# B.Sc. (General) in Mathematics

Gurukula Kangri VishwavidayalayaPrice on request

Price on request

£ 399 - (Rs 33,048)

£ 249 - (Rs 20,624) £ 39 - (Rs 3,230)

+ VAT

Rs 7,500

+ VAT

## Important information

- Bachelor
- Haridwar

Starts | Location |
---|---|

On request |
HaridwarGurukula Kangri Vishwavidayalaya P.O Gurukula Kangri Haridwar, 249404, Uttaranchal, India See map |

## Course programme

SYLLABUS

ABSTRACT ALGEBRA

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

3-D Coordinate Geometry & Trigonometry

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.

Linear Algebra

Unit-I

Vector Space: Field, Vector space, Subspaces, Base and dimension, Coordinates,

Summary of rows equivalence, Computations concerning subspaces.

Unit-II

Linear Transformations: Linear transformations and their algebra. Isomorphism,

Representation of transformations by matrices.

Linear functionals, Double dual, Transpose of linear transformations.

Unit-III

Polynomials: Algebra of polynomials, Polynomial ideals, Determinant functions and

simple properties.

Unit-IV

Canonical Form: Characteristic values and Characteristic vectors, Annihilating

polynomials, Examples of invariant subspaces.

Diagonalization, Orthogonal diagonalization, Applications to differential equations.

Unit-V

Quadratic forms: Quadratic forms in two and n variables, Cross-product terms of the

quadratic form. Positive definite Quadratic form, Diagonalization of quadratic forms,

Application to conic sections.