311.265 (17S) Ausgewählte Kapitel der Diskreten Mathematik (Algebraic Methods in Discrete Optimization)

Sommersemester 2017

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Erster Termin der LV
01.03.2017 16:00 - 17:30 , N.2.01
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Überblick

Lehrende/r
LV-Titel englisch
Selectied Topics in Discrete Mathematics
LV-Art
Vorlesung-Übung (prüfungsimmanente LV )
Semesterstunde/n
3.0
ECTS-Anrechungspunkte
5.0
Anmeldungen
12 (25 max.)
Organisationseinheit
Unterrichtssprache
Englisch
LV-Beginn
02.03.2017
eLearning
zum Moodle-Kurs
Anmerkungen
  • Please forgive the professor her poor German!
  • Students should bring their laptops to each class meeting, as coding demonstrations can happen at any time.
  • Students are encouraged to work with classmates and others in learning the material.
  • Phones and other distracting devices should be off during class.
  • If you know you are going to be absent on a particular day, it is common courtesy to notify the instructor in advance, preferably by email.
  • Information in this Course Policy Statement is subject to minor modi cations.
  • Collaborations with the professor are welcome!

LV-Beschreibung

Intendierte Lernergebnisse

By the end of this course students will be able to:

(1) Model discrete combinatorial problems as systems of polynomial equations, and then solve via a wide range of algorithms.

(2) Construct a small library of computer algebra programs that will aid them in their future research.

Lehrmethodik

 Lecture, and coding demostrations.


Inhalt/e

Course Topics:

1. Background in ideals, varieties and algorithms

2. Grobner bases

3. Buchberger's critieron

4. Faugere's F4/F5 algorithm

5. Elimination ideals

6. Hilbert's Nullstellensatz

7. Stengle's Positivstellensatz

8. Border bases

9. Combinatorial problems as systems of polynomial equations

10. Hidden Field Equation cryptosystem and algebraic attacks

Literatur

An Introduction to Polynomial and Semi-Algebraic Optimization (Lasserre), 

Algebraic and Geometric Ideas in the Theory of Discrete Optimization (De Loera, Hemmecke, Köppe), 

Ideals, Varieties, and Algorithms (Cox, Little, O`Shea)

Prüfungsinformationen

Prüfungsmethode/n

There will be one take-home midterm, and a take-home final

Homework: There will be a six to eight homework sets in this course. Each homework set will include programming problems. You are welcome to work in groups of three or less. Collaboration and discussion are encouraged!

Prüfungsinhalt/e

All topics from the lecture.

Beurteilungskriterien/-maßstäbe

The grades will be based on homework (65%), midterm (15%) and fi nal (20%).

Beurteilungsschema

Note/Grade Benotungsschema

Position im Curriculum

  • Bachelorstudium Technische Mathematik (SKZ: 201, Version: 12W.2)
    • Fach: Diskrete Mathematik (Wahlfach)
      • Ausgewählte Kapitel der Diskreten Mathematik ( 3.0h VU / 5.0 ECTS)
        • 311.265 Ausgewählte Kapitel der Diskreten Mathematik (Algebraic Methods in Discrete Optimization) (3.0h VU / 5.0 ECTS)
  • Masterstudium Technische Mathematik (SKZ: 401, Version: 13W.1)
    • Fach: Diskrete Mathematik (Wahlfach)
      • Ausgewählte Kapitel der Diskreten Mathematik ( 3.0h VU / 5.0 ECTS)
        • 311.265 Ausgewählte Kapitel der Diskreten Mathematik (Algebraic Methods in Discrete Optimization) (3.0h VU / 5.0 ECTS)

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