Algebraic and Geometric Combinatorics, 7.5 Credits

Contents

The course gives general knowledge in the research area algebraic and geometric combinatorics. Specific knowledge is acquired by acquaintance with selected tools and methods within finite geometry, spectral graph theory, geometric graphtheory, group theory, and algebraic structures constructed from combinatorial objects.

Expected learning outcomes

For a passing grade, the student must be able to
Knowledge and understanding

• give a detailed account of the tools and method in algebraic and geometric combinatorics
• give a detailed account and exemplify how these tools and methods can be used within algebraic and geometriccombinatorics
• formulate selected theorems and results from algebraic and geometric combinatorics

Skills and abilities

• prove selected theorems in algebraic and geometric combinatorics
• use the tools and methods presented in the course to solve problems in algebraic and geometric combinatorics
• communicate mathematical arguments in both written and oral form

Judgement and approach

• determine the stringency of the mathematical arguments presented in the course
• show a critical approach regarding the use of mathematical tools and methods.

Required Knowledge

The course requires 90 ECTS including a course in Discrete Mathematics minimum 7,5 ECTS, and a course in Linear Algebra minimum 7,5 ECTS. Proficiency in English equivalent to the level required for basic eligibility for higher studies. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish to the level required for basic eligibility for higher studies.

Form of instruction

The teaching in this course consists of lectures, exercise classes and seminars.

Examination modes

The course is examined through written assignments and active seminar attendence. On either part, the following gradesare assigned: Fail (U), Pass (G) or Pass with distinction (VG). For the whole course, one of the following grades is assigned: Fail (U), Pass (G), Pass with distinction (VG). In order to receive the grade of Pass (G) for the whole course, the student must obtain grades G or VG on all parts of the assessment. In order to receive the grade of Pass with distinction(VG) for the whole course, the student must in addition obtain the grade VG on all examinable components.

A student who has been awarded a passing grade for the course cannot be reassessed for a higher grade. Students who do not pass a test or examination on the original date are given another date to retake the examination. A student who has sat two examinations for a course or a part of a course, without passing either examination, has the right to have anotherexaminer appointed, provided there are no specific reasons for not doing so (Chapter 6, Section 22, HEO). The request fora new examiner is made to the Head of the Department of Mathematics and Mathematical Statistics. Examinations basedon this course syllabus are guaranteed to be offered for two years after the date of the student's first registration for the course.

Examiners may decide to deviate from the modes of assessment in the course syllabus. Individual adaption of modes ofassessment must give due consideration to the student's needs. The adaption of modes of assessment must remainwithin the framework of the intended learning outcomes in the course syllabus. Students who require an adapted examination must submit a request to the department holding the course no later than 10 days before the examination.The examiner decides on the adaption of the examination, after which the student will be notified.

Credit transfer
All students have the right to have their previous education or equivalent, and their working life experience evaluated for possible consideration in the corresponding education at Umeå university. Application forms should be addressed to Student services/Degree evaluation office. More information regarding credit transfer can be found on the student webpages of Umeå university, http://www.student.umu.se, and in the Higher Education Ordinance (chapter 6). If denied, theapplication can be appealed (as per the Higher Education Ordinance, chapter 12) to Överklagandenämnden förhögskolan. This includes partially denied applications