ADVANCED ALGEBRA

Paper Code: 
MAT 121
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 
This course will enable the students to -
  1. Demonstrate knowledge of conjugacy relation and class equation. 
  2. Identify the irreducibility of polynomials.
  3. Develop the concepts of extension fields. 
  4. Find the splitting field for a given polynomial.

Course Outcomes (COs):

 

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Paper Code

Paper Title

MAT 121

 

 

 

 

 

 

Advanced Algebra (Theory)

 

 

 

 

 

 

The students will be able to –

 

CO1: Understand and introduce the language and precision of abstract algebra.

CO2: The course is proof-based, in the sense that students will be expected to understand, construct, and write proofs.

CO3: The course will create the tendency to think of why a mathematical statement is true or false.

CO4: In fact the course inculcates the way thoughts because constructing a legitimate proof involves different skills and expertise than the discovery part of the process.

CO5: In this course both angles of problem-solving will be stressed.

Approach in teaching:

 

Interactive Lectures, Discussion, Power Point Presentations, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions, presentations, Field trips

 

 

Quiz, Poster Presentations,

Power Point Presentations, Individual and group projects,

Open Book Test, Semester End Examination

 

 

 

 

Unit I: 
I
15.00
Direct product of groups (external and internal), Isomorphism theorems, Diamond isomorphism theorem,  Butterfly lemma,  Conjugate classes.
Unit II: 
II
15.00
Commutators, Derived subgroups, Normal series and solvable groups, Composition series, Refinement theorem and Jordan-Holder theorem for infinite groups.
 
Unit III: 
III
15.00
Module, Submodules , Quotient modules , Direct sums and module homomorphisms , Generation of modules , Cyclic modules.
 

 

Unit IV: 
IV
15.00
Field theory: Extension fields, Algebraic and transcendental extensions, Separable and inseparable extensions, Normal extensions, Splitting fields. 
 

 

Unit V: 
V
15.00
Galois Theory: Elements of Galois Theory, Fundamental theorem of Galois Theory, Solvability by radicals. 
Essential Readings: 

 

 

  • Dileep S. Chauhan and K.N. Singh, Studies in Algebra, JPH, Jaipur, 2011.
  • P.B. Bhattacharya, S.K. Jain, S.R. Nagpaul, Basic Abstract Algebra, Cambridge University Press, 1995.
  • I.N. Herstein, Topics in Algebra, Wiley Eastern Ltd., New Delhi, 1975.
  • Knapp, W. Anthony, Advanced Algebra, Springer, 2008.
  • Deepak Chatterjee, Abstract Algebra, PHI. Ltd. New Delhi, 2015.
  • S. David, Richard M. Foote Dummit, Abstract Algebra, John Wiely & Sons Inc. USA, 2003.
  • S. Hang, Algebra, Addison Wesley, 1993.
  • N. Jacobson, Basic Algebra, Hindustan Publishing Co, 1988.
  •  M. Artin, Algebra, Prentice Hall India, 1991.
  •  C. Musili, Introduction to Rings and Modules, Narosa Publishing House, New Delhi, 1994.
  • John B. Fraleigh, A First Course in Abstract Algebra, Narosa Publishing House, New Delhi, 2002.
Academic Year: 
2020-2021
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