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Dalhousie University

MATH 3070

Theory of Numbers

Course Information, Fall 2008

**The Final Exam Schedule is available here. The exam will be on Friday December 5 at 3:30 PM.**

Here is a list of some practice problems. Note that it is not an exhaustive accounting of examinable topics, but is only intended to give extra practice on __some__ of the key ideas and theorems covered in the course.
__General Information:__

Instructor: Dr. O-Yeat Chan

E-mail address: math@oyeat.com

Course website: http://www.oyeat.com/courses/math3070/

Office: Chase 251

Office hours: Wed 1400-1530 / Thurs 1430-1630 / By appointment

Office phone: 494-3896

Class hours: Tues / Thurs 1305-1425

Class meets at: LSC-Psych P5208

Text: James Tattersall, *Elementary Number Theory in Nine Chapters, 2nd ed.* Cambridge University Press,
ISBN 0-521-61524-0.

Important information about the course, as well as any updates, will be posted to the website.
__Course Description:__

Math 3070 is intended to be a first course in the theory of numbers, serving as an introduction to the subject. In this course, we will discuss the major theorems in elementary number theory and examine the diversity of problems in the field. It is expected that you are familiar with basic proof techniques such as mathematical induction. Knowledge of calculus is an asset but not required.
__Syllabus:__

We will cover the following topics
- Primes, divisibility, gcd, and the Euclidean algorithm
- Congruences, modular arithmetic, and the Chinese Remainder Theorem
- Wilson's Theorem, Fermat's little Theorem, and Euler's Generalization
- Higher order congruences and primitive roots, quadratic reciprocity
- Cryptography, primality testing, and factoring
- Continued fractions and Pell's equation
- Other topics of interest: partitions, analytic number theory, summation techniques, etc.

__Grading Policy:__

The course grade will be determined as follows:

Homework | 15% |

Midterms | 25% x 2 |

Final exam | 35% |

**Total ** | 100% |

Your final grade will be determined using the following grading scale (slightly modified from the default Faculty of Science conversion scheme):

**Score** | 90-100 | 85-89.9 | 80-84.9 | 76-79.9 | 72-75.9 | 68-71.9 | 65-67.9 | 62-64.9 | 58-61.9 | 50-57.9 | below 50 |

**Grade** | A+ | A | A- | B+ | B | B- | C+ | C | C- | D | F |

__Homework:__

Homework will be assigned weekly and will be worth 15% of the course grade. The lowest homework score will be dropped.

Homework 1 is due Tuesday September 16.
Solutions

Homework 2 is due Thursday September 25.
Solutions

Homework 3 is due Thursday October 2.
Solutions

Homework 4 is due Thursday October 23.
Solutions

Homework 5 is due Thursday October 30.
Solutions

Homework 6 is due Thursday November 27.
Solutions

__Midterms:__

There will be two midterm exams worth 25% each, to be given in class on Tuesdays October 7 and November 4. There will be no make-up exams except in very exceptional cases.

Solutions to Midterm 1.

Solutions to Midterm 2.
__The Final Exam:__

The final examination will be worth 35% of the course grade and will cover everything in the course. It will be held on Friday December 5 at 3:30 PM. There will be no make-up exams except in very exceptional cases. If your final exam score is higher than your lowest midterm score, the final exam score will replace that midterm score in the calculation of your final grade.
__Getting Extra Help:__

You are always welcome to stop by my office during the day or make an appointment to see me.
I can also be reached by e-mail at math@oyeat.com. I will try to respond to your questions within 24-48 hours.
__Students with Disabilities:__

Students with disabilities should register as quickly as possible at Student Accessibility Services if they want to receive academic accommodations. To do so please phone 494-2836, e-mail disabilities@dal.ca, or drop in at the Killam, G28.