Dalhousie University
Mathematics and Statistics

C.F. Gauss

Algebraic Number Theory

MATH 4070/5070

Dalhousie University
Department of Mathematics and Statistics
Pierre de Fermat

  • Basic Information:
    • Instructor: Karl Dilcher (dilcher@mathstat.dal.ca)
    • Office: Chase Building Room 325
    • ph.: 902-494-3784
    • Office hours: Mon., Wed. 2:30-3:30 pm, Fri. 2:00-3:00 pm, or by appointment
    • Class time: M-W-F, 9:30 - 10:30
    • First class: Wednesday, Sept. 5, 2018
    • Place: Chase Building, Seminar Room (Room 227)

  • Textbook:
      Algebraic Number Theory and Fermat's Last Theorem, 3rd Ed. (Not required)
      by Ian Stewart and David Tall
      A K Peters, 2001
      A copy of this book will be on reserve in the Killan Library

      A set of course notes will also be made available in class (required).

  • Prerequisites:
      MATH 3070.03, or instructor's permission

  • Course content
    The purpose of the course is to give an introduction to some advanced topics of number theory, especially algebraic number theory, guided by "Fermat's Last Theorem", one of the most famous (no longer unsolved) problems in mathematics.
      1. Introduction
      2. Algebraic Background
      3. Algebraic Numbers
      4. Quadratic and Cyclotomic Fields
      5. Factorization into Irreducibles
      6. Ideals
      7. Class Groups and Class Numbers
      8. Fermat's Last Theorem

  • Evaluation:
    • Weekly assignments: 30%
    • Take-home midterm: 30%
    • Final exam: 40%

  • Difference between MATH 4070 and MATH 5070:
    The course content will be the same for both undergraduate and graduate students. However, half of the questions on the take-home and a quarter of the questions of the final exam will be different, and more challenging, for students registered in MATH 5070.

  • Conversion to letter grades (Dalhousie common grade scale):
    90-100 A+    77-79 B+    65-69 C+    50-54 D
    85-89 A 73-76 B 60-64 C 0-49 F
    80-84A-  70-72 B- 55-59 C-

Last update: September 18, 2018
Created and maintained by Karl Dilcher