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| Mathematics ---- Number Theory
Elementary Number Theory, Algebraic Number Theory, Analytic Number Theory.
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| 1) Distribution of Prime Numbers by W.W.L. Chen
(Topics) Arithmetic functions, elementary prime number theory, Dirichlet series, primes in arithmetic progressions, the prime number theorem, the Riemann zeta function.
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| 2) Analytic Number Theory course by Graham Everest, lecture notes by Christian Rottger
(Topics) Elementary number theory, Euler's summation formula, Dirichlet convolution, Euler products, analytic continuation of the Riemann zeta function, the gamma function, the theta function, Fourier analysis, The functional equation, primes in an arithmetic progression, characters of finite Abelian groups, Dirichlet characters and L-functions, analytic continuation of L-functions.
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| 3) Algebraic Number Theory by Robin Chapman (lecture notes)
(Topics) Algebraic numbers, number fields and number rings, norm, trace, discriminant, factorization in number rings, ideal classes, geometric methods
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| 4) Elementary Number Theory by Michael Filaseta (course notes)
(Topics)Elementary number theory, rational and irrational numbers, the division algorithm, the Euclidean algorithm, continued fractions, modular arithmetic, Fermat's Little Theorem, public-key encryptions, the Chinese Remainder Theorem, primitive roots, quadratic reciprocity, asymptotics, the distribution of primes, sieve techniques.
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| 5) Number Theory by J. E. Cremona (lecture notes)
(Topics)Factorization, divisibility, g.c.d.s and the Euclidean algorithm, Euclidean domains, linear congruences, Chinese Remainder Theorem, integers and units modulo n, Euler's phi function and applications, quadratic congruences, law of quadratic reciprocity, diophantine equations, Gaussian Integers and applications, p-adic numbers.
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