401-3050-64L  Student Seminar in Combinatorics: Mathematical Software

SemesterAutumn Semester 2014
LecturersK. Fukuda
Periodicityyearly recurring course
Language of instructionEnglish


AbstractIn this seminar we study how computer can be used to do rigorous mathematics. More explicitly we will have case studies on how computer programs and systems have been developed and used for mathematics. Since the computer runs on finite resources. writing rigorous mathematical programs is essentially combinatorial mathematics itself.
ObjectiveThe main objective is to learn how rigorous mathematical tools can be made for the purpose of doing mathematics with help of computers.
ContentIn this seminar we study how computer can be used to do rigorous mathematics. More explicitly we will have case studies on how computer programs and systems have been developed and used for mathematics. Since the computer runs on finite resources. writing rigorous mathematical programs is essentially combinatorial mathematics itself.

There are two different types of mathematical software:
(1) mathematical software systems, such as maple, mathematica and sage, which are general platforms to do mathematics with computers,
(2) mathematical software tools (including callable libraries), targeted to deal with a special class of mathematical disciplines or problems, such as linear algebra, graphs, combinatorics, polynomial systems, optimization, polyhedra, geometry, number theory, etc.

For our study, we mainly focus on open-source software tools because without source codes it is difficult to learn how to write rigorous mathematical tools.

Each student is expected to select one mathematical software tool. The presentation is first to review the basic mathematical concepts and theory that are addressed by the solfware tool. Then he/she gives how the tool can be used to solve or deal with concrete examples with this tool. Most importantly, each presenter understands what it takes to write the software tool.
Lecture notesWe will have a list of recommended papers for presentation. Typically these papers are available from the website of International Congress of Mathematical Software:
http://www.math.kobe-u.ac.jp/icms2010/
http://voronoi.hanyang.ac.kr/icms2014/
and proceedings:
http://link.springer.com/book/10.1007%2F978-3-642-15582-6 .
LiteratureHere is a document containing articles and scheduling for the seminar:
http://www.inf.ethz.ch/personal/fukudak/lect/mssemi/msseminar2014_ref.pdf (last update on 2014-10-17). It will get updated as the seminar progresses. Please check the revised dates frequently.

You can find students' presentation files in http://www.inf.ethz.ch/personal/fukudak/lect/mssemi/presentation .

Final reports:
http://www.inf.ethz.ch/personal/fukudak/lect/mssemi/reports .
Prerequisites / NoticeGood knowledge of mathematics and basic programming languages