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Shanghai Jiao Tong University

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....

立即開始，按照自己的計劃學習。

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完成時間大約為48 小時

字幕：English

立即開始，按照自己的計劃學習。

根據您的日程表重置截止日期。

完成時間大約為48 小時

字幕：English

章節

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....

2 個視頻（共 27 分鐘）, 3 個測驗

Sets, relations, and functions30分鐘

章節

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....

2 個視頻（共 28 分鐘）, 2 個測驗

Partial orders, maximal and minimal elements, chains, antichains分鐘

章節

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 個視頻（共 35 分鐘）, 2 個測驗

Evaluating Simple Sums8分鐘

Pascal's Triangle14分鐘

Counting Basic Objects分鐘

章節

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 個視頻（共 55 分鐘）, 3 個測驗

Estimating the Binomial Coefficient22分鐘

Excursion to Discrete Probability: Computing the Expected Minimum of k Random Elements from {1,...,n}18分鐘

An Eagle's View of Pascal's Triangle8分鐘

3.6

創建者 NP•Oct 23rd 2017

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

創建者 MY•Aug 9th 2017

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

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....

When will I have access to the lectures and assignments?

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.

What will I get if I purchase the Certificate?

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.

What is the refund policy?

Is financial aid available?

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