Number Theory (FA23)

Course Info:

• Lectures: Monday, Wednesday, Friday, block 10 (10:10 a.m. - 11:15 a.m.)
• x-period: Thursday, block 10X (12:15 - 1:05 p.m.)
• Dates: 11 September 2023 - 14 November 2023
• Room: 108 Kemeny Hall

• Instructor: John Voight
• Office: 341 Kemeny Hall
• E-mail: jvoight@gmail.com
• Office hours:
  • Mondays, 2:30-4:30 p.m.,
  • Tuesdays, 9:00-10:00 a.m.,
  • or please make an appointment by email!
• Course Web Page: https://canvas.dartmouth.edu/courses/61083

• Prerequisites: Math 8, or equivalent. If you are unsure about your preparation, please talk to the instructor!
• Required Text: David Burton, Elementary Number Theory, 7th edition, 2012.
• Grading: Grade will be based on reading and class participation, daily homework, weekly homework, quizzes, an in class final exam, and a takehome final exam.

Course Catalogue 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.

Learning Outcomes:

By the end of this course, you should be able to:

1. Understand of the basic structures of number theory: define terms, explain their significance, and apply them in context;
2. Solve mathematical problems: utilize abstraction and think creatively; and
3. Write clear mathematical proofs: recognize and construct mathematically rigorous arguments.
   

Additional Pages:

1. Academic Honor Principle
2. Expectations
3. Homework
4. Student Accessibility Needs
5. Mental Health
6. Religious Observances
7. Additional Support for your Learning