|Course Type||Course Code||No. Of Credits|
Semester and Year Offered: Monsoon Semester 2013-14
Course Coordinator and Team: Kranti Kumar, Balchand Prajapati, Geetha Venkataraman
Email of course coordinator: balchand[at]aud[dot]ac[dot]in
Pre-requisites: Pre-requisite for this course is Mathematics at the XII grade level and 4 credits of SUS1MA506 (Algebra II)
Aim: This course helps students develop their ability to think abstractly within the setting offered through abstract and linear algebra. Such skills would add to a student’s ability to analyse and solve problems even in real life.
After completing this course, students will be able
Brief description of modules/ Main modules:
The following topics will be covered in the course under the four main modules as described below.
Cayley’s theorem, automorphisms, external direct products: definition, examples and properties, criterion for external direct product of a finite number of finite cyclic groups to be cyclic, the group of units modulo n as an external direct product, applications of external direct product, fundamental theorem of finite abelian groups, the isomorphism classes of abelian groups, proof of the fundamental theorem.
Polynomial rings: rings of polynomials over a commutative ring R, the division algorithm and its consequences; factorization of polynomials: definition of irreducible and reducible polynomials, reducibility tests, content of a polynomial, Gauss’s lemma, irreducibility tests including Eisenstein’s criterion, unique factorization in the polynomial ring over the integers, weird dice: an application of unique factorization; divisibility in integral domains: associates, irreducible and primes, unique factorization domains, principal ideal domains, Euclidean domains, relationship between Euclidean domains, principal ideal domains and unique factorization domains.
Change of basis, applications to difference equations, applications to Markov chains, eigenvalues and eigenvectors, eigenspaces and similarity, representation by a diagonal matrix.
Assessment Details with weights:
Date/period in which Assessment will take place
Mid Semester Exam
End September/ early October
Lab/ Home Assignments
Throughout the semester
End October/ early November
End Semester Exam
As per AUD Academic Calendar