grade will be based upon the scores on the midterm exams, homework, and the final exam as follows:

Weekly homework 25%
Midterm Exam 1 20%
Midterm Exam 2 20%
Final Exam 35%

The Honor Principle

Academic integrity is at the core of our mission as mathematicians and educators, and we take it very seriously. We also believe in working and learning together.

Collaboration on homework is permitted and encouraged, but obviously it is a violation of the honor code for someone to provide the answers for you.

On written homework, you are encouraged to work together, and you may get help from others, but you must write up the answers yourself. If you are part of a group of students that produces an answer to a problem, you cannot then copy that group answer. You must write up the answer individually, in your own words. A good practice is to discuss ideas on a blackboard, then erase the blackboard and try to reproduce the arguments later, on your own paper, and without assistance.

On exams, you may not give or receive help from anyone.In-class exams in this course are closed book, and no notes, calculators or other electronic devices are permitted. For take-home portions of exams, the textbook (Elementary Number Theory by Jones and Jones) and your class notes may be used, but no other sources are permitted.

Special Considerations

Accessibility Services etc.
Students with disabilities who may need disability-related academic adjustments and services for this course are encouraged to see me privately as early in the term as possible. Students requiring disability-related academic adjustments and services must consult the Student Accessibility Services office (Carson Hall, Suite 125, 646-9900, Once SAS has authorized services, students must show the originally signed SAS Services and Consent Form and/or a letter on SAS letterhead to their instructor. As a first step, if you have questions about whether you qualify to receive academic adjustments and services, you should contact the SAS office. All inquiries and discussions will remain confidential.

Mental Health
The academic environment at Dartmouth is challenging, our terms are intensive, and classes are not the only demanding part of your life. There are a number of resources available to you on campus to support your wellness, including your undergraduate dean (, Counseling and Human Development (, and the Student Wellness Center (

Religious Observances
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 your instructor before the end of the second week of the term to discuss appropriate accommodations.