├── .github └── workflows │ └── compile.yml ├── .gitignore ├── .vscode ├── extensions.json ├── launch.json └── settings.json ├── README.md ├── book_template.tex ├── cmd ├── build.go ├── clean.go ├── extract.go ├── files.go ├── fmt.go ├── html.go ├── optimise.go ├── root.go └── setup.go ├── fonts ├── STIXTwoMath-Regular.otf ├── STIXTwoText-Bold.otf ├── STIXTwoText-BoldItalic.otf ├── STIXTwoText-Italic.otf ├── STIXTwoText-Medium.otf ├── STIXTwoText-MediumItalic.otf ├── STIXTwoText-Regular.otf ├── STIXTwoText-SemiBold.otf ├── STIXTwoText-SemiBoldItalic.otf └── TeXGyrePagellaMath.otf ├── go.mod ├── go.sum ├── html ├── header.html ├── main.css └── normalize.css ├── ia ├── analysis │ ├── 01_limits_and_convergence.tex │ ├── 02_series.tex │ ├── 03_convergence_tests.tex │ ├── 04_absolute_convergence.tex │ ├── 05_continuity.tex │ ├── 06_limit_of_a_function.tex │ ├── 07_differentiability.tex │ ├── 08_taylor_s_theorem.tex │ ├── 09_power_series.tex │ ├── 10_integration.tex │ ├── 11_fundamental_theorem_of_calculus.tex │ ├── 12_integration_techniques.tex │ ├── 13_integrals_in_taylor_s_theorem.tex │ ├── 14_uses_of_integration.tex │ ├── import.tex │ └── main.tex ├── book │ └── main.tex ├── de │ ├── 01_differentiation.tex │ ├── 02_integration.tex │ ├── 03_multivariate_functions.tex │ ├── 04_linear_ordinary_differential_equations.tex │ ├── 05_discrete_equations.tex │ ├── 06_isoclines_and_solution_curves.tex │ ├── 07_phase_portraits.tex │ ├── 08_higher_order_linear_odes.tex │ ├── 09_forced_second_order_odes.tex │ ├── 10_impulse_forcing.tex │ ├── 11_discrete_equations_and_the_method_of_frobenius.tex │ ├── 12_multivariate_calculus.tex │ ├── 13_systems_of_odes.tex │ ├── 14_more_pdes.tex │ ├── import.tex │ └── main.tex ├── dr │ ├── 01_basic_definitions_and_newton_s_laws.tex │ ├── 02_dimensional_analysis.tex │ ├── 03_forces_and_potential_energy.tex │ ├── 04_gravitational_and_electromagnetic_forces.tex │ ├── 05_friction.tex │ ├── 06_angular_motion_and_orbits.tex │ ├── 07_orbits_and_stability.tex │ ├── 09_rotating_frames.tex │ ├── 10_systems_of_particles.tex │ ├── 11_applications_of_orbits.tex │ ├── 12_rigid_bodies.tex │ ├── 13_special_relativity.tex │ ├── 14_space_time_diagrams_simultaneity_and_causality.tex │ ├── 15_geometry_of_spacetime.tex │ ├── 16_relativistic_physics.tex │ ├── import.tex │ └── main.tex ├── groups │ ├── 01_axiomatic_definition.tex │ ├── 02_homomorphisms.tex │ ├── 03_types_of_groups.tex │ ├── 04_permutation_groups.tex │ ├── 05_m_obius_transformations.tex │ ├── 06_cosets_and_lagrange_s_theorem.tex │ ├── 07_normal_subgroups_and_quotients.tex │ ├── 08_isomorphism_theorems.tex │ ├── 09_group_actions.tex │ ├── 10_conjugation.tex │ ├── 11_action_of_the_m_obius_group.tex │ ├── 12_matrix_groups.tex │ ├── 13_groups_of_order_8.tex │ ├── import.tex │ └── main.tex ├── ns │ ├── 01_proofs.tex │ ├── 02_elementary_number_theory.tex │ ├── 03_modular_arithmetic.tex │ ├── 04_the_reals.tex │ ├── 05_sets.tex │ ├── 06_functions.tex │ ├── 07_countability.tex │ ├── import.tex │ └── main.tex ├── probability │ ├── 01_probability_spaces.tex │ ├── 02_inclusion_exclusion.tex │ ├── 03_independence_and_dependence_of_events.tex │ ├── 04_discrete_distributions.tex │ ├── 05_discrete_random_variables.tex │ ├── 