Course Archives Theoretical Statistics and Mathematics Unit
Course: Elementary Number Theory
Level: Undergraduate
Time: Currently not offered
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:
Midterm 10 marks
Assignments 40 marks
Final Exam 50 marks
Total 100 marks


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Past Exams
Semestral
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