Technical Books

This note describes the following topics, Metric spaces, Topological spaces, Products, sequential continuity and nets, Compactness, Tychonoffs theorem and the separation axioms, Connectedness and local compactness, Paths, homotopy and the fundamental group, Retractions and homotopy equivalence, Van Kampens theorem, Normal subgroups, generators and relations, The Seifertvan Kampen theorem and of surfaces, Torus knots, The lifting theorem, The universal cover and group actions, Manifolds, Surfaces and triangulations, Orientations and higher homotopy groups, Bordism groups and simplicial homology, Singular homology, Relative homology and long exact sequences, Homotopy invariance and excision, The homology of the spheres, Excision, The EilenbergSteenrod axioms, The MayerVietoris sequence, Mapping tori and the degree of maps, ocal mapping degree on manifolds Degrees, triangulations and coefficients, CWcomplexes, Invariance of cellular homology.

This PDF covers the following topics related to Topology, Topology of Metric Spaces, Topological Spaces, Basis for a Topology, Topology Generated by a Basis, Infinitude of Prime Numbers, Product Topology, Subspace Topology, Closed Sets, Hausdorff Spaces, and Closure of a Set, Continuous Functions, A Theorem of Volterra Vito, Homeomorphisms, Product, Box, and Uniform Topologies, Compact Spaces, Quotient Topology, Connected and Pathconnected Spaces, Compactness Revisited, Countability Axioms, Separation Axioms, Tychonoffs Theorem.

This note covers topological spaces, Continuous functions, Compact topological spaces, Compact metric spaces, Separability axioms and theorems, Metrizations.

This note contains below topics, Heegaard splittings, Generalized Heegaard splittings, Show Remark, Hence we have Claim, We give a proof of Proposition, By Lemma, Show the claim in the proof of Theorem, We prove Theorem, It follows from Lemma.

This note contains below topics, Introduction and survey of main results, Some notation and general tools, Applications of strict Cldfans in General Topology, SFans Ssemifans and Dcofans in topological spaces, Strong Finfans in functions spaces, Strong Finfans in locally convex and Banach spaces with the weak topology, Topological functors and their properties, Constructing Finfans in topological algebras, Constructing fans in free universal algebras, Free objects in some varieties of topologized algebras.

This is a review of the fundamental concepts of general topology. This note contains below topics, Topological Spaces, Continuous Maps, Connectedness, Separation Axioms, Compactness, A Taste of Topology in Functional Analysis.

This note contains below topics, is a prere quisite for almost everything else, while some of the later parts o, are u sed in, Canonical Decomposition, Prime Decomposition, Torus Decomposition, Seifert Manifolds, Torus Bundles and SemiBundles, Homotopy Properties, Canonical Decomposition The rst section of this.

This PDF covers the following topics related to Calculus : Functions and Graphs, Limits, Derivatives, Applications of Derivatives, Integration.

This PDF covers the following topics related to Calculus : Algebra or Precalculus Review, Limits, Computing Limits, Introduction to Derivatives, Elementary Differentiation Rules, Intermediate Differentiation Rules, Optimization Analysis, Other Applications of Differentiation, Theory of the Definite Integral, Integration Rules, Introduction to Differential Equations.

This note covers introduction, Conceptual framework, Research questions and methodology, Forms and functions of proof in mathematics and I mathematics education, the historical development of the FTC and its proof, The mathematicians views, Outcomes and conclusions.

The aim is to introduce fundamental concepts and techniques in set theory in preparation for its many applications in computer science. Topics covered includes, Mathematical argument, Sets and Logic, Relations and functions, Constructions on sets, Inductive definitions, Wellfounded induction, Inductivelydefined classes and FraenkelMostowski sets.

Set theory is the branch of mathematical logic that studies sets, which informally are collections of objects. Topics covered includes, The Axioms of Set Theory, The Natural Numbers, The Ordinal Numbers, Relations and Orderings, Cardinality, There Is Nothing Real About The Real Numbers, The Universe, Reflection, Elementary Submodels and Constructibility.

This note covers the following topics, Logic, Elementary Set Theory, Generic Sets And Forcing, Infinite Combinatorics, Pcf, Continuum Cardinals.

This note explains the following topics, The language of set theory and wellformed formulas, Classes vs. Sets, Notational remarks, Some axioms of ZFC and their elementary, Consequences, From Pairs to Products, Relations, Functions, Products and sequences, Equivalence Relations and Order Relations, Equivalence relations, partitions and transversals, A Game of Thrones, Prisoners and Hats, Wellorders, Wellfounded relations and the Axiom of Foundation, Natural Numbers, The construction of the set of natural numbers, Arithmetic on the set of natural numbers, Equinumerosity, Finite sets, To infinity and beyond, Construction of various number systems, Integers, Rational numbers, Real numbers, Ordinal numbers.

This note covers the following topics, Classical Descriptive Set Theory, Polish Spaces, Borel Sets, Effective Descriptive Set Theory, The Arithmetic Hierarchy, Analytic Sets, Coanalytic Sets, Determinacy, Hyperarithmetic Sets, Borel Equivalence Relations, Equivalence Relations, Tame Borel Equivalence Relations, Countable Borel Equivalence Relations, Hyperfinite Equivalence Relations.