312.258 (20W) Mathematical Analysis of Algorithms
Überblick
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- Lehrende/r
- LV-Titel englisch Mathematical Analysis of Algorithms
- LV-Art Vorlesung
- LV-Modell Präsenzlehrveranstaltung
- Semesterstunde/n 2.0
- ECTS-Anrechnungspunkte 4.0
- Anmeldungen 12
- Organisationseinheit
- Unterrichtssprache Englisch
- mögliche Sprache/n der Leistungserbringung Englisch
- LV-Beginn 06.10.2020
- eLearning zum Moodle-Kurs
Zeit und Ort
LV-Beschreibung
Intendierte Lernergebnisse
After successful completion of this course, students will know methods and corresponding 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
Lecture with an emphasis on examples concerning the analysis of algorithms.
Inhalt/e
This course discusses tools which are useful in determining the asymptotic behaviour of functions. As an example, the factorial function n! can be approximated by sqrt(2 pi n)*(n/e)^n. These tools are very useful in combinatorial analysis, for example in determining an approximation for large coefficients of a given generating function which are in turn used to analyse algorithms.
Contents:
- 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
Geänderte Prüfungsinformationen (COVID-19 Ausnahmeregelung)
If necessary, oral exams will be held via video conference.
Prüfungsmethode/n
Oral exam
Prüfungsinhalt/e
Contents of the lectures.
Beurteilungskriterien/-maßstäbe
- The grade is obtained by a single oral exam (45 minutes), until November 30th, 2021.
- 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 Mathematics
(SKZ: 401, Version: 18W.1)
-
Fach: Discrete Mathematics
(Wahlfach)
-
6.5 Mathematical Analysis of Algorithms (
2.0h VO / 4.0 ECTS)
- 312.258 Mathematical Analysis of Algorithms (2.0h VO / 4.0 ECTS)
-
6.5 Mathematical Analysis of Algorithms (
2.0h VO / 4.0 ECTS)
-
Fach: Discrete Mathematics
(Wahlfach)
- Masterstudium Mathematics
(SKZ: 401, Version: 18W.1)
-
Fach: Applied Mathematics
(Wahlfach)
-
Lehrveranstaltungen aus den Vertiefungsfächern (
0.0h XX / 12.0 ECTS)
- 312.258 Mathematical Analysis of Algorithms (2.0h VO / 4.0 ECTS)
-
Lehrveranstaltungen aus den Vertiefungsfächern (
0.0h XX / 12.0 ECTS)
-
Fach: Applied Mathematics
(Wahlfach)