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教學大綱 - 您將從這門課程中學到什麼

1
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.

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2 個視頻 (總計 27 分鐘), 3 個測驗
1 個練習
Sets, relations, and functions1 小時 30 分
2
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.

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2 個視頻 (總計 28 分鐘), 2 個測驗
1 個練習
Partial orders, maximal and minimal elements, chains, antichains2小時
3
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.

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3 個視頻 (總計 35 分鐘), 2 個測驗
1 個練習
Counting Basic Objects2小時
4
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.

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3 個視頻 (總計 55 分鐘), 3 個測驗
3.5
32 個審閱Chevron Right

來自离散数学的熱門評論

創建者 NPOct 23rd 2017

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

創建者 AGDec 5th 2018

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

講師

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Dominik Scheder

Assistant Professor
The Department of Computer Science and Engineering

關於 上海交通大学

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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