Office Hours: - 1:30-3:00 Tuesday, Wednesday; 9:00 – 10:00, 2:00 - 3:00 Thursday; or by appointment

Course Goals: Number theory has a rich history in mathematics and many of the most famous mathematical problems have come from number theory. In this course an introduction to the fundamentals of the subject will be provided along with a historical perspective. This course will include a substantial amount of proof-writing, so it will be expected that students spend plenty of time constructing, writing, and revising quality proofs. Your progress in proof-writing throughout the semester is a primary goal of this course. Modern applications, such as public-key cryptography, will also be included.

Topics Covered: Topics will include, but not necessarily be limited to, divisibility theory in the integers, primes and their distributions, theory of congruences, theorems of Fermat, Little, and Wilson, number theoretic functions, and other topics as time permits such as Fibonacci numbers, Quadratic Reciprocity, Continued Fractions, Primality Testing and Factorization, ect.

Tests and Homework: There will be 2 tests and a final exam. No make-up tests will be given. Certain homework problems will be collected and graded. Others will be presented by students in class. The time and care spent on the homework problems usually determines how a student performs in this course. Number theory, like all other mathematics courses, cannot be learned without working through numerous homework problems, examples, and proofs from class and/or the textbook.

Projects: Students will also be required to complete several projects throughout the semester. These will be longer than standard homework assignments and must be typed. Not all students will be required to complete the same projects. Examples may include some computer activities, public-key cryptography applications, etc. These will be described in more detail during the semester.

Grading: The final exam will count 20%, the tests will count 12.5% each, the homework average will count 35%, and the projects will count 20%. 90% guarantees an A, 80% a B, 70% a C, and 60% a D. If these cutoffs are adjusted downward it will be done at the end of the semester.

** For graduate credit students will be required to write a portfolio consisting of a select number of proofs and examples from the homework. The portfolio must be a comprehensive overview of major topics from this course. In addition, it must reflect and solidify the underlying connections between the topics presented. The portfolio will count as one half of the student's homework grade.

Honor System: You must follow the University Policy on Academic Integrity. You are free to work with others on the (un-graded) homework assignments.