課程信息

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學生職業成果

50%

完成這些課程後已開始新的職業生涯

40%

通過此課程獲得實實在在的工作福利
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完成後獲得證書
100% 在線
立即開始,按照自己的計劃學習。
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初級
完成時間大約為19 小時
英語(English)
字幕:英語(English), 希臘語

您將獲得的技能

Number TheoryCryptographyModular Exponentiation

學生職業成果

50%

完成這些課程後已開始新的職業生涯

40%

通過此課程獲得實實在在的工作福利
可分享的證書
完成後獲得證書
100% 在線
立即開始,按照自己的計劃學習。
可靈活調整截止日期
根據您的日程表重置截止日期。
初級
完成時間大約為19 小時
英語(English)
字幕:英語(English), 希臘語

提供方

加州大学圣地亚哥分校 徽標

加州大学圣地亚哥分校

国立高等经济大学 徽標

国立高等经济大学

教學大綱 - 您將從這門課程中學到什麼

內容評分Thumbs Up87%(3,538 個評分)Info
1

1

完成時間為 4 小時

Modular Arithmetic

完成時間為 4 小時
10 個視頻 (總計 90 分鐘), 4 個閱讀材料, 13 個測驗
10 個視頻
Numbers6分鐘
Divisibility6分鐘
Remainders9分鐘
Problems6分鐘
Divisibility Tests5分鐘
Division by 212分鐘
Binary System11分鐘
Modular Arithmetic12分鐘
Applications7分鐘
Modular Subtraction and Division11分鐘
4 個閱讀材料
Python Code for Remainders5分鐘
Slides1分鐘
Slides1分鐘
Slides1分鐘
12 個練習
Divisibility15分鐘
Remainders10分鐘
Division by 45分鐘
Four Numbers10分鐘
Division by 10110分鐘
Properties of Divisibility10分鐘
Divisibility Tests8分鐘
Division by 24分鐘
Binary System30分鐘
Modular Arithmetic8分鐘
Remainders of Large Numbers10分鐘
Modular Division10分鐘
2

2

完成時間為 4 小時

Euclid's Algorithm

完成時間為 4 小時
7 個視頻 (總計 78 分鐘), 4 個閱讀材料, 7 個測驗
7 個視頻
Euclid’s Algorithm15分鐘
Extended Euclid’s Algorithm10分鐘
Least Common Multiple8分鐘
Diophantine Equations: Examples5分鐘
Diophantine Equations: Theorem15分鐘
Modular Division12分鐘
4 個閱讀材料
Greatest Common Divisor: Code15分鐘
Extended Euclid's Algorithm: Code10分鐘
Slides1分鐘
Slides10分鐘
7 個練習
Greatest Common Divisor10分鐘
Tile a Rectangle with Squares20分鐘
Least Common Multiple10分鐘
Least Common Multiple: Code15分鐘
Diophantine Equations15分鐘
Diophantine Equations: Code20分鐘
Modular Division: Code20分鐘
3

3

完成時間為 5 小時

Building Blocks for Cryptography

完成時間為 5 小時
14 個視頻 (總計 91 分鐘), 4 個閱讀材料, 6 個測驗
14 個視頻
Prime Numbers3分鐘
Integers as Products of Primes3分鐘
Existence of Prime Factorization2分鐘
Euclid's Lemma4分鐘
Unique Factorization9分鐘
Implications of Unique Factorization10分鐘
Remainders7分鐘
Chinese Remainder Theorem7分鐘
Many Modules5分鐘
Fast Modular Exponentiation10分鐘
Fermat's Little Theorem7分鐘
Euler's Totient Function6分鐘
Euler's Theorem4分鐘
4 個閱讀材料
Slides10分鐘
Slides10分鐘
Fast Modular Exponentiation7分鐘
Slides10分鐘
5 個練習
Integer Factorization20分鐘
Remainders30分鐘
Chinese Remainder Theorem: Code15分鐘
Fast Modular Exponentiation: Code20分鐘
Modular Exponentiation30分鐘
4

4

完成時間為 5 小時

Cryptography

完成時間為 5 小時
9 個視頻 (總計 67 分鐘), 4 個閱讀材料, 2 個測驗
9 個視頻
One-time Pad4分鐘
Many Messages7分鐘
RSA Cryptosystem14分鐘
Simple Attacks5分鐘
Small Difference5分鐘
Insufficient Randomness7分鐘
Hastad's Broadcast Attack8分鐘
More Attacks and Conclusion5分鐘
4 個閱讀材料
Many Time Pad Attack10分鐘
Slides10分鐘
Randomness Generation10分鐘
Slides and External References10分鐘
2 個練習
RSA Quiz: Code2小時
RSA Quest - Quiz30分鐘

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關於 Introduction to Discrete Mathematics for Computer Science 專項課程

Discrete Mathematics is the language of Computer Science. One needs to be fluent in it to work in many fields including data science, machine learning, and software engineering (it is not a coincidence that math puzzles are often used for interviews). We introduce you to this language through a fun try-this-before-we-explain-everything approach: first you solve many interactive puzzles that are carefully designed specifically for this online specialization, and then we explain how to solve the puzzles, and introduce important ideas along the way. We believe that this way, you will get a deeper understanding and will better appreciate the beauty of the underlying ideas (not to mention the self confidence that you gain if you invent these ideas on your own!). To bring your experience closer to IT-applications, we incorporate programming examples, problems, and projects in the specialization....
Introduction to Discrete Mathematics for Computer Science

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