06-26-2026, 02:39 PM
Lectures notes on number theory
by Alexandros V. Gerbessiotis
Summary
This lecture note provides a clear and practical introduction to number theory for computer science students, making fundamental mathematical ideas accessible without assuming extensive prior knowledge. It begins with core concepts such as divisibility, prime numbers, modular arithmetic, and congruences before gradually introducing more advanced topics, including Euler's totient function, the Chinese Remainder Theorem, primitive roots, quadratic residues, and the mathematical foundations of modern cryptography.
The notes also explain classical primality-testing algorithms like Miller–Rabin and Solovay–Strassen, and conclude with higher-level concepts such as multiplicative functions, the Möbius function, Dirichlet products, and inversion formulas. Designed as both a textbook companion and a self-study resource, the material bridges pure mathematics and real-world computing applications, making it especially valuable for students interested in algorithms, discrete mathematics, cybersecurity, and cryptography.
NOTES (PDF)
by Alexandros V. Gerbessiotis
Summary
This lecture note provides a clear and practical introduction to number theory for computer science students, making fundamental mathematical ideas accessible without assuming extensive prior knowledge. It begins with core concepts such as divisibility, prime numbers, modular arithmetic, and congruences before gradually introducing more advanced topics, including Euler's totient function, the Chinese Remainder Theorem, primitive roots, quadratic residues, and the mathematical foundations of modern cryptography.
The notes also explain classical primality-testing algorithms like Miller–Rabin and Solovay–Strassen, and conclude with higher-level concepts such as multiplicative functions, the Möbius function, Dirichlet products, and inversion formulas. Designed as both a textbook companion and a self-study resource, the material bridges pure mathematics and real-world computing applications, making it especially valuable for students interested in algorithms, discrete mathematics, cybersecurity, and cryptography.
NOTES (PDF)
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