Mathematics Syllabus : www.jiwaji.edu University

[mariammal]

Mathematics Syllabus

Unit-1 :
Rank of a matrix. Eigen values, eigen vectors.Characteristic equation of a matrix. Cayley Hamilton theorem and its use in finding inverse of marix. Application of matrix to a system of linear ( both homogenous and non - homogenous) equations. Theorems on consistency and inconsistency of a system of linear equations. Solving the linear equations with three unknowns. Relation between the roots and coefficients of a general polynomial equation in one variable. Transformation of equations, Descarte’s rule of signs.

http://www.jiwaji.edu/syllabus-08-09.asp
http://www.mp.gov.in/highereducation...erSyllabus.pdf

Unit-2 :
De Moivre’s theorem and its application. Direct and inverse circular and hyperbolic functions, Expansion of trignometrical function. Gregory’s Series, Summation of Series,

Unit-3 :
Definition and basic properties of group. Order of an element of a group. Subgroups, algebra of subgroups. Cyclic groups, and their simple properties. Coset decomposition and related theorems. Lagrange’s theorem andits consequences, Normal sub groups, quotient groups.

Unit-4 :
Homomorphism and isomorphism of groups, kernel of Homomorphism of groups and fundamental theorem of Homomorphism of groups Permutation groups (even and odd permutations) Alternating groups An, Cayley’s theorem. Introduction to rings, subrings, integral domains and fields, simple properties and examples.

Unit-5 :
General equation of second degree. Tracing of conics. Equation of cone with given base, generators of cone, condition for three mutually
perpendicular generators, Right circular cone. Equation of Cylinder and its properties. Right circular cylinder, enveloping cylinder and
their properties Central conicoids, Paraboloids. Plane sections of Conicoids.

Texts Books :
1. S.L. Loney – Plane Trigonometry Part II
2. K.B. Datta – Matrix and Linear Algebra Prentice Hall of India Pvt. New Delhi 2000
3. Chandrika Prasad – A Text Book on Algebra and Theory of Equations, Pothishala Pvt. Ltd. Allahabad
4. I. N. Herstein – Topics in Algebra, Wiley Eastern Ltd. New Delhi 1977
5. N. Saran & R.S. Gupta : Analytical Geometry of Three dimensions. Pothishala Pvt. Ltd. Allahabad
6. S.L. Loney, Elements of Coordinate Geometry, Macmillan and Co. London.

Reference Books :
1. P. B. Bhattacharya, S. K. Jain and S.R. Nagpaul, First Courses in Linear Algebra, Wiley Eastern, New Delhi. 1983.
2. S. K. Jain, A. Gunewardena and P. B. Bhattacharya, Basic Linear Algebra with MATLAB, Key CollegePpublishing, 2001. Allahabad
3. H.S. Hall and S.R. Knight, Higher Algebra, H.M. publication, 1994.
4. R.S. Verma and K.S. Shukla, Text Book on Trigonometry Pothishala Pvt. Ltd.
5. P.B. Bhattacharya, S.K. Jain and S.R. Nagpaul, Basic Abstract Algebra, Wiley Eastern, New Delhi, 1997.
6. I. S. L.uther and I.B. S. Passi, Alegebra Vol- I , II, Narosa Publishing House.
7. P.K. Jain & Khalil Ahmad, A text book of Analytical Geometry of Two Dimensions, Wiley Eastern Ltd. 1994
8. P.K. Jain & Khalil Ahmad, A text book of Analytical Geometry of Three Dimensions, Wiley Eastern Ltd. 1999
9. R.J.T. Bell: Elementary Treatise on Coordinate Geometry of Three dimensions, Macmillan India Ltd. 1994.