MS-E199501 - Matroid Theory, Lectures, 1.3.2022-8.4.2022

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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

Credits: 5

Schedule: 01.03.2022 - 08.04.2022

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Camilla Hollanti, Diego Villamizar Rubiano

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

Lecturer: Diego Villamizar Rubiano, diego.villamizarrubiano@aalto.fi

Responsible teacher: Camilla Hollanti, camilla.hollanti@aalto.fi

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

  • applies in this implementation

    The concept of linear (in)dependence is one of the key concepts in linear algebra and its applications. In this course we will introduce the theory of Matroids, a combinatorial structure that captures the essence of linear (in)dependence. We will study different ways of looking at these objects, where do they come from, their properties, and some of the fundamental theorems, problems, and conjectures of the theory.

    We will focus on the combinatorial and algebraic point of view of the theory of matroids and the more recent geometrical flavor will be hinted at. Connections to other areas of mathematics, such as coding theory, graph theory, and combinatorial optimization will be given. Using these connections, we will see how some classical results (problems) in these areas are more suitably seen as results (problems) on Matroids.

    Prerequisites: Linear algebra and some mathematical maturity (i.e., some previous exposure to (dis)proving abstract mathematical claims).

    Students at any level of studies can take this course, provided that the prerequisites are met.

    The course can be found in Sisu and MyCourses soon, and the format (live/online) will be announced there closer to date.

    For more information, contact Diego at diego.villamizar@aalto.fi.

Assessment Methods and Criteria

  • applies in this implementation

    Evaluation criteria to be announced during the course. Grade scale 0-5.

DETAILS

Study Material

  • applies in this implementation

    Main references:

    Matroid theory, James Oxley.

    Matroid theory, D. J. A. Welsh.

Substitutes for Courses
Prerequisites

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

Aalto University Code of Academic Integrity and Handling Violations Thereof