Über diesen Kurs

14,629 kürzliche Aufrufe
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100 % online
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Stufe „Mittel“
Ca. 111 Stunden zum Abschließen
Englisch
Untertitel: Englisch, Arabischer Raum
Zertifikat zur Vorlage
Erhalten Sie nach Abschluss ein Zertifikat
100 % online
Beginnen Sie sofort und lernen Sie in Ihrem eigenen Tempo.
Flexible Fristen
Setzen Sie Fristen gemäß Ihrem Zeitplan zurück.
Stufe „Mittel“
Ca. 111 Stunden zum Abschließen
Englisch
Untertitel: Englisch, Arabischer Raum

von

National Research University Higher School of Economics-Logo

National Research University Higher School of Economics

Lehrplan - Was Sie in diesem Kurs lernen werden

Woche
1

Woche 1

11 Stunden zum Abschließen

Introduction

11 Stunden zum Abschließen
2 Videos (Gesamt 9 min), 5 Lektüren
2 Videos
Introduction7m
5 Lektüren
About the University10m
Course Overview10m
Grading and Logistics10m
Suggested Readings10h
About the Instructor10m
11 Stunden zum Abschließen

Permutations and binomial coefficients

11 Stunden zum Abschließen
7 Videos (Gesamt 78 min)
7 Videos
Permutations10m
k-permutations8m
Merry-go-rounds and Fermat’s little theorem 18m
Merry-go-rounds and Fermat’s little theorem 211m
Binomial coefficients14m
The Pascal triangle16m
1 praktische Übung
Quiz 210h
Woche
2

Woche 2

12 Stunden zum Abschließen

Binomial coefficients, continued. Inclusion and exclusion formula.

12 Stunden zum Abschließen
7 Videos (Gesamt 87 min)
7 Videos
Balls in boxes and multisets 110m
Balls in boxes and multisets 26m
Integer compositions11m
Principle of inclusion and exclusion: two examples12m
Principle of inclusion and exclusion: general statement9m
The derangement problem19m
1 praktische Übung
Quiz 310h
Woche
3

Woche 3

14 Stunden zum Abschließen

Linear recurrences. The Fibonacci sequence

14 Stunden zum Abschließen
11 Videos (Gesamt 105 min), 1 Lektüre, 1 Quiz
11 Videos
Fibonacci numbers and the Pascal triangle7m
Domino tilings8m
Vending machine problem10m
Linear recurrence relations: definition7m
The characteristic equation8m
Linear recurrence relations of order 211m
The Binet formula11m
Sidebar: the golden ratio9m
Linear recurrence relations of arbitrary order8m
The case of roots with multiplicities12m
1 Lektüre
Spoilers! Solutions for quizzes 2, 3, and 4.2h
1 praktische Übung
Quiz 410h
Woche
4

Woche 4

14 Stunden zum Abschließen

A nonlinear recurrence: many faces of Catalan numbers

14 Stunden zum Abschließen
7 Videos (Gesamt 73 min), 2 Lektüren, 1 Quiz
7 Videos
Recurrence relation for triangulations11m
The cashier problem9m
Dyck paths5m
Recurrence relations for Dyck paths9m
Reflection trick and a formula for Catalan numbers12m
Binary trees15m
2 Lektüren
Solutions10m
!!!Solutions for the older version of the Middterm10m

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