MNIT Jaipur Syllabus computer science Abstract Algebra
Number Systems: Natural numbers. Counting. Cardinality of finite sets. Laws, Mathematical induction.
Prime numbers. Fundamental theorem of arithmetic. Well-ordering principle. Number bases. Modulo
arithmetic. Greatest Common Divisor, Euler’s extended algorithm, Chinese Remainder Theorem,
Primality testing, Integers. Laws of arithmetic. Integer powers and logarithms. Recurrence relations.
Group Theory: Groups, Semi groups and Monoids, Cyclic semi graphs and sub monoids, Subgroups
and cosets, Congruence relations on Semi groups, Factor groups and homomorphisms, Morphisms
Normal sub groups. Structure of cyclic groups, Permutation groups, dihedral groups, Sylow theorems,
abelian groups; solvable groups, Nilpotent groups; groups of small order, elementary applications in
Rings: Rings, Subrings, Morphism of rings, ideal and quotient rings, Euclidean domains, Commutative
rings; integral domains, noncommutative examples, Structure of Noncommutative Rings, Ideal Theoryof Commutative Rings
Field Theory: Integral domains and Fields, polynomial representation of binary number, Galois fields,
primitive roots, discrete logarithms, split search algorithm.
Modules: Sums and products; chain conditions, Composition series; tensor products.
1. John Fraleigh. First Course in Abstract Algebra, Pearson Education.
2. Michael Artin. Algebra, Pearson Education.
3. John A. Beachy and William D. Blair. Abstract Algebra, Second Edition, Waveland Press.
4. John A. Beachy. Abstract Algebra II, Cambridge University Press, London Mathematical Society
Student Texts #47, 1999.