About this Course

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Learner Career Outcomes

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Flexible deadlines
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Beginner Level
Approx. 19 hours to complete
English

Skills you will gain

Number TheoryCryptographyModular Exponentiation

Learner Career Outcomes

50%

started a new career after completing these courses

40%

got a tangible career benefit from this course
Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Flexible deadlines
Reset deadlines in accordance to your schedule.
Beginner Level
Approx. 19 hours to complete
English

Offered by

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University of California San Diego

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National Research University Higher School of Economics

Syllabus - What you will learn from this course

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Week
1

Week 1

4 hours to complete

Modular Arithmetic

4 hours to complete
10 videos (Total 90 min), 5 readings, 13 quizzes
10 videos
Divisibility6m
Remainders9m
Problems6m
Divisibility Tests5m
Division by 212m
Binary System11m
Modular Arithmetic12m
Applications7m
Modular Subtraction and Division11m
5 readings
Rules on the academic integrity in the course10m
Python Code for Remainders5m
Slides1m
Slides1m
Slides1m
12 practice exercises
Divisibility15m
Remainders10m
Division by 45m
Four Numbers10m
Division by 10110m
Properties of Divisibility10m
Divisibility Tests8m
Division by 24m
Binary System30m
Modular Arithmetic8m
Remainders of Large Numbers10m
Modular Division10m
Week
2

Week 2

4 hours to complete

Euclid's Algorithm

4 hours to complete
7 videos (Total 78 min), 4 readings, 7 quizzes
7 videos
Euclid’s Algorithm15m
Extended Euclid’s Algorithm10m
Least Common Multiple8m
Diophantine Equations: Examples5m
Diophantine Equations: Theorem15m
Modular Division12m
4 readings
Greatest Common Divisor: Code15m
Extended Euclid's Algorithm: Code10m
Slides1m
Slides10m
7 practice exercises
Greatest Common Divisor10m
Tile a Rectangle with Squares20m
Least Common Multiple10m
Least Common Multiple: Code15m
Diophantine Equations15m
Diophantine Equations: Code20m
Modular Division: Code20m
Week
3

Week 3

5 hours to complete

Building Blocks for Cryptography

5 hours to complete
14 videos (Total 91 min), 4 readings, 6 quizzes
14 videos
Prime Numbers3m
Integers as Products of Primes3m
Existence of Prime Factorization2m
Euclid's Lemma4m
Unique Factorization9m
Implications of Unique Factorization10m
Remainders7m
Chinese Remainder Theorem7m
Many Modules5m
Fast Modular Exponentiation10m
Fermat's Little Theorem7m
Euler's Totient Function6m
Euler's Theorem4m
4 readings
Slides10m
Slides10m
Fast Modular Exponentiation7m
Slides10m
5 practice exercises
Integer Factorization20m
Remainders30m
Chinese Remainder Theorem: Code15m
Fast Modular Exponentiation: Code20m
Modular Exponentiation30m
Week
4

Week 4

5 hours to complete

Cryptography

5 hours to complete
9 videos (Total 67 min), 4 readings, 2 quizzes
9 videos
One-time Pad4m
Many Messages7m
RSA Cryptosystem14m
Simple Attacks5m
Small Difference5m
Insufficient Randomness7m
Hastad's Broadcast Attack8m
More Attacks and Conclusion5m
4 readings
Many Time Pad Attack10m
Slides10m
Randomness Generation10m
Slides and External References10m
2 practice exercises
RSA Quiz: Code2h
RSA Quest - Quiz30m

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About the Introduction to Discrete Mathematics for Computer Science Specialization

Introduction to Discrete Mathematics for Computer Science

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