课程信息
3.6
60 ratings
22 reviews
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....
Globe

100% 在线课程

立即开始,按照自己的计划学习。
Calendar

可灵活调整截止日期

根据您的日程表重置截止日期。
Intermediate Level

中级

Clock

建议:11 weeks of study, 3-5 hours per week.

完成时间大约为46 小时
Comment Dots

English

字幕:English
Globe

100% 在线课程

立即开始,按照自己的计划学习。
Calendar

可灵活调整截止日期

根据您的日程表重置截止日期。
Intermediate Level

中级

Clock

建议:11 weeks of study, 3-5 hours per week.

完成时间大约为46 小时
Comment Dots

English

字幕:English

教学大纲 - 您将从这门课程中学到什么

1

章节
Clock
完成时间为 5 小时

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 个视频(共 27 分钟), 3 个测验
Video2 个视频
Sets, Relations, Functions10分钟
Quiz1 个练习
Sets, relations, and functions30分钟

2

章节
Clock
完成时间为 4 小时

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 个视频(共 28 分钟), 2 个测验
Video2 个视频
Mirsky's and Dilworth's Theorem14分钟
Quiz1 个练习
Partial orders, maximal and minimal elements, chains, antichains分钟

3

章节
Clock
完成时间为 5 小时

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 个视频(共 35 分钟), 2 个测验
Video3 个视频
Evaluating Simple Sums8分钟
Pascal's Triangle14分钟
Quiz1 个练习
Counting Basic Objects分钟

4

章节
Clock
完成时间为 4 小时

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 个视频(共 55 分钟), 3 个测验
Video3 个视频
Estimating the Binomial Coefficient22分钟
Excursion to Discrete Probability: Computing the Expected Minimum of k Random Elements from {1,...,n}18分钟
Quiz1 个练习
An Eagle's View of Pascal's Triangle8分钟
3.6

热门审阅

创建者 NPOct 23rd 2017

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

创建者 MYAug 9th 2017

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

讲师

Dominik Scheder

Assistant Professor
The Department of Computer Science and Engineering

关于 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....

常见问题

  • 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.

还有其他问题吗?请访问 学生帮助中心