An Introduction to Mathematics Beyond Calculus (SP19)

Course Info:

• Lectures: Monday, Wednesday, Friday, block 11 (11:30 a.m. - 12:35 p.m.)
• x-period: Tuesday, block 11X (12:15 - 1:05 p.m.)
• Dates: 25 March 2019 - 29 May 2019
• Room: 343 Kemeny Hall

• Instructor: John Voight
• Office: 341 Kemeny Hall
• E-mail: jvoight@gmail.com
• Office hours: Monday 4:00-5:00 p.m. and Tuesday 12:00 noon-1:00 p.m. (when no x-hour), or please make an appointment by email.
• Course Web Page: https://canvas.dartmouth.edu/courses/32764

• Prerequisites: Math 8 or advanced placement into Math 11. 
• Required Texts:
  • Tom Wright, Trolling Euclid, 2016.
  • Joseph Silverman, A Friendly Introduction to Number Theory, 4th edition, 2017.
• Grading: Grade will be based on occasional homework, class participation, and a final project (see Grading).

Course Catalogue Description:

Gives prospective Mathematics majors an early opportunity to delve into topics outside the standard calculus sequence. Specific topics will vary from term to term, according to the interests and expertise of the instructor. Designed to be accessible to bright and curious students who have mastered BC Calculus, or its equivalent. This course counts toward the Mathematics major, and is open to all students, but enrollment may be limited, with preference given to first-year students.

Course Topic:

The abc conjecture states that if a, b, and c are relatively prime integers satisfying a + b = c, then a, b, c cannot all have many repeated prime factors. In this course, we will make this conjecture precise, consider polynomial analogues, and discuss the controversy surrounding the announced proof of the conjecture by Shinichi Mochizuki.

Learning Outcomes:

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

1. Understand some basic structures of algebra and number theory: define terms, explain their significance, and apply them in context; 
2. Solve mathematical problems: utilize abstraction and think creatively; and
3. Discover mathematical patterns and then recognize and construct mathematically rigorous arguments.

Additional Pages:

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