About this Course
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Intermediate Level

English

Subtitles: English

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Intermediate Level

English

Subtitles: English

Syllabus - What you will learn from this course

Week
1
5 hours to complete

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.

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2 videos (Total 27 min), 3 quizzes
1 practice exercise
Sets, relations, and functions1h 30m
Week
2
4 hours to complete

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.

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2 videos (Total 28 min), 2 quizzes
1 practice exercise
Partial orders, maximal and minimal elements, chains, antichains2h
Week
3
5 hours to complete

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.

...
3 videos (Total 35 min), 2 quizzes
1 practice exercise
Counting Basic Objects2h
Week
4
4 hours to complete

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.

...
3 videos (Total 55 min), 3 quizzes
3.5
32 ReviewsChevron Right

Top reviews from Discrete Mathematics

By NPOct 23rd 2017

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

By AGDec 5th 2018

This course is good to comprehend relation, function and combinations.

Instructor

Avatar

Dominik Scheder

Assistant Professor
The Department of Computer Science and Engineering

About 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....

Frequently Asked Questions

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  • When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

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