Assam University BA Mathematics Syllabus 2nd sem pass

SECOND SEMESTER  MTMP-201  MODERN ALGEBRA & GEOMETRY (2-D)  Full Marks : 50  Pass Marks: 17  (To answer one question from eac...

SECOND SEMESTER 

MTMP-201 

MODERN ALGEBRA & GEOMETRY (2-D) 

Full Marks : 50 

Pass Marks: 17 

(To answer one question from each unit. Each unit will have provision for internal choice.)

GROUP-A 

MODERN ALGEBRA 

(Marks —30) 

Pre-requisites: Theory of sets, Mapping, Equivalence relation.

Unit — I 

Marks-lO
Group, Permutation group, Cyclic group, Subgroup, Cosets and their properties, Lagrange’s theorem for order of a subgroup, Normal subgroup, Quotient group.

Unit — II 

Marks-lO
Definitions, examples and simple properties of Rings, Integral domains, Skew fields, Fields

Unit —III 

Marks-lO
vector spaces, subspace, Linear independence, Basis and dimension.

GROUP-B 

GEOMETRY(2-D) 

(Marks-20) 

Unit-IV 

Marks-lO
Thange of axes, pair of straight lines, general equation of second degree, reduction to standard rms.

Unit-V 

Marks-lO
properties of a parabola, an ellipse,a hyperbola, equations of chord, tangent & normal, polar equation of a conic.