University of Pittsburgh Math 1020 : Applied Elementary Number Theory : Fall 2017

Math 1020 : Applied Elementary Number Theory

Mon, Wed 4:00 - 5:15pm -- Allen Hall 103

Instructor. Dr. Marta Lewicka (office hours in Thackeray 408, Monday 5:30 - 6:30pm, or by appointment)
Textbook. George E. Andrews 'Number Theory'.
Prerequisites. This course is an introduction to number theory and some of its applications. Prerequisite is Math 0430: Introduction to Abstract Algebraic Systems. If you do not feel comfortable with the prerequisite material, please contact the instructor in the beginning of the course.
Grades. Your final grade depends on your performance on the final exam as well as on your total grade. Grades will be based on homework (30%), one midterm (30%) and the final exam (40%). There will be no make up midterm exams. If you miss the midterm exam for a *documented* medical reason, your grade on it will be the prorated grade of your final exam. Incompletes will almost never be given, and only for cases of extreme personal tragedy.
Homework. Weekly homework assignments will be collected at the beginning of the lecture every Monday. Late homework will not be accepted. There will be five problems assigned each week and you have to solve all of them, but only one problem (the same for the whole class) will be graded. The solution of the graded problem will be evaluated in the scale 0-5 points, taking into account the correctness, clarity and neatness of presentation. Solutions should be writen up independently.
Core topics.
1. Mathematical induction, integer representations and operations.
2. Primes and greates common divisors, Euclidean algorithm, Fundamental Theorem of Arithmetic, linear Diophantine equations.
3. Congruences and modular arithmetic, Fermat's and Euler's theorems, Wilson's theorem.
4. Multiplicative functions such as Euler's phi function, Mobius function and Mobius inversion.
5. Some applictions in cryptography, RSA, primitive roots, discrete logarithm and index arithmetic.
6. Quadratic residues and Gauss's quadratic reciprocity.

Calendar.

28 Aug (Mon): First Class
4 Sept (Mon): Labor Day -- no class
9 Oct (Mon): Fall Break -- no class
10 Oct (Tue): Monday class
8 Nov (Wed): Midterm
22 Nov (Wed): Thanksgiving recess -- no class
6 Dec (Wed): Last Class
Final Exam: to be determined by the University