ABSTRACT ALGEBRA

Dr. Savitha K S
Mathematics
₹1,000.00
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  • 2 lessons
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  • 10 week duration
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PROGRAMME :BSc MATHEMATICS

COURSE: ABSTRACT ALGEBRA

SEMESTER :V

CREDITS: 4

INTRODUCTION: In Algebra, a broad division of Mathematics,  Abstract  Algebra is the study of Algebraic Structures which includes Groups, Rings, Fields,Vector Spaces etc. This  is one of the basic pillars of Modern Mathematics and is also referred to as Modern Algebra. Because of its generality, abstract algebra is used in many fields of science.

OBJECTIVE OF THIS COURSE : This course is intended to provide a first approach to the subject of algebra by studying some basic algebraic structures , mapping between them and their substructures. It also envisages to develop basic skill and proficiency in the concepts and methods of abstract algebra.

EXPECTED LEARNING OUTCOME:

The students who succeeded in this course

  • will be able to define algebraic structures
  • will be able to construct substructures.
  • will be able to analyze a given structure in detail.
  • will be able to develop new structures based on given structures.
  • will be able to compare structures.
  • Will be able to demonstrate examples of structures
  • Will be able to understand the concept of isomorphism

Text book :John B. Fraleigh : A First Course in Abstract Algebra ( 7th Edition) (Pearson)

REFERENCES:

  1. I.N. Herstein – Topics in Algebra
  2. Joseph A Gallian – Contemporary Abstract Algebra, Narosa Pub. House .
  3. Artin – Algebra , PHI
  4. https://ocw.mit.edu/courses/mathematics/18-703-modern-algebra-spring-2013/lecture-notes/
  5. https://cosmolearning.org/courses/abstract-algebra-groups-rings-fields/video-lectures/
  6. https://www.youtube.com/playlist?list=PLzVTusWerVcIzewg9dQxOKl9_62kTgOg

Syllabus

Course Outline

  • Module I-Groups and Subgroups

    Binary operations, Isomorphic binary structures, Groups-definition and examples, elementary properties of groups, finite groups and group tables, subgroups, cyclic subgroups, cyclic groups, elementary properties of cyclic groups.

  • Module II- Permutations, Cosets, and Direct products

    groups of permutations, Cayley’s theorem, orbits, cycles and the alternating groups, cosets and the theorem of Lagrange, direct products

    No items in this section
  • Module III-Homomorphisms and Factor groups

    Homomorphisms, properties of homomorphisms, factor groups, The Fundamental Homomorphism theorem, normal subgroups and inner automorphisms, simple groups.

    No items in this section
  • Module IV-Rings and fields

    Definitions and basic properties, homomorphisms and isomorphisms, Integral domains- divisors of zero and cancellation, integral domains, the characteristic of a ring. Ideals and factor rings. Homomorphisms and factor rings

    No items in this section
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Dr. Savitha K S
Dr Savitha started her teaching career in 1999 and joined St. Paul's in 2005. Her areas of interest include Abstract Algebra, Linear Algebra and Graph Theory. She was awarded the PhD Degree from CUSAT for her work entitled " Studies on the Network Topological Properties of Some Graph Classes"under the guidance of Prof. A Vijayakumar, Department of Mathematics. She has presented her research works in various National/International conferences and also has published a few of her works in some international journals .

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₹1,000.00