311.265 (17S) Ausgewählte Kapitel der Diskreten Mathematik (Algebraic Methods in Discrete Optimization)
Überblick
- Lehrende/r
- LV-Titel englisch Selectied Topics in Discrete Mathematics
- LV-Art Vorlesung-Übung (prüfungsimmanente LV )
- Semesterstunde/n 3.0
- ECTS-Anrechnungspunkte 5.0
- Anmeldungen 12 (25 max.)
- Organisationseinheit
- Unterrichtssprache Englisch
- LV-Beginn 01.03.2017
- 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 modications.
- Collaborations with the professor are welcome!
Zeit und Ort
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 inkl. Einsatz von eLearning-Tools
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 final (20%).
Beurteilungsschema
Note BenotungsschemaPosition 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)
-
Ausgewählte Kapitel der Diskreten Mathematik (
3.0h VU / 5.0 ECTS)
-
Fach: Diskrete Mathematik
(Wahlfach)
- 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)
-
Ausgewählte Kapitel der Diskreten Mathematik (
3.0h VU / 5.0 ECTS)
-
Fach: Diskrete Mathematik
(Wahlfach)