Simon Fraser University
Engaging the World

Course Outlines

Spring 2020 - MATH 894 G100

Reading (2)

Class Number: 3751

Delivery Method: In Person

Overview

  • Course Times + Location:

    Location: TBA

Description

COURSE DETAILS:

This course serves as an introduction to the arithmetic of elliptic curves over finite fields.

Topics: We will cover the following topics from the textbook in detail:  

  • The Geometry of Elliptic Curves
  • Weierstrass Equations
  • The Group Law Elliptic Curves
  • Isogenies
  • The Invariant Differential
  • The Dual Isogeny
  • The Tate Module
  • The Weil Pairing
  • The Endomorphism Ring
  • The Automorphism Group  

Elliptic Curves over Finite Fields
  • Number of Rational Points
  • The Weil Conjectures
  • The Endomorphism Ring
  • Calculating the Hasse Invariant

The group will meet weekly for a two hour session. Participants (including the instructor) will take turns presenting the sections listed above. Exercises will be assigned and solutions presented at the sessions or submitted in writing.

Grading

  • Presentations 60%
  • Exercises 20%
  • Participation 20%

NOTES:

Enrollment through permission of instructor only; use Add/Drop form. Contact mathgsec@sfu.ca.

Materials

REQUIRED READING:

Silverman, Joseph H. The arithmetic of elliptic curves. Graduate Texts in Mathematics, 106, Springer-Verlag, New York, 2016. xv+513 pp. ISBN: 0387094938.

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:

SFU’s Academic Integrity web site http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating.  Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the University community.  Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s10-01.html

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS