Math 406 -- Introduction to Number Theory

Course guide:

Text: Underwood Dudley, Elementary Number Theory, Second edition, Dover 2008.

Content:

This is a first course in elementary number theory. Although the mathematical prerequisites for the course are few, there will be many proofs done in class, and you will also need to prove results in the homework and provide (simpler) proofs on exams. The core topics covered are divisibility, prime numbers, congruences, the theorems of Fermat, Euler, and Wilson, primitive roots for primes and the law of quadratic reciprocity.

Homework:

The best and only way to learn mathematics is to do mathematics! Your weekly homework assignments are therefore the most important part of this course. Homework will be assigned on Thursday and is due in class on the Thursday of the following week. I urge you to hand in all of your assignments on time - however my policy is to allow up to TWO late homework assignments per student (any further late assignments will not be graded). You may discuss the problems with others if you wish, but whatever you turn in should be written up on your own. The extra credit problems are optional - they can improve your grade, but you do not need to solve them to do well in the course. People looking for a challenge are encouraged to attempt them! Our homework grader is TBA, and his email is TBA. Please contact him with any questions you may have about the homework grading and solutions to the problems.

Exams:

We will have three exams during the course, two midterms and a final exam. The two midterms will be held in class from 11:00 - 12:15 on the following dates: Thursday, October 16 and Thursday, November 20. The final exam has been scheduled for Monday, December 15, 10:30 -- 12:30. Make-up exams will only be given for compelling and documented reasons.

Grading Policy:

The course grade will be determined by adding your two midterm test scores (20%+20%) to your final exam score (30%) and your homework total (30%). Participating in class and working on extra credit problems is encouraged and will help to improve your grade.

READ THIS:

University of Maryland course related policies. Includes a discussion of academic integrity, the honor pledge, and accommodations for students with disabilities.

Calculators:

No calculators are required for this course, and they will not be allowed in class during exams.

Office Hours:

I will be available at these times specifically to help you: Tuesdays from 1:00 - 2:00 (in person) and Wednesdays from 10:00 - 11:00 (on Zoom). Feel free to come by my office and talk at any time, either by chance or by appointment.

Resources:

The testbank archive of past exams has examples of tests from past years, and is a good source of problems.