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Dalhousie University
Mathematics and Statistics
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- 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:
Course Notes (available only after classes start)
Elementary Number Theory, 2nd Edition
Dover Publications, 2008, Paperback
Both will be available in the Dalhousie Bookstore
- Prerequisites:
- 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
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