Elementary Number Theory and Algebra

Code: MA2121 | L-T-P-C: 3-0-0-6

Number theory: Well ordering principle, principle of mathematical induction; Division algorithm, GCD and LCM, Euclidean algorithm, linear Diophantine equation; Primes, the fundamental theorem of arithmetic; Properties of congruences, linear congruences, chinese remainder theorem; Fermat's little theorem; Arithmetic functions, Mobius inversion formula, Euler's theorem; Primitive roots; Introduction to cryptography, RSA cryptosystem, distribution of primes.

Algebra: Groups, subgroups, cyclic groups, permutation groups, Cayley's theorem, cosets and Lagrange's theorem, normal subgroups, quotient groups, homomorphisms and isomorphism theorems; Rings, integral domains, ideals, quotient rings, prime and maximal ideals, ring homomorphisms, field of quotients, polynomial rings, factorization in polynomial rings, fields, characteristic of a field, field extensions, splitting fields, finite fields.

Texts:

• D. M. Burton, Elementary Number Theory, Seventh Edition, McGraw Hill, 2017.
• J. A. Gallian, Contemporary Abstract Algebra, Fourth Edition, Narosa, 1998.

 

References:

• I. Niven, S. Zuckerman and H. L. Montgomery, An Introduction to the Theory of Numbers, Fifth Edition, Wiley-India, 1991.
• G. A. Jones and J. M. Jones, Elementary Number Theory, Springer, 1998.
• K. H. Rosen, Elementary Number Theory and its Applications, Pearson, 2015.
• I. N. Herstein, Topics in Algebra, Wiley, 2004.
• J. B. Fraleigh, A First Course in Abstract Algebra, Addison Wesley, 2002.