Integrated Ph.D entrance exam (Mathematical Science) syllabus

Can you provide me the Indian Institute of Science Education and Research Integrated Ph.D entrance exam (Mathematical Science) syllabus???????

[Arvind Kumar]

This is the Indian Institute of Science Education and Research Integrated Ph.D entrance exam (Mathematical Science) syllabus:

SYLLABUS
1. Algebra:
Theory of Equations: Relation between roots and coefficients of an equation, Symmetric functions of roots, Rolle’s theorem, Reciprocal Equations, Descartes’ Rule of Signs, Cubic and quartic equations, Complex numbers and De Moivre’s Theorem.

Determinants: Properties of determinants, Solution of a Linear System, Cramer’s Rule

Inequalities: AM‐GM inequality, Cauchy‐Schwarz inequality.

Set Theory: Relations, Functions, Bijections, Cardinality, Permutations and combinations of sets and multisets, Discrete probability.

Algebraic Structures: Groups, Subgroups, Cosets, Normal subgroups, Symmetric group, Homomorphisms. Rings, Integral Domains, Ideals, Prime and Maximal Ideals, Polynomial Rings.

Vector Spaces: Subspaces, Linear independence, Bases and dimension, Linear transform