### MS-E1110 - Number Theory D, 26.10.2020-02.12.2020

Please note! Course description is confirmed for two academic years (1.8.2018-31.7.2020), which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.

#### 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: 26.10.2020 - 02.12.2020

Teacher in charge (valid 01.08.2020-31.07.2022): Camilla Hollanti

Teacher in charge (applies in this implementation): Camilla Hollanti

Contact information for the course (applies in this implementation):

CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English

##### Content
• Valid 01.08.2020-31.07.2022:

integer factorization, primes, pseudo primes, modular arithmetics, squares and nonsquares in modular arithmetics, quadratic reciprocity, primititive roots, applications to cryptography.

##### Assessment Methods and Criteria
• Valid 01.08.2020-31.07.2022:

Lectures, homework, project work

• Valid 01.08.2020-31.07.2022:

16h lectures+12h exercise session (4h+2h / week) + self-study. Some of the scheduled lectures (in Oodi/MyCourses) and exercise sessions are used for project work.

#### DETAILS

##### Study Material
• Valid 01.08.2020-31.07.2022:

William Stein: Elementary Number Theory: Primes, Congruences, and Secrets
http://wstein.org/ent

##### Substitutes for Courses
• Valid 01.08.2020-31.07.2022:

Mat-1.3111, MS-C1110.

##### Prerequisites
• Valid 01.08.2020-31.07.2022:

High school mathematics. MS-A040X OR MS-C1080 is recommended.