Course Archives Theoretical Statistics and Mathematics Unit | ||||||||
Course: Elementary Number Theory Level: Undergraduate Time: Currently not offered |
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Syllabus Past Exams Syllabus: i) Basic set theory, Equivalence relations and partitions. Mathematical Induction, Binomial theorem, principle of inclusion-exclusion and pigeonhole. ii) Divisibility, Division algorithm, Euclidean algorithm, Fundamental theorem of arithmetic and Sieve of Eratosthenes. iii) Basic properties, Fermats little theorem, Euler and Wilson congruences, RSA, Chinese remainder theorem, Group structure of U(Z/nZ), Primitive roots. iv) Quadratic residues, Quadratic reciprocity law, Jacobi symbol, Binary Quadratic forms, Sum of two squares. v) Arithmetic Functions, Mobius inversion formula, Linear recurrences, Linear Diophantine equations. Reference Texts: (a) I. Niven, H. S. Zuckermann and H. L. Montgomery: An Introduction to the Theory of Numbers. (b) J. Kraft and L. Washington: An Introduction to Number Theory with Cryptography. (c) D. Burton: Elementary Number Theory. Evaluation:
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