MS-E1110 - Number Theory D, Lecture, 1.11.2021-8.12.2021

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Please note! Course description is confirmed for two academic years, 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: 01.11.2021 - 08.12.2021

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, applications to cryptography.

Assessment Methods and Criteria

  • valid for whole curriculum period:

     Lectures, homework, project work

Workload

  • valid for whole curriculum period:

    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 for whole curriculum period:

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

     

Substitutes for Courses
Prerequisites

FURTHER INFORMATION

Further Information

  • valid for whole curriculum period:

    Teaching Period:

    2020-2021 Autumn II

    2021-2022 Autumn II

    Course Homepage: https://mycourses.aalto.fi/course/search.php?search=MS-E1110

    Registration for Courses: In the academic year 2021-2022, registration for courses will take place on Sisu (sisu.aalto.fi) instead of WebOodi.

Rules of Conduct - Students´ Rights and Responsibilities (in force from 1 August 2020)

Aalto University Code of Academic Integrity and Handling Violations Thereof