B.SC I YEAR math Syllabus

SYLLABUS

B. Sc. Mathematics

BMG: 101 ABSTRACT ALGEBRA Max Marks: 50

Unit-I
Sets and Logic (No question should be asked on this part). The well-ordering principle.
The division algorithm. The fundamental theorem of arithmetic, Congruence modulo.
Equivalance relations and Equivalance classes.
Unit-II
Groups: Definition, Examples and Properties, Permutation and Permutation group,
Subgroups and their properties.
Unit-III
Cosets and Coset decomposition, Lagrange’s theorem and its corollaries, Farmat’s
theorem, Cyclic group.
Unit-IV
Normal subgroup, Centre of a group, Quotient group, Homomorphism and Isomorphism,
Fundamental theorem of homomorphism, Cayley’s theorem.
Unit-V
Ring, Examples and simple properties, Different types of rings, Subring and Ideals,
Divisibility in an integral domain, Polynomial ring, Field and simple properties.


Books Recommended:
1. Thomas A.Whitelaw Introduction to Abstract (Blakie & Son Ltd.)
2. R.S. Mishra and N.N.Bhattacharya Fundamental structure in Modern Algebra
3. Bhattacharya ,Jain & Nagpal Abstract Algebra (Cambridge Uni. Press)

BMG: 102 CALCULUS Max Marks: 50

Unit-I
Successive differentiation: Expansion of functions, Maclaurin’s and Taylor’s theorems.
Unit-II
Maxima and minima up to two independent variables, Indeterminate form , Jacobian of
three functions, Partial differentiation.
Unit-III
Asymptotes, Curvature, Envelop, Double point and curve tracing (Polar and Cartesian).
Unit-IV
Standard reduction formula, Integration, as the limit of sum, Simple definite integrals.
Unit-V
Rectification, Quadrature, Volumes and Surfaces solids of revolution, Beta and Gamma
functions with their properties.


Books Recommended:
1. Gorakh Prasad Differential Calculus
2. Gorakh Prasad Integral Calculus

BMG: 103 3-D Coordinate Geometry & Trigonometry Max Marks: 50

Unit-I
System of coordinates, Direction Cosine, Angle between two lines, Projections, Distance of a
point from a line.
The plane: General form,Normal form, Intercept form, Reduction of the general form to normal
form , Equation of plane through three points, Angle between two planes, Parallel planes,
Perpendicular distance of a point from the planes, Pair of the planes ,Area of a triangle and
volume of a tetrahedron.
Unit-II
The straight line: Equation of a line in general form, Symmetric form, Two point form,
Reduction of the general equation to the symmetrical form, Straight line and the planes,
Conditions of parallelism and perpendicularity of a line and a plane ,Plane through a given line,
Perpendicular distance formula for the line, Projection of a line on a given plane containing them,
Equation of a straight line intersecting two given lines, Perpendicular distance formula for the line
and coordinates of the foot of the perpendicular, Shortest distance between two lines.
Unit-III
Sphere: General equation of a sphere, Plane section of a sphere, Intersection of two spheres,
Sphere through a given circle, Intersection of a straight line and a sphere, Equation of a tangent
plane to sphere, Condition of tangency. Plane of contact, Polar plane of a given plane, Angle of
intersection of two spheres, Length of tangent, Radical plane, Coaxial system of spheres.
Unit-IV
Cone:Equation of a cone whose vertex is at origin, Equation of a cone with a given vertex and a
given conic as base, Condition that general equation of second degree represent a cone, Equation
of a tangent plane, Condition of tangency of a plane and a cone, Reciprocal cone, Right circular
cone.
Unit-V
Expansions of sine and cosine of multiple angles in series, Expansion of sine, cosine and tan in
power of angles, Expansion of power of sines and cosines in multiples angles, Exponential series
for complex numbers, Circular and inverse circular functions for complex numbers, Hyperbolic
functions, Inverse hyperbolic functions, Logarithm of complex numbers, Summation of
trigonometric series.
Books Recommended:
1. Shanti Narayan Coordinate Geometry of 3-Dimension.
2. S.LL.Loney Trigonometry part III
3. Schaum’s series Coordinate Geometry