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Lecture
Number Theory: Prime Numbers and Modular Arithmetic
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Related lectures (32)
Course Overview: Teaser on Course Contents
Offers an overview of propositional and predicate logic, sets, functions, relations, algorithms, Swiss cities, sorting tables, Covid infections, poker hands, and prime numbers.
Modular Arithmetic: Understanding RSA Cryptosystem
Explores modular arithmetic and its role in the RSA cryptosystem for error detection.
Multicorrelation Sequences and Primes
Explores multicorrelation sequences, primes, and their intricate connections in number theory and ergodic theory.
Fundamental Theorem of Arithmetic
Covers prime numbers, unique decomposition of natural numbers into prime factors, and practical implications for calculations.
Algebraic Structures: Groups and Rings
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Covers groups, rings, number theory, atomic bonds, and materials structure, setting the foundation for further exploration.
Cyclotomic Extensions: Norms, Ideals, and Primes
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Explores cyclotomic extensions, prime numbers, and ideal norms in number theory.
Integers: Sets, Maps, and Principles
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Introduces sets, maps, divisors, prime numbers, and arithmetic principles related to integers.
Prime Number Theorem
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Explores the proof of the Prime Number Theorem and its implications in number theory.
Prime Gaps and Multiplicative Sieve Inequalities
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Covers the Bombieri-Vinogradov theorem and its implications for prime gaps and multiplicative sieve inequalities.
RSA Cryptosystem: Encryption and Decryption Process
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Covers the RSA cryptosystem, encryption, decryption, group theory, Lagrange's theorem, and practical applications in secure communication.
Prime Number Theorem
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Covers the proof of Von Mangoldt's formula and the Prime Number Theorem using Zeta functions and pole analysis.
Groups and Numbers: Hidden Subgroup Problem
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Explores groups and numbers, emphasizing the hidden subgroup problem and its complexities in classic and quantum algorithms.
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