Inter Automorphism(Modern Algebra) by Dr.Neha Arora, ANAND INSTITUTE OF MATHEMATICS.

Open Mapping Theorem#Analyticity#RealAnalysis #finite_set, #countable_set,#uncountable_sets,#Real_number_system as complete ordered field, #Archimedean_property, #supremum, #infimum.# Sequences_and_series,#convergence,# limsup,# liminf. #Bolzano_Weierstrass-theorem, #Heine_Borel_theorem. #Continuity, #uniform-continuity, #differentiability,#mean-valu- theorem. #Sequences_and_series_of_functions, #uniform convergence. #Rieman sums #Riemann _integral, #Improper_Integrals. #Monotonic_functions, #types_of _discontinuity,# functions _of_bounded_variation, #Lebesgue_measure, #Lebesgue_integral. #Functions_of_several variables, #directional_derivative, #partial_derivative, linear, #transformation,# inverse_function , #implicit_function #Metric_spaces, #compactness, #connectedness. #Normed_linear_Spaces. #Spaces_of_continuous_functions #Linear_Algebra #Complex_Analysis# Algebra_of_complex_ numbers, #the_complex_plane, #polynomials, #power_series, #transcendental_functions #exponential_functions,# trigonometri_functions #hyperbolic_functions #Analytic_functions, #Cauchy-Riemann equations. #Contour integral, #Cauchy’s_theorem, #Cauchy’s_integral_formula, #Liouville’s_theorem, #Maximum_modulus_principle, #Schwarz_lemma,#Open_mapping_theorem. #Taylor_series, #Laurent_series, #calculus_of_residues. #Conformal_mappings, #Mobius_transformations. #Algebra #Permutations, #combinations, #pigeon-hole_principle,#inclusion-exclusion_principle, #derangements. #Fundamental_theorem_of_arithmetic, #divisibilit in_Z, #congruences, #Chines-Remainde_Theorem, #Euler’s Ø-function, #primitive_roots. #Groups, #subgroups,#normal_subgroups, #quotient_groups, #homomorphisms, #cycli groups, #permutation_groups, Cayley’stheorem, class_equations, Sylow_theorems. #Rings, #ideals, #prime_and_maximal_ideals, #quotient_rings, #uniqu_ factorization_domain, #principal_ideal_domain, #Euclidean_domain. #Polynomial_rings_and_irreducibility_criteria. #Fields, #finite_fields, #field_extensions, #Galois_Theory. #Topology #basis, #dense_sets, #subspace_and_product_topology, #separation_axioms, #connectedness_and_compactness #Ordinary_Differential_Equations #ODE #Existence_and_uniqueness of solutions,#singular_solutions_of_first_order_ODEs, #system_of_first_order_ODEs,#General_theory_of_homogenous and non-homogeneous linear ODEs, #variation_of_parameters,#Sturm-Liouville_boundary_value_problem, #Green’s_function. #Partial-Differential_Equations #PDE #Lagrange_method,#Charpit_methods_for_solving_first_order_PDEs, #Cauch_ problem #Classification_of_second_order,#General_solution_of_higher_order_PDEs_with_constant_coefficients, #Method_of_separation_of_variables_for_Laplace, #Heat_and_Wave_equations. #Numerical_Analysis ,#Numerical solutions of algebraic equations, #Method_of_iteration ,#Newton-Raphson_method, #Rate_of_convergence, #Solution_of_systems_of_linear_algebraic_equations #Gauss_elimination method ,#Gauss-Seidel_methods, #Finite_differences_method, #Lagrange_method, #Hermite_method #spline_interpolation_method, #Numerical_differentiation_method #integration_method, #Numerical_solutions #Picard_method, Euler_method, #modified Euler_method #Runge-Kutta_methods. #Calculus_of Variations:#Variation _of_a_functional, #Euler-Lagrange _equation, #Necessary_and_sufficient_conditions_for_extrema. #Variational_methods _for_boundary_value_problems #ordinary_and_partial_differential_equations. #Linear_Integral_Equations, #anand kumar,#anand_institute_of_mathematics, #maths,#matrices,#matrices_by_anandsir ,#anand_sir_video_lecture,#education,#piaim ,#piaim_video ,#piaim_video_lecture #csirjrf_question_solution #viralvideos, #gatestatistics #csirnet_question_solution_video, #net, #jrf, #csir, #iitjam #positivitylecture #goals, #delhiuniversity_lecture , #iitlectures, #iitjam ,#iit_motivation, similar_matrix _by_anand_sir, #linear_algebra Linear_Algebra,#Vector_spaces, #subspaces, #linear dependence, #basis, #dimension, #algebra_of_linear_transformations. #Algebra_of_matrices, #rank_matrices,#determinant_of_matrices, #linear_equations, #Eigenvalues #eigenvectors, #Cayley_Hamilton_theorem. #Matrix_representation_of_linear_transformations. #Change_of_basis, #canonical_forms, #diagonal_forms, #triangular_forms, #Jordan_forms. #Inner_product_spaces,#Linear_integral_equation_of_the_first_and_second_kind_of_Fredholm_and_Volterra_type, #Solutions_with_separable_kernels. #Characteristic_numbers_and_eigenfunctions, #resolvent_kernel.#CSIR_NET_Maths_coaching_in_Delhi,#UGC_NET_maths_coaching,#NETcoaching_in_Delhi_for_maths,#CSIR_mathematics_coaching, #UG NET_coaching_in_Delhi, #CSIR_coaching_centre_in_Delhi,#Math_coaching, #Online_mathematics_coaching, #IIT-JAM_for _mathematics, #Coaching_for_IIT-JAM_maths,#Coaching_for_IIT-JAM_Mathematics,#IIT-JAM_coaching_in_Delhi,#IIT-JAM_Mathematics_coaching,#IIT-JAM_coaching_for_mathematics_in_Delhi, #Jam_maths_coaching, #IIT-JAM_coaching,#IIT-JAM_online_coaching, #IIT-JAM_online_mathematics_coaching,