School of Mathematics and Computer Sciences

DSA is a core computer science course that covers the aspects of algorithm analysis, algorithm paradigms, data structures, various problems and solving methods and NP Completeness

1. Solvable groups. Nilpotent groups.
2. Definition and examples of rings. Fields, subrings. homomorphism of rings. Kernel
and image of a homomorphism. Kernel is NOT a subring. Characteristic of a ring.
Quotient rings. Prime ideals, maximal ideals and their characterization. Polynomial
rings. Divisibility. units. Factorization in a ring. Irreducible and prime elements in a
ring. Unique factorization domain, principal ideal domain and euclidean domains.
3. Fields. Field extensions. Finite fields. Finite and algebraic extensions. Classical
geometric constructions. Galois theory- fundamental theorem of Galois theory and
Abel’s theorem.

References:
1. Joseph A Gallian, Contemporary abstract algebra, Narosa Publishers, India.
2. John B Fraleigh, A First Course in Abstract Algebra, Narosa Publishers, India.
3. M Artin, Algebra, Prentice Hall India.
4. Joseph Rotman, Galois Theory, Universitext, Springer.

This course describes the methods to solve ODE and PDE with applications