Algebra & Trigonometry

SYLLABUS- ALGEBRA & TRIGONOMETRY,
Section-A
Properties of Integers - 1 Question
Division algorithm. Euclidean algorithm. Fundamental theorem of arithmetic. Congruence and residue classes. Fermat's and Wilson's theorem.
Algebraic Equations - 1 Question
Relations between the roots and coefficients of general polynomial equation in one variable. Trans-formation of equations. Descarte's rule of signs. Solution of cubic equations (Cardon's method). Solution of bi-quadratic equations.
Groups - 3 Questions
Definition of a group with examples and simple properties. Subgroups Cyclic groups. Coset decomposition. Lagrange's theorem and its consequences. Fermat's and Euler's theorems. Homomorphism and Isomorphism. Normal subgroups. Quotient groups.
The fundamental theorem of homomorphism. Permutation groups. Even and odd permutations. The alternating group A. Cayley's theorem.
Section-B
Trigonometry - 3 Questions
Applications of De-Moivre s theorem. Expansion of trigonometrical functions. Exponential, circular, logarithmic, inverse circular, hyperbolic and inverse hyperbolic functions of a complex variable. Gregory's series. Summation of trigonometrical
series.