Dalhousie University
Mathematics and Statistics


C.F. Gauss
(1777-1855)
           

Theory of Numbers

MATH 3070

Dalhousie University
Department of Mathematics and Statistics
           
Pierre de Fermat
(1601-1665)

  • Basic Information:
    • Instructor: Karl Dilcher (dilcher@mathstat.dal.ca)
    • Office: Chase Building Room 325; ph.: 902-494-3784
    • Office hours: TBA, or by appointment.
    • Class time: Tues. & Thurs. 1:05 - 2:25 pm
    • First class: Tuesday, September 3, 2019
    • Classroom: LSC-208

  • Textbook:
      Required:
      Course Notes (available only after classes start)

      Recommended:
      Elementary Number Theory, 2nd Edition
      by Underwood Dudley
      Dover Publications, 2008, Paperback

      Both will be available in the Dalhousie Bookstore

  • Prerequisites:
      MATH 2040 or MATH 2135

  • Calendar Entry:
    The following topics are discussed: congruences and residues; elementary properties of congruences; linear congruences; theorems of Fermat, Euler and Wilson; Chinese remainder theorem; quadratic residues; law of quadratic reciprocity; Legendre, Jacobi and Kronecker symbols, arithmetic functions; algebraic fields; algebraic numbers and integers; uniqueness of factorization, definition and elementary properties of ideals; ideal classes and class number.

    (Note: The material starting with "properties of ideals" will not be covered).

  • Course content
    • 1. Introduction
    • 2. The Factorization of Integers
    • 3. Congruences
    • 4. Quadratic Residues
    • 5. Sums of Squares
    • 6. Continued Fractions
    • 7. Number Theoretic Function
    • 8. Algebraic and Transcendental Numbers
    • 9. Applications of Number Theory (if time allows)

  • Evaluation (subject to change until after classes have started):
    • Weekly assignments: 30%
    • Midterm test: 30%
    • Final exam: 40%

    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: August 16, 2019
Created and maintained by Karl Dilcher