Technical Books

This note covers the following topics, Primary Decomposition, Filtrations and Completions, Dimension Theory, Integral Extensions, Homological Methods, Depth and Cohen Macaulay Modules, Injective Modules over Noetherian Rings, Local Cohomology, Applications and Generalizations.

This note explains the following topics, Polynomial algebras, Localisation, Dimension theory, Discrete valuation rings.

This note covers basic notions, Local properties, Integral dependence, valuations and completions, Noetherian rings and modules, Dedekind domains, Dimension theory.

This note contains below topics, The Frobenius Map for Rings the local theory, Frobenius for Schemes the Global Theory, The Test Ideal, Test Ideals for Pairs, So what does CohenMacaulay mean.

The purpose of this note is to give students a broad exposure to combinatorial mathematics, using applications to emphasize fundamental concepts and techniques. Topics covered includes, Introduction to Combinatorics, Strings, Sets, and Binomial Coefficients, Induction, Combinatorial Basics, Graph Theory, Partially Ordered Sets, Generating Functions, Recurrence Equations, Probability, Applying Probability to Combinatorics, Combinatorial Applications of Network Flows, Polyas Enumeration Theorem.

This book will bring enjoyment to many future generations of mathematicians and aspiring mathematicians as they are exposed to the beauties and pleasures of enumerative combinatorics. Topics covered includes, What is Enumerative Combinatorics, Sieve Methods, Partially Ordered Sets, Rational Generating Functions, Graph Theory Terminology.

The contents of this book include, Selections and arrangements, Power series, Recurrence relations, Partitions and permutations, The Principle of Inclusion and Exclusion, Families of sets, Systems of distinct representatives, Latin squares, Steiner triple systems.

This book explains the following topics, Diagram Algebras and Hopf Algebras, Group Representations, SnRepresentations Intro, Decomposition and Specht Modules, Fundamental Specht Module Properties and Branching Rules, Representation Ring for Sn and its Pieri Formula, Pieri for Schurs, Kostka Numbers, Dual Bases, Cauchy Identity, Finishing Cauchy, LittlewoodRichardson Rule, Frobenius Characteristic Map, Algebras and Coalgebras, Skew Schur Functions and Comultiplication, Sweedler Notation, kCoalgebra Homomorphisms, Subcoalgebras, Coideals, Bialgebras, Bialgebra Examples, Hopf Algebras Defined, Properties of Antipodes and Takeuchis Formula, etc.

The contents of this book include, Basic Counting, Counting with Signs, Counting with Ordinary Generating Functions, Counting with Exponential Generating Functions, Counting with Partially Ordered Sets, Counting with Group Actions, Counting with Symmetric Functions, Counting with Quasisymmetric Functions, Introduction to Representation Theory.

Combinatotics is about counting without really counting all possible cases one by one. This PDF covers the following topics related to Combinatorics, Introduction, The Pigeonhole Principle, The Principle of Extremals, The Principle of Invariants, Permutations and Combinations, Combinations with Repetition, InclusionExclusion principle, Recurrence Relations, Generating Functions, Partitions of Natural Numbers.

This PDF covers the following topics related to Combinatorics, Introduction, Enumeration, Sequences and the Multiplication Principle, Permutations and Combinations, Bijections and Double Counting, Estimation, InclusionExclusion, Generating Functions, Formal Power Series, Generating Functions Redux, Change making, Compositions, Counting Subsets, Counting Strings, The Probabilistic Method, Preliminaries, The first moment method, Linearity of expectation, Alterations, Markov and Chebyshev, Chernoff Bound, Lovasz Local Lemma, Extremal Graph Theory, Turans Theorem, Projective planes, Sidon sets, Constructing C4free graphs, Ramsey numbers, Combinatorial Number Theory, Erd osKoRado Theorem, Spectral graph theory, Linear Algebra Preliminaries, The adjacency matrix, Short proofs of old results using spectral graph theory, The GrahamPollak Theorem, The ExpanderMixing Lemma, The HoffmanSingleton Theorem.

This PDF book Combinatorics of Centers of 0Hecke Algebrasin Type A covers the following topics related to Combinatorics, Introduction, Preliminaries, Coxeter groups, The symmetric group, Combinatorics, enters of 0Hecke algebras, Elements in stair form, Equivalence classes, etc.

This PDF book covers the following topics related to Combinatorics, What is Combinatorics, Basic Counting Techniques, Permutations, Combinations, and the Binomial Theorem, Bijections and Combinatorial Proofs, Counting with Repetitions, Induction and Recursion, Generating Functions, Generating Functions and Recursion, Some Important RecursivelyDefined Sequences, Other Basic Counting Techniques, Basics of Graph Theory, Moving through graphs,Euler and Hamilton, Graph Colouring, Planar graphs, Latin squares, Designs, More designs, Designs and Codes.

This book describes the following topics, The Derangements Problem, Binomial coefficients, Principle of Inclusion and Exclusion, Rook Polynomials, Recurrences and asymptotics, Convolutions and the Catalan Numbers, Exponential generating functions, Ramsey Theory, Lovasz Local Lemma.

This book contains below topics, What is combinatorics, Counting principles, Counting combinations, Pascals triangle and the Binomial Theorem, Proof Techniques in Combinatorics, Recurrence relations, Generating Functions, Graph Theory Basics, Trees, Graph optimization, Planar Graphs, Graph Coloring.