MS-EV0006 - Geometry of Numbers, Lectures, 27.10.2022-13.4.2023

Guest access
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 Geometry of Numbers and is able
to perform approximations of linear forms in real numbers.
- The student understands the Minkowkski's convex body theorems, the most im-
portant theorems in Geometry of Numbers.
- The student is familiar how to prove classical Diophantine inequalities by Minkowski's
theorems.

Credits: 5

Schedule: 27.10.2022 - 13.04.2023

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Tapani Matala-aho, 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:

    Lattice, fundamental domain, determinant of lattice, convex set, compact set, con-
    vex body, linear transformation, Blichfeldt's theorem, Minkowski's convex body the-
    orems, linear form, approximation of one linear form, simultaneous approximations,
    Dirichlet's theorems.

DETAILS

Substitutes for Courses
Prerequisites

FURTHER INFORMATION

Further Information

  • valid for whole curriculum period:

    Lectures, exercises, homework, project work.

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

Aalto University Code of Academic Integrity and Handling Violations Thereof