312.258 (17W) Mathematische Analyse von Algorithmen
Überblick
- Lehrende/r
- LV-Titel englisch Mathematical Analysis of Algorithms
- LV-Art Vorlesung
- Semesterstunde/n 2.0
- ECTS-Anrechnungspunkte 4.0
- Anmeldungen 9
- Organisationseinheit
- Unterrichtssprache Englisch
- mögliche Sprache/n der Leistungserbringung Deutsch , Englisch
- LV-Beginn 02.10.2017
- eLearning zum Moodle-Kurs
-
Anmerkungen
People who analyze algorithms have double happiness. First of all they experience the sheer beauty of elegant mathematical patterns that surround elegant computational procedures. Then they receive a practical payoff when their theories make it possible to get other jobs done more quickly and more economically. D. E. Knuth
Zeit und Ort
LV-Beschreibung
Intendierte Lernergebnisse
After successful completion of this course, students will know methods and correspondings theorems in (analytic) combinatorics as listed in the contents section below. They will understand and will be able to prove these theorems and will be able to apply these methods to the analysis of algorithms.
Lehrmethodik inkl. Einsatz von eLearning-Tools
Lecture with an emphasis on examples concerning the analysis of algorithms.
Inhalt/e
- Introduction. Example: Sorting algorithms.
- Generating Functions (Review and Advanced Techniques)
- Mellin Transform and Mellin-Perron Summation
- Singularity Analysis
- Saddle-Point Method
- Limiting Distributions (Overview)
Erwartete Vorkenntnisse
Basic knowledge on generating functions is useful, a review will be given at the beginning of the course. Complex analysis is an important tool.
Literatur
- R. Sedgewick and Ph. Flajolet, An Introduction to the Analysis of Algorithms (Book Site, Lecture Videos)
- Ph. Flajolet and R. Sedgewick, Analytic Combinatorics (Book Site, PDF Version, Lecture Videos)
- Ph. Flajolet, X. Gourdon, Ph. Dumas, Mellin Transforms and Aysmptotics: Harmonic Sums
Prüfungsinformationen
Prüfungsmethode/n
Oral exam
Prüfungsinhalt/e
Contents of the lecture.
Beurteilungskriterien/-maßstäbe
- The grade is obtained by a single oral exam (45 minutes), until November 30th, 2018.
- For the oral exam, you may bring copies of the slides of the lecture (containing formulae) and additional cheat-sheets containing formulae. How much and what you look up influences the grade.
Beurteilungsschema
Note BenotungsschemaPosition im Curriculum
- Masterstudium Technische Mathematik
(SKZ: 401, Version: 13W.1)
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Fach: Diskrete Mathematik
(Wahlfach)
-
Mathematische Analyse von Algorithmen (
2.0h VO / 4.0 ECTS)
- 312.258 Mathematische Analyse von Algorithmen (2.0h VO / 4.0 ECTS)
-
Mathematische Analyse von Algorithmen (
2.0h VO / 4.0 ECTS)
-
Fach: Diskrete Mathematik
(Wahlfach)