課程信息
3.6
64 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....
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Intermediate Level

中級

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

完成時間大約為48 小時
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字幕:English
Globe

100% 在線課程

立即開始,按照自己的計劃學習。
Calendar

可靈活調整截止日期

根據您的日程表重置截止日期。
Intermediate Level

中級

Clock

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

完成時間大約為48 小時
Comment Dots

English

字幕:English

教學大綱 - 您將從這門課程中學到什麼

1

章節
Clock
完成時間為 5 小時

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 個視頻(共 27 分鐘), 3 個測驗
Video2 個視頻
Sets, Relations, Functions10分鐘
Quiz1 個練習
Sets, relations, and functions30分鐘

2

章節
Clock
完成時間為 4 小時

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 個視頻(共 28 分鐘), 2 個測驗
Video2 個視頻
Mirsky's and Dilworth's Theorem14分鐘
Quiz1 個練習
Partial orders, maximal and minimal elements, chains, antichains分鐘

3

章節
Clock
完成時間為 5 小時

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 個視頻(共 35 分鐘), 2 個測驗
Video3 個視頻
Evaluating Simple Sums8分鐘
Pascal's Triangle14分鐘
Quiz1 個練習
Counting Basic Objects分鐘

4

章節
Clock
完成時間為 4 小時

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 個視頻(共 55 分鐘), 3 個測驗
Video3 個視頻
Estimating the Binomial Coefficient22分鐘
Excursion to Discrete Probability: Computing the Expected Minimum of k Random Elements from {1,...,n}18分鐘
Quiz1 個練習
An Eagle's View of Pascal's Triangle8分鐘
3.6

熱門審閱

創建者 NPOct 23rd 2017

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

創建者 MYAug 9th 2017

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

講師

Dominik Scheder

Assistant Professor
The Department of Computer Science and Engineering

關於 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....

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