******WRITTEN ACCORDING TO NEW ISI CMI MSC MATHEMATICS ENTRANCE EXAM PATTERN ******ALL SECTIONS ARE THOROUGHLY EXPLAINED WITH AMPLE SHORT AND LONG QUESTIONS WITH THEIR ANSWERS AND EXPLANATIONS AS WELL. ******20 MODEL PAPERS THOROUGHLY SOLVED. ******COMPLETE TOPIC WISE EXPLANANTION ACCORDING TO CMI MSC MATHEMATICS ENTRANCE SYLLABUS ******THEORY AND PRACTISE EXAMPLES ARE ALSO INCLUDED SOLUTIONS OF MCQ AND LONG BOTH SECTIONS ******TOPICS COVERED ARE ****ALGEBRA ****A) GROUPS, HOMOMORPHISMS, COSETS, LAGRANGE'S THEOREM, SYLOW THEOREMS, SYMMETRIC GROUP SN, CONJUGACY CLASS, RINGS, IDEALS, QUOTIENT BY IDEALS, MAXIMAL AND PRIME IDEALS, FI ELDS, ALGEBRAIC EXTENSIONS, FINITE FIELDS (****B) MATRICES, DETERMINANTS, VECTOR SPACES, LINEAR TRANSFORMATIONS, SPAN, LINEAR INDEPENDENCE, BASIS, DIMENSION, RANK OF A MATRIX, CHARACTERISTIC POLYNOMIAL, EIGENVALUES, EIGENVECTORS, ****UPPER TRIANGULATION, DIAGONALIZATION, NILPOTENT MATRICES, SCALAR (DOT) PRODUCTS, ANGLE, ROTATIONS, ORTHOGONAL MATRICES, GLN, SLN, ON, SO2, SO3. ****COMPLEX ANALYSIS HOLOMORPHIC FUNCTIONS, CAUCHY-RIEMANN EQUATIONS, INTEGRATION, ZEROES OF ANALYTIC FUNCTIONS, CAUCHY FORMULAS, MAXIMUM MODULUS THEOREM, OPEN MAPPING THEOREM, LOUVILLE'S THEOREM, POLES AND SINGULARITIES, RESIDUES ****CALCULUS AND REAL ANALYSIS **** (A) REAL LINE: LIMITS, CONTINUITY, DIFFERENTIABLITY, REIMANN INTEGRATION, SEQUENCES, SERIES, LIMSUP, LIMINF, POINTWISE AND UNIFORM CONVERGENCE, UNIFORM CONTINUITY, TAYLOR EXPANSIONS, **** (B) MULTIVARIABLE: LIMITS, CONTINUITY, PARTIAL DERIVATIVES, CHAIN RULE, DIRECTIONAL DERIVATIVES,TOTAL DERIVATIVE,SEQUENCES,COMPLETENESS, WEIERSTRASS APPROXIMATION. ****TOPOLOGY. TOPOLOGICAL SPACES, BASE OF OPEN SETS, PRODUCT TOPOLOGY, ACCUMULATION POINTS, BOUNDARY, CONTINUITY, CONNECTEDNESS, PATH CONNECTEDNESS, COMPACTNESS, HAUSDOR SPACES, NORMAL SPACES, ****URYSOHN'S LEMMA, TIETZE EXTENSION, TYCHONO'S THEOREM,