LEARNING OUTCOMES
- The student understands the basic concepts of number theory and is able to perform modular arithmetics.
- The student understands the quadratic reciprocity law, one of the most important theorems in Number Theory.
- The student is familiar with some applications of Number Theory in Cryptography.
Credits: 5
Schedule: 21.10.2024 - 27.11.2024
Teacher in charge (valid for whole curriculum period):
Teacher in charge (applies in this implementation): Camilla Hollanti
Contact information for the course (applies in this implementation):
CEFR level (valid for whole curriculum period):
Language of instruction and studies (applies in this implementation):
Teaching language: English. Languages of study attainment: English
CONTENT, ASSESSMENT AND WORKLOAD
Content
valid for whole curriculum period:
Integer factorization, primes, pseudo primes, modular arithmetics, squares and nonsquares in modular arithmetics, quadratic reciprocity, primititive roots, continued fractions, applications to cryptography. Some of these topics are covered in the lecture program, some in the student projects.
Assessment Methods and Criteria
valid for whole curriculum period:
Homework, project work.
Workload
valid for whole curriculum period:
Lectures, exercises, homework, project work.
DETAILS
Study Material
valid for whole curriculum period:
William Stein: Elementary Number Theory: Primes, Congruences, and Secrets
http://wstein.org/ent
Substitutes for Courses
valid for whole curriculum period:
Prerequisites
valid for whole curriculum period:
FURTHER INFORMATION
Further Information
valid for whole curriculum period:
Teaching Language: English
Teaching Period: 2024-2025 Autumn II
2025-2026 Autumn II