Dalhousie University Mathematics and Statistics

C.F. Gauss
(1777-1855)

# 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 80-84 A- 70-72 B- 55-59 C-

Last update: August 16, 2019
Created and maintained by Karl Dilcher