About this Course
3.5
75 ratings
26 reviews
100% online

100% online

Start instantly and learn at your own schedule.
Flexible deadlines

Flexible deadlines

Reset deadlines in accordance to your schedule.
Intermediate Level

Intermediate Level

Hours to complete

Approx. 41 hours to complete

Suggested: 11 weeks of study, 3-5 hours per week....
Available languages

English

Subtitles: English
100% online

100% online

Start instantly and learn at your own schedule.
Flexible deadlines

Flexible deadlines

Reset deadlines in accordance to your schedule.
Intermediate Level

Intermediate Level

Hours to complete

Approx. 41 hours to complete

Suggested: 11 weeks of study, 3-5 hours per week....
Available languages

English

Subtitles: English

Syllabus - What you will learn from this course

Week
1
Hours to complete
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....
Reading
2 videos (Total 27 min), 3 quizzes
Video2 videos
Sets, Relations, Functions10m
Quiz1 practice exercise
Sets, relations, and functions30m
Week
2
Hours to complete
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....
Reading
2 videos (Total 28 min), 2 quizzes
Video2 videos
Mirsky's and Dilworth's Theorem14m
Quiz1 practice exercise
Partial orders, maximal and minimal elements, chains, antichainsm
Week
3
Hours to complete
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....
Reading
3 videos (Total 35 min), 2 quizzes
Video3 videos
Evaluating Simple Sums8m
Pascal's Triangle14m
Quiz1 practice exercise
Counting Basic Objectsm
Week
4
Hours to complete
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....
Reading
3 videos (Total 55 min), 3 quizzes
Video3 videos
Estimating the Binomial Coefficient22m
Excursion to Discrete Probability: Computing the Expected Minimum of k Random Elements from {1,...,n}18m
Quiz1 practice exercise
An Eagle's View of Pascal's Triangle8m
3.5
26 ReviewsChevron Right

Top Reviews

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

  • Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

  • 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.

More questions? Visit the Learner Help Center.