MA 523 Basic Number Theory (Autumn 2018-19)

Instructor: Prof. Ronnie M. Sebastain

Course Name: Basic Number Theory ( MA 523 )

Course Type: Theory (Elective)

Credits: 6

Pre-requisites: MA 419 Basic Algebra

Course Content: 

Infinitude of primes, discussion of Dirichlet's theorem (without proof). Congruences, Fermat's little theorem, Wilson's theorem, linear congruences. Structure of units modulo n, Euler's phi function. Quadratic residues, law of quadratic reciprocity. Binary quadratics forms, equivalence, reduction, Fermat's two square theorem, Lagrange's four square theorem. Continued fractions, rational approximations, Liouville's theorem

Transcendence of e, Transcendence of π,  Meromorphic continuation of the Riemann Zeta function,  Proof of Dirichlet's Theorem on infinitely many primes in an arithmetic progression

Books:

A Concise Introduction to The Theory of Number by Alan Baker

Lectures:

Strict attendance for every lecture. Only Blackboard.

Assignments:

Each of us were tasked with making a presentation on the extra topics and also make a Latex document of it as well. They were challenging and very interesting mathematical results. This took some time.

Exams and Grading:

There were no exams or quizzes in this course when i took it

Online Useful Material:

Advanced Follow up Courses:

Pro-Tips:

Enjoy the classes. The professor cares that you learn new things and enjoy the classes than assessing you. Doesn't mean it is easy.

Personal Comments:

Respondent: Edwin Saji Uthuppan