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Breaking News Loading Dear Btechallsolutions readers This list of books is sufficient to solve engineering mathematics gate papers. If you want to read only one book rather then the chapter wise details then see another book which is published by GATE Institutes. Author: Manu Kaushik The author is a verified editor and creator at Btechallsolutions.
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WHICH INSTITUTION FOR GATE PREPARATION IS BEST IN DELHI?
Set Theory - sets and classes, relations and functions, recursive definitions, posets, Zorn - s lemma, cardinal and ordinal numbers; Logic - propositional and predicate calculus, well-formed formulas, tautologies, equivalence, normal forms, theory of inference. Combinatorics - permutation and combinations, partitions, pigeonhole principle, inclusion-exclusion principle, generating functions, recurrence relations. Graph Theory - graphs and digraphs, Eulerian cycle and Hamiltonian cycle, adjacency and incidence matrices, vertex colouring, planarity, trees. Programming laboratory will be set in consonance with the material covered in lectures. Groups, subgroups, homomorphism; Group actions, Sylow theorems; Solvable and nilpotent groups; Rings, ideals and quotient rings, maximal, prime and principal ideals; Euclidean and polynomial rings; Modules; Field extensions, Finite fields. Systems of linear equations, vector spaces, bases and dimensions, change of bases and change of coordinates, sums and direct sums; Linear transformations, matrix representations of linear transformations, the rank and nullity theorem; Dual spaces, transposes of linear transformations; trace and determinant, eigenvalues and eigenvectors, invariant subspaces, generalized eigenvectors; Cyclic subspaces and annihilators, the minimal polynomial, the Jordan canonical form; Inner product spaces, orthonormal bases, Gram-Schmidt process; Adjoint operators, normal, unitary, and self-adjoint operators, Schur's theorem, spectral theorem for normal operators. Convergence of sequence of real numbers, real valued functions of real variables, differentiability, Taylor's theorem; Functions of several variables - limit, continuity, partial and directional derivatives, differentiability, chain rule, Taylor's theorem, inverse function theorem, implicit function theorem, maxima and minima, multiple integral, change of variables, Fubini's theorem; Metrics and norms - metric spaces, convergence in metric spaces, completeness, compactness, contraction mapping, Banach fixed point theorem; Sequences and series of functions, uniform convergence, equicontinuity, Ascoli's theorem, Weierstrass approximation theorem.
GATE Reference Books for Computer Science & IT