Syllabus: Chapter 1 (Logic and Proofs): 1.1, 1.3, 1.4 -1.6  , Chapter 2 (Sets and Functions), Chapter 5 (Induction): 5.1-5.3, Chapter 9 (Relations)

The Zermelo Fraenkel Axioms; Equivalence of Sets in form of  my notes.

Grading: Midterm is worth  40%, the final is worth 40% and Homework is worth 20%.

For turning in Homework, students need to get the software program Scientific Notebook.

Instructor's lecture notes. The reference book will be "Beginning Number Theory" by Neville Robbins, second Edition.

Number theory is a subject that has interested people for thousand of years. This course is a one-semester long graduate course on number theory. Topics to be covered include divisibility and factorization, linear Diophantine equations, congruences, applications of congruences, solving linear congruences, primes of special forms, the Chinese Remainder Theorem, multiplicative orders, the Euler function, primitive roots, quadratic congruences, and introduction to cryptography . There'll be no specific prerequisites beyond basic algebra and some ability in reading and writing mathematical proofs.

The purpose of this course is to acquire/improve programming skills in order to tackle mathematical problems that require computations (e.g. numerically solving ODEs, PDEs, SDEs). The emphasis is on converting an algorithm or theoretical result into a good code, and presenting the results in a convenient format.

Students can use a language they are familiar with or, if needed, learn a new one. Some material will be posted on-line. After presenting the basic principles, students will work on projects. During the face-to-face meetings we will discuss and debug code.

The course is suitable both for students who have very little/no programming experience and more advanced students. The individual projects will be tailored to each student's level. Alternatively, students can work on projects that are relevant to their own research.