For Tutorial Activities
- Teacher: C6243 INDHUMATHI
Course: Abstract Algebra
Course code: 20XT23
Syllabus:
4 0 0 4
Groups: Introduction to algebraic structures: Groups – Definition and examples, properties of groups, Permutation groups, Symmetric groups, Cyclic groups, Check digit scheme. (12)
Subgroups and Normal subgroups: Subgroups – Definition, Cosets and Lagrange’s theorem, Homomorphism, Isomorphism, Automorphism – Cayley’s theorem – Normal subgroups – Factor group – Fundamental theorem of group homomorphism. (12)
Group Coding: Coding of binary information and error detection – Group codes – Decoding and error correction. (8)
Rings: Definition and properties – Subrings, Ring of Quarternions, Integral domain – Homomorphism – Ideals and Quotient rings – Euclidean ring – Unique factorization theorem, Domain of Gaussian integers, Polynomial rings – Properties, Division algorithm – Factorization of polynomials – Primitive polynomials. (14)
Fields: Definition – Subfields – Finite fields – Structure of finite fields – GF(2^n ). (7)
Geometric Constructions: Constructible numbers, Angles, tri-sectors and circle-squares. (7)Text Book: Gallian, J.A., Contemporary Abstract Algebra, Brooks/Cole, 2013
Groups - Chapters 2,4,5
Subgroups and normal subgroups - Chapters 3,6,7,9,10
Group coding - Chapter 31 in Joseph A. Gallian, Contemporary Abstract Algebra, 8th edition, Brooks/Cole) and Chapter 16 in "Thomas W. Hungerford, Abstract Algebra an introduction, 3rd Edition, Brooks/Cole"
Rings - Chapters 12,13,15,14,18,16,17
Fields - Chapter 22
Geometric constructions - Chapter 23
Other Text Books:
1. Herstein, I.N., Topics in Algebra, John Wiley, 2012
2. Tremblay, J.P. and Manohar. R., Discrete Mathematical Structures with Applications to Computer Science, Tata McGraw Hill, 2017
Reference Books:
1. Ron M. Roth, Introduction to Coding Theory, Cambridge University Press, 2016
2. Ralph P. Grimaldi and Ramana B.V., Discrete and Combinatorial Mathematics: An Applied Introduction, Pearson Education, 2014
Web Sites:
https://isidore.co/calibre/get/pdf/4975
https://nptel.ac.in/courses/106/104/106104149/
http://www.d.umn.edu/~jgallian/
http://abstract.ups.edu/download/aata-20190710.pdf
Course Objectives:
CO1: To define and explain the concept of groups and be able to apply it in real life situations
CO2: To define and explain the concept of subgroups, cosets, homomorphism, isomorphism, automorphism, normal subgroups and factor groups and be apply to apply it in Lagrange’s theorem and fundamental theorem of homomorphism
CO3: To demonstrate coding and encoding of binary information with the use of group in coding theory. To define ring, subring, ring homomorphism, quotient ring, ideals and be able to relate them
CO4: To define polynomial rings and be able to apply its properties in division algorithm and factorization of polynomials
CO5: To describe finite fields and its structure and be able to apply it in geometric constructions
- Teacher: C6287 KRISHNASAMY R
Quiz
- Teacher: C3573 POONTHALIR G