06_variance_and_covariance.tex │ ├── 07_inequalities_for_random_variables.tex │ ├── 08_combinations_of_random_variables.tex │ ├── 09_random_walks.tex │ ├── 10_probability_generating_functions.tex │ ├── 11_branching_processes.tex │ ├── 12_continuous_random_variables.tex │ ├── 13_multivariate_density_functions.tex │ ├── 14_moment_generating_functions.tex │ ├── 15_limit_theorems.tex │ ├── 16_gaussian_vectors.tex │ ├── 17_simulation_of_random_variables.tex │ ├── import.tex │ └── main.tex ├── vc │ ├── 01_differential_geometry_of_curves.tex │ ├── 02_coordinates_differentials_and_gradients.tex │ ├── 03_integration_over_lines.tex │ ├── 04_integration_in_euclidean_space.tex │ ├── 05_integration_over_surfaces.tex │ ├── 06_differential_operators.tex │ ├── 07_integral_theorems.tex │ ├── 08_maxwell_s_equations.tex │ ├── 09_poisson_s_and_laplace_s_equations.tex │ ├── 10_cartesian_tensors.tex │ ├── 11_tensor_calculus.tex │ ├── 12_properties_of_tensors.tex │ ├── import.tex │ └── main.tex ├── vm │ ├── 01_complex_numbers.tex │ ├── 02_vectors_in_three_dimensions.tex │ ├── 04_index_notation_and_the_summation_convention.tex │ ├── 05_vectors_in_real_euclidean_space.tex │ ├── 08_linear_maps.tex │ ├── 09_transpose_and_hermitian_conjugate.tex │ ├── 10_adjugates_and_alternating_forms.tex │ ├── 11_determinant.tex │ ├── 13_eigenvalues_and_eigenvectors.tex │ ├── 16_quadratic_forms.tex │ ├── 17_cayley_hamilton_theorem.tex │ ├── 18_changing_bases.tex │ ├── 19_conics_and_quadrics.tex │ ├── 20_symmetries_and_transformation_groups.tex │ ├── import.tex │ └── main.tex ├── vol1 │ └── main.tex └── vol2 │ └── main.tex ├── ib ├── antop │ ├── 01_uniform_convergence.tex │ ├── 02_uniform_continuity.tex │ ├── 03_metric_spaces.tex │ ├── 04_topology_of_metric_spaces.tex │ ├── 05_completeness.tex │ ├── 06_contraction_mapping_theorem.tex │ ├── 07_topology.tex │ ├── 08_connectedness.tex │ ├── 09_compactness.tex │ ├── 10_differentiation.tex │ ├── 11_partial_derivatives.tex │ ├── 12_second_derivatives.tex │ ├── import.tex │ └── main.tex ├── book │ └── main.tex ├── ca │ ├── 01_differentiation.tex │ ├── 02_integration.tex │ ├── 03_more_integration.tex │ ├── 04_singularities.tex │ ├── 05_argument_principle.tex │ ├── import.tex │ └── main.tex ├── geom │ ├── 01_surfaces.tex │ ├── 02_smooth_surfaces.tex │ ├── 03_smooth_surfaces_in_R3.tex │ ├── 04_geometry_of_surfaces.tex │ ├── 05_geodesics.tex │ ├── 06_riemannian_metrics.tex │ ├── double_torus_polygon.tikz │ ├── double_torus_polygon_expanded.tikz │ ├── hexagon.tikz │ ├── hyperbolic_angles_at_centre.tikz │ ├── hyperbolic_general_triangle.tikz │ ├── hyperbolic_slide.tikz │ ├── hyperbolic_triangle_sum.tikz │ ├── import.tex │ ├── main.tex │ ├── mobius_band.tikz │ ├── other_square_polygon.tikz │ ├── right_angled_hexagon.tikz │ ├── rp2_polygon.tikz │ ├── s2_degenerate.tikz │ ├── torus_polygon.tikz │ ├── torus_polygon_subdivided.tikz │ ├── torus_polygon_triangulated.tikz │ ├── torus_polygon_with_loop.tikz │ ├── triangle_fan.tikz │ └── triangulation_local_move.tikz ├── grm │ ├── 01_review.tex │ ├── 02_simple_groups.tex │ ├── 03_group_actions.tex │ ├── 04_alternating_groups.tex │ ├── 05_p_groups.tex │ ├── 06_matrix_groups.tex │ ├── 07_finite_abelian_groups.tex │ ├── 08_rings.tex │ ├── 09_factorisation.tex │ ├── 10_algebraic_integers.tex │ ├── 11_noetherian_rings.tex │ ├── 12_modules.tex │ ├── import.tex │ └── main.tex ├── linalg │ ├── 01_vector_spaces_and_linear_dependence.tex │ ├── 02_linear_maps.tex │ ├── 03_dual_spaces.tex │ ├── 04_bilinear_forms.tex │ ├── 05_trace_and_determinant.tex │ ├── 06_adjugate_matrices.tex │ ├── 07_eigenvectors_and_eigenvalues.tex │ ├── 08_jordan_normal_form.tex │ ├── 09_properties_of_bilinear_forms.tex │ ├── 10_inner_product_spaces.tex │ ├── import.tex │ └── main.tex ├── markov │ ├── 01_introduction.tex │ ├── 02_elementary_properties.tex │ ├── 03_transience_and_recurrence.tex │ ├── 04_p_olya_s_recurrence_theorem.tex │ ├── 05_invariant_distributions.tex │ ├── import.tex │ └── main.tex ├── methods │ ├── 01_fourier_series.tex │ ├── 02_sturm_liouville_theory.tex │ ├── 03_separation_of_variables.tex │ ├── 04_green_s_functions.tex │ ├── 05_fourier_transforms.tex │ ├── 06_method_of_characteristics.tex │ ├── 07_solving_partial_differential_equations_with_green_s_functions.tex │ ├── import.tex │ └── main.tex ├── opt │ ├── 01_introduction_and_convex_functions.tex │ ├── 02_optimisation_algorithms.tex │ ├── 03_lagrange_multipliers.tex │ ├── 04_linear_programming.tex │ ├── 05_duality_in_linear_programming.tex │ ├── 06_simplex_method.tex │ ├── 07_game_theory.tex │ ├── 08_network_flows.tex │ ├── 09_the_transport_algorithm.tex │ ├── 10_maximum_flow_minimum_cut.tex │ ├── import.tex │ └── main.tex ├── quantum │ ├── 01_historical_introduction.tex │ ├── 02_wavefunctions.tex │ ├── 03_observables_and_operators.tex │ ├── 04_one_dimensional_solutions_to_the_schr_odinger_equation.tex │ ├── 05_operators_and_measurements.tex │ ├── 06_three_dimensional_solutions_to_the_schr_odinger_equation.tex │ ├── 07_solution_to_hydrogen_atom.tex │ ├── import.tex │ └── main.tex ├── stats │ ├── 01_introduction_and_review.tex │ ├── 02_estimation.tex │ ├── 03_inference.tex │ ├── 04_bayesian_analysis.tex │ ├── 05_hypothesis_testing.tex │ ├── 06_normal_linear_model.tex │ ├── import.tex │ └── main.tex ├── vol3 │ └── main.tex ├── vol4 │ └── main.tex └── vp │ ├── 01_history_and_motivation.tex │ ├── 02_calculus_for_functions_on_mathbb_r_n_.tex │ ├── 03_euler_lagrange_equation.tex │ ├── 04_extensions_to_the_euler_lagrange_equation.tex │ ├── 05_noether_s_theorem.tex │ ├── 06_convexity_and_the_legendre_transform.tex │ ├── 07_second_variations.tex │ ├── import.tex │ └── main.tex ├── ii ├── afl │ ├── 01_introduction.tex │ ├── 02_rewrite_systems.tex │ ├── 03_regular_languages.tex │ ├── 04_context_free_languages.tex │ ├── 05_register_machines.tex │ ├── 06_computability_theory.tex │ ├── import.tex │ └── main.tex ├── alggeom │ ├── 01_affine_varieties.tex │ ├── 02_structures_on_varieties.tex │ ├── 03_projective_varieties.tex │ ├── 04_dimension.tex │ ├── 05_algebraic_curves.tex │ ├── 06_differentials.tex │ ├── import.tex │ └── main.tex ├── algtop │ ├── 01_motivation.tex │ ├── 02_homotopy.tex │ ├── 03_groups_from_loops.tex │ ├── 04_covering_spaces.tex │ ├── 05_seifert_van_kampen_theorem.tex │ ├── 06_simplicial_complexes.tex │ ├── 07_simplicial_homology.tex │ ├── im_homotopy.tikz │ ├── import.tex │ └── main.tex ├── book │ └── main.tex ├── cc │ ├── 00_modelling_communication.tex │ ├── 01_noiseless_coding.tex │ ├── 