À propos de ce cours
3.6
65 notes
22 avis
Discrete mathematics forms the mathematical foundation of computer and information science. It is also a fascinating subject in itself. Learners will become familiar with a broad range of mathematical objects like sets, functions, relations, graphs, that are omnipresent in computer science. Perhaps more importantly, they will reach a certain level of mathematical maturity - being able to understand formal statements and their proofs; coming up with rigorous proofs themselves; and coming up with interesting results. This course attempts to be rigorous without being overly formal. This means, for every concept we introduce we will show at least one interesting and non-trivial result and give a full proof. However, we will do so without too much formal notation, employing examples and figures whenever possible. The main topics of this course are (1) sets, functions, relations, (2) enumerative combinatorics, (3) graph theory, (4) network flow and matchings. It does not cover modular arithmetic, algebra, and logic, since these topics have a slightly different flavor and because there are already several courses on Coursera specifically on these topics....
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Intermediate Level

Niveau intermédiaire

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Approx. 47 hours to complete

Recommandé : 11 weeks of study, 3-5 hours per week....
Comment Dots

English

Sous-titres : English...
Globe

Cours en ligne à 100 %

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.
Calendar

Dates limites flexibles

Réinitialisez les dates limites selon votre disponibilité.
Intermediate Level

Niveau intermédiaire

Clock

Approx. 47 hours to complete

Recommandé : 11 weeks of study, 3-5 hours per week....
Comment Dots

English

Sous-titres : English...

Programme du cours : ce que vous apprendrez dans ce cours

Week
1
Clock
5 heures pour terminer

Introduction - Basic Objects in Discrete Mathematics

This module gives the learner a first impression of what discrete mathematics is about, and in which ways its "flavor" differs from other fields of mathematics. It introduces basic objects like sets, relations, functions, which form the foundation of discrete mathematics....
Reading
2 vidéos (Total 27 min), 3 quiz
Video2 vidéos
Sets, Relations, Functions10 min
Quiz1 exercice pour s'entraîner
Sets, relations, and functions30 min
Week
2
Clock
4 heures pour terminer

Partial Orders

Even without knowing, the learner has seen some orderings in the past. Numbers are ordered by <=. Integers can be partially ordered by the "divisible by" relation. In genealogy, people are ordered by the "A is an ancestor of B" relation. This module formally introduces partial orders and proves some fundamental and non-trivial facts about them....
Reading
2 vidéos (Total 28 min), 2 quiz
Video2 vidéos
Mirsky's and Dilworth's Theorem14 min
Quiz1 exercice pour s'entraîner
Partial orders, maximal and minimal elements, chains, antichains min
Week
3
Clock
5 heures pour terminer

Enumerative Combinatorics

A big part of discrete mathematics is about counting things. A classic example asks how many different words can be obtained by re-ordering the letters in the word Mississippi. Counting problems of this flavor abound in discrete mathematics discrete probability and also in the analysis of algorithms....
Reading
3 vidéos (Total 35 min), 2 quiz
Video3 vidéos
Evaluating Simple Sums8 min
Pascal's Triangle14 min
Quiz1 exercice pour s'entraîner
Counting Basic Objects min
Week
4
Clock
4 heures pour terminer

The Binomial Coefficient

The binomial coefficient (n choose k) counts the number of ways to select k elements from a set of size n. It appears all the time in enumerative combinatorics. A good understanding of (n choose k) is also extremely helpful for analysis of algorithms....
Reading
3 vidéos (Total 55 min), 3 quiz
Video3 vidéos
Estimating the Binomial Coefficient22 min
Excursion to Discrete Probability: Computing the Expected Minimum of k Random Elements from {1,...,n}18 min
Quiz1 exercice pour s'entraîner
An Eagle's View of Pascal's Triangle8 min
3.6

Meilleurs avis

par NPOct 23rd 2017

Fantastic course. Fascinating material, presented at a reasonably fast pace, and some really challenging assignments.

par MYAug 9th 2017

Short course!! I use it to review my discrete math knowledge.

Enseignant

Dominik Scheder

Assistant Professor
The Department of Computer Science and Engineering

À propos de Shanghai Jiao Tong University

Shanghai Jiao Tong University, a leading research university located in Shanghai, China, has been regarded as the fastest developing university in the country for the last decade. With special strengths in engineering, science, medicine and business, it now offers a comprehensive range of disciplines in 27 schools with more than 41,000 enrolled students from more than one hundred countries....

Foire Aux Questions

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