Number Theory (FA20)

Course Info:

• Lectures: Monday, Wednesday, Friday, block E (1:10 - 2:15 p.m. EDT/EST)
• Course type: Remote with synchronous components (RSC)
• x-period: Tuesday, block EX (1:40 - 2:30 p.m. EDT/EST)
• Dates: 14 September 2020 - 17 November 2020
• Zoom Link: Sent to registered students.  Send me an email if you have any problems.
• Instructor: John Voight
• E-mail: jvoight@gmail.com
• Office hours: Monday 5:00 - 6:00 p.m. EDT/EST and x-hour (Tuesday, 1:40 p.m. -  2:30 p.m. EDT/EST), or please make an appointment by email for a Zoom meeting.
• Course Web Page: https://canvas.dartmouth.edu/courses/43096 (or http://www.math.dartmouth.edu/~m25f20/ redirects)
• Prerequisites: Math 8, or equivalent. If you are unsure about your preparation, please talk to the instructor!
• Required Text: Kraft and Washington, An Introduction to Number Theory with Cryptography, 1st edition, 2013.  
• Recommended Texts: Kevin Houston, How to Think Like a Mathematician: A Companion to Undergraduate Mathematics, 2009; see also its Home page and the summary 10 Ways to Think Like a Mathematician.
• Grading: Grade will be based on reading and class participation, daily homework, weekly homework, quizzes, and a final exam (see Grading).

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; 
3. Write clear mathematical proofs: recognize and construct mathematically rigorous arguments; and
   
4. Modify and write programs in Python: solve cryptographic problems. 

Additional Pages:

1. Academic Honor Principle
2. Expectations
3. Grading
4. Written Homework
5. Daily Homework
6. Consent to Record
7. Student Accessibility Needs
8. Mental Health
9. Title IX
10. Religious Observances
11. Additional Support for your Learning