SPECIAL ELEMENT IN RING(ZERO,ADDITIVE INVERSE,UNIT,ZERO DIVISOR,NILPOTENT,IDEMPOTENT,CHARACTERISTIC)

1-Rings and Vector Spaces, 3 Cr. Hours,For students of B.S.Mathematics
2-Mathematics B-IV [ Metric Spaces & Group Theory] , 4 Cr. Hours,For students of B.S.Mathematics
3-Mathematics B-Course-Paper II -Mathematical Methods, Group Theory and Metric Spaces, 100 Marks, For students of Associate Degree in Science Part-2
SYLLABUS FOR 4 YEAR B.S. MATHEMATICS-(SEMESTER SYSTEM PROGRAMME)
Rings and Vector Spaces, 3 Cr. Hours.
RING THEORY
1-Definition and example of rings
2-Special classes of rings
3-Fields
4-Ideals and quotient rings
5-Ring homomorphisms
6-Prime and maximal ideals
7-Field of quotients

Recommended Books
1. J. Rose, A Course on Group Theory, (Cambridge University Press, 1978)
2. I. N. Herstein, Topics in Algebra, (Xerox Publishing Company, 1964)
3. G. Birkhoff and S. Maclane, A Survey of Modern Algebra, (Macmillan, New York, 1964)
4. P. B. Battacharya, S. K. Jain and S. R. Nagpaul, Basic Abstract Algebra, (Cambridge
University Press, 1986)
5. V. Sahai and V. Bist, Algebra, 2nd edition, (Narosa Publishing House, 2003)
6. W. Keith Nicholson, Elementary Linear Algebra, (PWS-Kent Publishing Company, Boston, 2004)
7. Seymour Lipschutz, Linear Algebra, 3rd edition, (McGraw Hill Book Company, 2001)
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SYLLABUS FOR 4 YEAR B.S. MATHEMATICS-(SEMESTER SYSTEM PROGRAMME)
Mathematics B Course-Paper IV [ Metric Spaces & Group Theory ]
GROUP THEORY
1-Binary operations
2-Definition, Examples and formation of groups
3-Order of group,
4-Order of an element
5-Abelian groups
6-Subgroups
7-Cyclic groups,
8-Cosets,
9-Lagrange’s theorem
10-Permutation,
11-Symmetric groups
12-Even and odd permutations
13-Introduction to rings
14- Introduction to fields
Recommended Books
1. Micheal, O. Searcoid, Metric Spaces, Springer, 2007
2. E. Kreyszig, Introduction to Functional Analysis with Applications, John Wiley and Sons, 1978
3. W.A. Sutherland, Introduction to Metric and Topological Spaces, Clarendon Press Oxford, 1975
4. E.T. Copson, Metric Spaces, Cambridge University, Press, 1968
5. G.F. Simmons, Introduction to Topology and Modern Analysis, McGraw Hill Company, 1963
6. I.N. Herstein, Topics in Algebra, Xerox Publishing Company, 1964.
7. Vivek Sahai and Vikas Bist, Algebra, Narosa Publishing House, 1999
8. P.B. Bhattacharya, S.K. Jain and S.R. Nagpaul, Basic Abstract Algebra, C.U.P.,
1986

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Mathematics B-Course-Paper II,Mathematical Methods, Group Theory and Metric Spaces 100 Marks
(Syllabi and Courses of Reading) Associate Degree in Arts/Science Part-I & Part-II Split Program.
Note: Attempt six questions by selecting two questions from Section I, two questions from Section II, one question from Section III and one question from Section IV
Section-III (2/12)
Group Theory
1-Binary operations
2-Definition, Examples and formation of groups
3-Order of group,
4-Order of an element
5-Abelian groups
6-Subgroups
7-Cyclic groups,
8-Cosets,
9-Lagrange’s theorem
10-Permutation,
11-Symmetric groups
12-Even and odd permutations
13-Introduction to rings
14- Introduction to fields
Recommended Books:
1. Thomas, Calculus, 11th Edition. Addison Wesley Publishing Company, 2005
2. H.Anton, I. Bevens, S. Davis, Calculus, 8th Edition, John Wiley & Sons, In. 2005
3. Micheal, O. Searcoid, Metric Spaces, Springer, 2007
4. E. Kreyszig, Introduction to Functional Analysis with Applications, John Wiley and Sons, 1978
5. Erwin, Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons, 2004
6. l.N. Herstein, Topics in Algebra, Xerox Publishing Company, 1964.
7. Adler, Andrew, Coury, John E. The Theory of Numbers, Jones and Barttlet Publishers,Boston, 1995.
8. Burton, D.M. Elementary Number Theory McGraw Hill, 2000

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