Advanced Numbers Theory

Mode of Delivery

Face to Face

Prerequisites and Co-Requisites

None

Recommended Optional Programme Components

Algebra I, Algebra II

Course Contents

The series of primes, Farey series and a theorem of Minkowski, congruences and residues, general properties of congruences, Fermat’s theorem and its consequences, the representation of numbers by demicals, continued fractions, approximation of irrationals by rationals, some Diophantine equations, Quadratic fields, generating functions of arithmetical functions.

Weekly Schedule

1) Prime numbers and the series of primes
2) Farey series and a theorem of Minkowski
3) Congruences and residues
4) General properties of congruences
5) Fermat’s theorem and its consequences
6) The representation of numbers by demicals
7) Finite continued fractions
8) Midterm examination
9) Approximation of irrationals by rationals
10) Fermat’s last theorem and Diophantine equations
11) Algebraic fields, Complex Euclidean fields
12) Quadratic fields
13) Generating functions of arithmetical functions
14) Generating functions of arithmetical functions
15) Generating functions of other types
16) Generating functions of other types

Recommended or Required Reading

Planned Learning Activities and Teaching Methods

1) Lecture
2) Question-Answer
3) Discussion
4) Drill and Practice
5) Demonstration
6) Group Study
7) Self Study
8) Problem Solving
9) Project Based Learning

Assessment Methods and Criteria

Contribution of Semester Studies to Course Grade	50%
Number Percentage Semester Studies Midterm Examination 1 50% Quiz 1 50%
Contribution of Final Examination to Course Grade	50%
Total	100%

Language of Instruction

Turkish

Work Placement(s)

Not Required