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

Semester | Autumn Semester 2014 |

Lecturers | K. Fukuda |

Periodicity | yearly recurring course |

Language of instruction | English |

Abstract | In 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. |

Objective | The main objective is to learn how rigorous mathematical tools can be made for the purpose of doing mathematics with help of computers. |

Content | In 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 notes | We 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 . |

Literature | Here 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 / Notice | Good knowledge of mathematics and basic programming languages |