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Contents

Preface - Preface to the Second Edition - Introduction - Fundamentals of Unconstrained Optimization - Line 

Search Methods - Trust-Region Methods - Conjugate Gradient Methods - Quasi-Newton Methods - Large-

Scale Unconstrained Optimization - Calculating Derivatives - Derivative-Free Optimization - Least-Squares 

Problems - Nonlinear Equations - Theory of Constrained Optimization - Linear Programming: The Simplex 

Method - Linear Programming: Interior-Point Methods - Fundamentals of Algorithms for Nonlinear 

Constrained Optimization - Quadratic Programming - Penalty and Augmented Lagrangian Methods - 

Sequential Quadratic Programming - Interior-Point Methods for Nonlinear Programming - Background 

Material - Regularization Procedure.

Queueing Theory: A Linear Algebraic Approach, 2e

Lester Lipsky,  University of Connecticut, Storrs, CT, USA



About the Book

Queueing Theory deals with systems where there is contention for resources, but the demands are only 

known probabilistically. This book can be considered to be a monograph or a textbook, and thus is aimed 

at two audiences: those who already know Queueing Theory but would like to know more of the Linear 

Algebraic Approach; and as a rst course for students who don't already have a strong background in 

probability, and feel more comfortable with algebraic arguments. Also, the equations are well suited to 

easy computation. In fact, there is much discussion on how various properties can be easily computed 

in any language that has automatic matrix operations (e.g., MATLAB). To help with physical insight, there 

are over 80 gures, numerous examples and exercises distributed throughout the book. There are, perhaps 

50 books on QT that are available today, and most practitioners have several of them on their shelves. 

This book would be a good addition, as well as a good supplement to another text. This second edition 

has been updated throughout including a new chapter on Semi Markov Processes and new material on 

matrix representations of distributions and Power-tailed distribution. Lester Lipsky is a Professor in the 

Department of Computer Science and Engineering at the University of Connecticut.



Contents

Introduction - M/M/1 Queue - Matrix Exponential Functions - M/G/1 Queue - G/M/1 Queue - M/G/C-Type 

Systems - G/G/1//N Loop - Semi-Markov Processes - Linear Algebraic Approach - Glossary - References - 

Index.


ISBN: 9788132204800

Page:  XXII, 664 p. 85 

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ISBN: 9788132204770

Page:  XXII, 554 p.

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Stochastic Calculus for Finance I

Steven E. Shreve,  Carnegie Mellon University, Pittsburgh, PA, USA



About the Book

Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's 

program in Computational Finance. The content of this book has been used successfully with students 

whose mathematics background consists of calculus and calculus-based probability. The text gives 

both precise statements of results, plausibility arguments, and even some proofs, but more importantly 

intuitive explanations developed and refine through classroom experience with this material are provided. 

The book includes a self-contained treatment of the probability theory needed for stochastic calculus, 

including Brownian motion and its properties. Advanced topics include foreign exchange models, forward 

measures, and jump-diffusion processes. This book is being published in two volumes. The first volume 

presents the binomial asset-pricing model primarily as a vehicle for introducing in the simple setting the 

concepts needed for the continuous-time theory in the second volume. Chapter summaries and detailed 

illustrations are included. Classroom tested exercises conclude every chapter. Some of these extend the 

theory and others are drawn from practical problems in quantitative finance. Advanced undergraduates 

and Masters level students in mathematical finance and financial engineering will find this book useful. 

Steven E. Shreve is Co-Founder of the Carnegie Mellon MS Program in Computational Finance and winner 

of the Carnegie Mellon Doherty Prize for sustained contributions to education.



Contents

The Binomial No-Arbitrage Pricing Model - Probability Theory on Coin-Toss Space - State Prices - American 

Derivative Securities - Random Walk - Interest rate dependent assets.

Stochastic Calculus for Finance II

Steven E. Shreve,  Carnegie Mellon University, Pittsburgh, PA, USA



About the Book

Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's 

program in Computational Finance. The content of this book has been used successfully with students 

whose mathematics background consists of calculus and calculus-based probability. The text gives 

both precise statements of results, plausibility arguments, and even some proofs, but more importantly 

intuitive explanations developed and refine through classroom experience with this material are provided. 

The book includes a self-contained treatment of the probability theory needed for stochastic calculus, 

including Brownian motion and its properties. Advanced topics include foreign exchange models, forward 

measures, and jump-diffusion processes. This book is being published in two volumes. This second volume 

develops stochastic calculus, martingales, risk-neutral pricing, exotic options and term structure models, 

all in continuous time. Master's level students and researchers in mathematical finance and financial 

engineering will find this book useful.



Contents

General Probability Theory.- Information and Conditioning.- Brownian Motion.- Stochastic Calculus.- Risk 

Neutral Pricing.- Connections with Partial Differential Equations.- Exotic Options.- