# EdCET Syllabus – Mathematics

## EdCET Syllabus – Mathematics

1. Sets – relations – binary operations – semi groups – groups – subgroups -normal subgroups- homomorphism-Functions permutations permutation groups – cyclic groups – quotient group – automorphism.
2. Rings – Integral domains – fields – characteristic – homomorphism – Ideals – Prime Ideals – maximal ideals – Rings of permutations – polynomials – polynomial rings.
3. Vector spaces – linearly independent vectors – Basis – dimension – linear transformation — Null space — Range — Rank of a linear transformation.
4. Elementary matrix operations – Elementary matrices – Determinants – properties – rank of matrix – inverse of a matrix – Eigen vectors – Eigen values – systems of linear equations.
5. Three dimensional geometry — Coordinates — distance formula – direction cosines – plane – angle between two planes – perpendicular distance from a point – Equation of a line – skew lines – shortest distance – The sphere – tangent plane power of a point – polar plane and pole – radical plane – coaxial system of spheres – The circle – radius – centre.
6. Real numbers – properties – functions – range – sequences – series – limits – continuity – differentiability – differentiation – mean value theorems — L’Hospital rules — Integration definite integrals – Reimann integral.
7. Differential equations – first order and first degree – different forms – Exact differential equations – change of variables – equation of first order but not of first degree – higher order linear differential equations – system of linear differential equations.
8. Elements of Number theory – Divisibility – primes – congruences – solutions of congruences – congruences of degree 1 The Euler function O.
9. Quadratic equations – quadratic expressions – change of sign – roots – maximum – minimum values