| Course Type | Course Code | No. Of Credits |
|---|---|---|
| Foundation Core | SUS1MA509 | 4 |
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.
Course Outcomes:
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.
Group Theory
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.
Ring Theory
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.
Linear Algebra
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:
S.No | Assessment | Date/period in which Assessment will take place | Weightage |
1 | Class test | End August | 10% |
2 | Mid Semester Exam | End September/ early October | 25% |
3 | Lab/ Home Assignments | Throughout the semester | 15% |
4 | Presentation/ Viva | End October/ early November | 15% |
5 | End Semester Exam | As per AUD Academic Calendar | 35% |
Reading List:
