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To introduce students to classical analytic Number Theory.
Topics to include some of the following: The arithmetic functions and identities. Algebraic and transcendental numbers. Continued fractions (including solving congruence equations by continued fractions, periodic continued fractions, Brounkner's Algorithm and Pell's equation). Approximation of irrationals by rationals (Liouville's theorem and construction of transcendental number). Quadratic residues, Euler's criterion and the Quadratic Reciprocity Law (with proof). Jacobi symbol, its reciprocity law and applications. Distribution of primes. Chebyshev's Theorem.