Number Theory

Instructor | Samantha Allen |
---|---|

Lecture | (11) MWF 11:30 - 12:35 |

x-Hour | Tu 12:15 - 1:05 |

Classroom | Kemeny 201 |

samantha.g.allen AT dartmouth.edu | |

Office Hours |
Tu 1:30-3:30, Th 11-12, or by appointment. |

Office | Kemeny 311 |

Canvas | We will use Canvas for the gradebook. |

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 | Location TBA |

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.

- 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% |

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.

**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, Student.Accessibility.Services@Dartmouth.edu). 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
(http://www.dartmouth.edu/~upperde),
Counseling and Human Development
(http://www.dartmouth.edu/~chd/), and the Student Wellness Center
(http://www.dartmouth.edu/~healthed/).

**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.