Technical Books

The goal of this book is to present several central topics in geometric group theory, primarily related to the large scale geometry of infinite groups and spaces on which such groups act, and to illustrate them with fundamental theorems such as Gromov�s Theorem on groups of polynomial growth. Topics covered includes: Geometry and Topology, Metric spaces, Differential geometry, Hyperbolic Space, Groups and their actions, Median spaces and spaces with measured walls, Finitely generated and finitely presented groups, Coarse geometry, Coarse topology, Geometric aspects of solvable groups, Gromov�s Theorem, Amenability and paradoxical decomposition, Proof of Stallings� Theorem using harmonic functions.

Group Theory can be viewed as the mathematical theory that deals with symmetry, where symmetry has a very general meaning. This PDF book covers the following topics related to Group Theory : Introduction, Definitions and basic properties, Direct products and abelian groups, Composition series and solvable groups, Permutation groups and group actions, Finite groups and Sylow Theory, Semidirect products and groups of order less than 15.

This note describes the following topics: Abstract Group Theory, Theory of Group Representations, Group Theory in Quantum Mechanics, Lie Groups, Atomic Physics, The Group SU2: Isospin, The Point Groups, The Group SU3.

This note explains the following topics: mapping, Basic algebra, Modular arithmetic, Groups, Cosets and Lagranges theorem, Isomorphisms and quotient group, The permutation group Sn, Finite abelian groups, Group actions, Group solvability and the semi direct product.

This note covers Notation for sets and functions, Basic group theory, The symmetric group, Group actions, Linear groups, Affine groups, Projective groups, Abelian groups, Finite linear groups, Sylow theorems and applications, Solvable and nilpotent groups, p groups, a second look, Presentations of groups, Building new groups from old.

The focus of this book is on applications and the aim is to improve the problem solving skills of the students through numerous wellexplained examples. Topics covered includes, General Theory, Shortest Paths, Euler Tours and The Chinese Postman Problem, Spanning Trees, Matchings and Coverings, Benzenoids, Network Flow and Electrical Network.

This note covers the following topics, Basic theory about graphs, Connectivity, Paths, Trees, Networks and flows, Eulerian and Hamiltonian graphs, Coloring problems and Complexity issues, A number of applications, Large scale problems in graphs, Similarity of nodes in large graphs, Telephony problems and graphs, Ranking in large graphs, Clustering of large graphs.

This note explains the following topics, Theorems, Representations of Graphs, Data Structures, Traversal, Eulerian and Hamiltonian Graphs, Graph Optimization, Planarity and Colorings.

This PDF book covers the following topics related to Graph Theory, Introduction, Paths and Circuits, Trees and Fundamental Circuits, Cutsets and Cutvertices, Planar and Dual Graphs, Vector Spaces of a Graph, Matrix Representation of Graphs, Coloring, Covering, and Partitioning, Directed Graphs, Enumeration of Graphs, Graph Theoretic Algorithms and Computer, Graphs in Switching and Coding Theory, Electrical Network Analysis by Graph Theory, Graph Theory in Operations Research, Survey of Other Applications, Binetcauchy Theorem, Nullity of a Matrix and Sylvesters Law.

This note covers basics, Proofs, Constructions, Algorithms and applications, Bipartite graphs and trees, Eulerian and Hamiltonian graphs, Coloring, Planar graphs, Digraphs and connectivity.

This note explains introduction to graphs, The very basics, Spanning trees, Extremal graph theory, Matchings, covers and factor, Flows on networks, vertex and edge connectivity, Chromatic number and polynomials, Graphs and matrices and planar graphs.

This note contains below topics, Properties of the Greens functions, Local law for random dregular graphs, Edge universality, Local resampling, Concentration via exchangeable pair, Expectation of Qz, Switching edges the forest and admissible functions, Switching using the Schur complement formula, Switching using the Woodbury formula, Proof for the selfconsistent equation, Proof of the first loop equation, Error from local resampling.

This note contains below topics, GRAPHS AND GRAPH LAPLACIANS, BASIC F ACTS, SPECTRAL GRAPH DRA WING, SPECTRAL GRAPH DRA WING Example.

This book contains below topics, The cycle graph Cn has n vertices, and it is regular of degree, We claim that, in fact, They also have the same chromatic number, Two views of the octahedral graph FIGURE, Two views of the icosahedral graph FIGURE, The degree is d, The verication is left to the reader.

This book contains below topics, Lets Define the graph of ndimensional cube by following, Adjacency matrix is symmetrical for undirected graph, Adjacency matrix always square matrix, Incidence matrix is rectangular matrix with dimensions V E, A graph contains a cycle iff it contains a simple cycle Proof, If a graph contains a simple cycle then it obviously contains a cycle, Necessarity Holds from theorem, Laplacian matrix is symmetrical matrix, Laplacian matrix is square matrix, Laplacian matrix is degenerate matrix, rk L G n, the sum of rows of the matrix K equals.