About the Book
***WRITTEN ACCORDING TO LATEST PATTERN OF THE EXAMINATIONS ALL OVER INDIA. ***ALL SECTIONS ARE THOROUGHLY EXPLAINED WITH AMPLE SHORT. ***MCQ QUESTIONS WITH THEIR ANSWERS AND EXPLANATIONS AS WELL. ***5000+ MCQ ARE SOLVED WITH EXPLANATIONS 20 MODEL PAPERS ALL SOLVED ARE ADDED. ***SELECTIVE PREVIOUS YEAR PAPERS ARE SOLVED SUGGESTION PAPERS ALSO ADDED TOPICS COVERED ARE AS FOLLOWS. BOOK I Groups, homomorphisms, cosets, Lagrange’s Theorem, group actions, Sylow Theorems, symmetric group Sn, conjugacy class, rings, ideals, quotient by ideals, maximal and prime ideals, fields, algebraic extensions, finite fields Matrices, determinants, vector spaces, linear transformations, span, linear independence, basis, dimension, rank of a matrix. BOOK II 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 and contour integration, conformal maps, Rouche’s theorem, Morera’s theorem BOOK III Real Line: Limits, continuity, differentiablity, Reimann integration, sequences, series, limsup, liminf, pointwise and uniform convergence, uniform continuity, Taylor expansions, Multivariable: Limits, continuity, partial derivatives, chain rule, directional derivatives, total derivative, Jacobian, gradient, line integrals, surface integrals, vector fields, curl, divergence, Stoke’s theorem Metric spaces, Heine Borel theorem. BOOK IV Topological spaces, base of open sets, product topology, accumulation points, boundary, continuity, connectedness, path connectedness, compactness, Hausdorff spaces, normal spaces, Urysohn’s lemma, Tietze extension, Tychonoff’s theorem,
