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Introduction to Number Theory

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Lecturer of the course: Michael Th. Rassias


Lecture:
Wednesday 15:00-17:00, HG F 5

First lecture: February 19, 2014.

Exam: May 28, 2014. Time: 15:15. Place: HG F 5. Duration: 90 minutes.

Description

This course will introduce some of the fundamental theorems and results of classical Number Theory.

The objective is for the students to obtain a foundational knowledge of elements of Number Theory through step-by-step proofs of classical theorems, as well as to sharpen theirs skills through problem-solving. The material of the course will be such that one can be initiated to the subject gradually and thus future study, possibly at a graduate level, will be made more natural.

Content

The course will start with basic notions, including the fundamental theorem of arithmetic, Euclid's theorem for the infinitude of primes, rational/irrational numbers and it will continue with the study of arithmetic functions, perfect numbers and Fermat numbers, congruences, quadratic residues, Dirichlet series and also aspects of the prime counting function and the Riemann zeta function. During the class, some special topics such as the proof of Bertrand's postulate will be presented as well.


Recommended Literature

T. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, New York, 1984.

G. H. Hardy and E. W. Wright, An Introduction to the Theory of Numbers, 5th edition, Clarendon Press, Oxford, 1979.

H. Iwaniec and E. Kowalski, Analytic Number Theory, A.M.S Colloq. Publ. 53, A.M.S, 2004.

M. Th. Rassias, Problem-Solving and Selected Topics in Number Theory, Springer, New York, 2011.

Prerequisites

Principles of Mathematical Analysis

 

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