02_noisy_channels.tex │ ├── 03_information_theory.tex │ ├── 04_algebraic_coding_theory.tex │ ├── 05_cryptography.tex │ ├── import.tex │ └── main.tex ├── galois │ ├── 01_polynomials.tex │ ├── 02_fields.tex │ ├── 03_types_of_extensions.tex │ ├── 04_galois_theory.tex │ ├── 05_finite_fields.tex │ ├── 06_cyclotomic_extensions.tex │ ├── 07_trace_and_norm.tex │ ├── 08_algebraic_closure.tex │ ├── 09_solving_polynomial_equations.tex │ ├── 10_miscellaneous_results.tex │ ├── import.tex │ └── main.tex ├── graph │ ├── 01_introduction.tex │ ├── 02_connectivity_and_matching.tex │ ├── 03_colouring.tex │ ├── 04_extremal_graph_theory.tex │ ├── 05_ramsey_theory.tex │ ├── 06_random_graphs.tex │ ├── 07_algebraic_graph_theory.tex │ ├── import.tex │ ├── k7_torus.tikz │ └── main.tex ├── lst │ ├── 01_propositional_logic.tex │ ├── 02_well_orderings.tex │ ├── 03_posets.tex │ ├── 04_predicate_logic.tex │ ├── 05_set_theory.tex │ ├── 06_cardinals.tex │ ├── 07_incompleteness.tex │ ├── import.tex │ └── main.tex ├── nf │ ├── 01_number_fields.tex │ ├── 02_ideals.tex │ ├── 03_geometry_of_numbers.tex │ ├── 04_dirichlet_unit_theorem.tex │ ├── 05_dirichlet_series.tex │ ├── import.tex │ └── main.tex ├── pm │ ├── 01_measures.tex │ ├── 02_measurable_functions.tex │ ├── 03_integration.tex │ ├── 04_product_measures.tex │ ├── 05_function_spaces_and_norms.tex │ ├── 06_fourier_analysis.tex │ ├── 07_ergodic_theory.tex │ ├── import.tex │ └── main.tex ├── qic │ ├── 01_mathematical_background.tex │ ├── 02_quantum_states_as_information_carriers.tex │ ├── 03_quantum_cryptography.tex │ ├── 04_quantum_computation.tex │ ├── import.tex │ └── main.tex ├── vol5 │ └── main.tex └── vol6 │ └── main.tex ├── iii ├── alggeom │ ├── 01_introduction.tex │ ├── 02_sheaves.tex │ ├── 03_schemes.tex │ ├── 04_morphisms.tex │ ├── 05_modules_over_the_structure_sheaf.tex │ ├── 06_divisors.tex │ ├── 07_sheaf_cohomology.tex │ ├── import.tex │ └── main.tex ├── book │ └── main.tex ├── cat │ ├── 01_definitions_and_examples.tex │ ├── 02_yoneda_lemma.tex │ ├── 03_adjunctions.tex │ ├── 04_limits.tex │ ├── 05_monads.tex │ ├── 06_monoidal_and_enriched_categories.tex │ ├── 07_additive_and_abelian_categories.tex │ ├── import.tex │ └── main.tex ├── commalg │ ├── 01_chain_conditions.tex │ ├── 02_tensor_products.tex │ ├── 03_localisation.tex │ ├── 04_integrality_finiteness_finite_generation.tex │ ├── 05_primary_decomposition.tex │ ├── 06_direct_and_inverse_limits.tex │ ├── 07_dimension_theory.tex │ ├── import.tex │ └── main.tex ├── forcing │ ├── 01_set_theory.tex │ ├── 02_constructibility.tex │ ├── 03_forcing.tex │ ├── 04_forcing_and_independence.tex │ ├── import.tex │ └── main.tex ├── gc │ ├── 01_definitions_and_resolutions.tex │ ├── 02_low_degree_cohomology.tex │ ├── import.tex │ └── main.tex ├── lc │ ├── 01_inaccessible_cardinals.tex │ ├── 02_medium_large_cardinals.tex │ ├── 03_reflection.tex │ ├── 04_large_large_cardinals.tex │ ├── import.tex │ └── main.tex ├── mtncl │ ├── 01_substructures.tex │ ├── 02_quantifier_elimination.tex │ ├── 03_ultraproducts.tex │ ├── 04_types.tex │ ├── 05_indiscernibles.tex │ ├── 06_intuitionistic_logic.tex │ ├── 07_intuitionistic_semantics.tex │ ├── import.tex │ └── main.tex ├── vol7 │ 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