| Course Name | Modern Algebra |
| Course Code | 25MAT211 |
| Program | B. Sc. in Physics, Mathematics & Computer Science (with Minor in Artificial Intelligence and Data Science) |
| Semester | 4 |
| Credits | 4 |
| Campus | Mysuru |
Introduction to Groups – Symmetries of a Square – The Dihedral Groups – Definition and Examples of Groups – Elementary Properties of Groups – Finite Groups – Subgroups: Terminology and Notation – Subgroup Tests – Examples of Subgroups.
(Chapters 1-3)
Cyclic Groups – Properties of Cyclic Groups – Classification of Subgroups of Cyclic Groups – Permutation Groups – Properties of Permutations – Isomorphisms: Definition and Examples – Cayley’s Theorem – Properties of Isomorphisms – Automorphisms.(Chapters 4-6)
Cosets and Lagrange’s Theorem – Application of Cosets to Permutation Groups – Normal Subgroups – Factor Groups – Applications of Factor Groups – Group Homomorphisms: Definition and Examples – Properties of Homomorphisms – The First Isomorphism Theorem.(Chapters 7, 9, 10)
Rings – Motivation and Definition – Examples of Rings – Properties of Rings – Subrings – Integral Domains – Fields – Characteristic of a Ring.(Chapters 12, 13)
Quotient Rings and Ideals – Homomorphism of rings and rings of polynomials.(Chapters 28-30)
Ideals – Factor Rings – Prime Ideals and Maximal Ideals – Ring Homomorphisms: Definition and Examples – Properties of Ring Homomorphisms – The Field of Quotients – Polynomial Rings: Notation and Terminology – The Division Algorithm and Consequences.
(Chapters 14-16)
Course Objectives:
Course Outcomes:
| COs | Description |
| CO1 | Effectively write abstract mathematical proofs in a clear and logical manner |
| CO2 | Locate and use theorems to solve problems in number theory and theory of polynomials over a field |
| CO3 | Demonstrate ability to think critically by interpreting theorems and relating results to problems in other mathematical disciplines |
| CO4 | Demonstrate ability to think critically by recognizing patterns and principles of algebra and relating them to the number system |
CO-PO Mapping
| PO/PSO | PO1 | PO2 | PO3 | PO4 | PO5 | PO6 | PO7 | PO8 | PO9 | PO10 | PSO1 | PSO2 | PSO3 | PSO4 |
| CO | ||||||||||||||
| CO1 | 3 | – | 2 | 2 | 2 | – | 1 | – | – | – | – | 2 | 2 | – |
| CO2 | 2 | – | 2 | 2 | 2 | – | 1 | – | – | – | – | 2 | 3 | – |
| CO3 | 2 | – | 3 | 1 | 2 | – | 1 | – | – | – | – | 2 | 2 | – |
| CO4 | 3 | – | 3 | 1 | 2 | – | 1 | – | – | – | – | 3 | 3 | – |
TEXTBOOKS:
1) Johan B. Fraleigh, A First course in abstract algebra, 3rd edition, Narosa, 2000.
2) Joseph A. Gallian, Contemporary Abstract Algebra, 4th edition, Narosa, 2008.
REFERENCES:
1) Garrett Birkoff and Saunders Mac Lane, A Survey of Modern Algebra, 1st edition, Universities Press, 2003.
2) I. N. Herstein, Topics in Algebra, 2nd Edition, John Wiley and Sons, 2000.
3) M. Artin, Algebra, 2nd Edition, Prentice Hall inc., 1994.
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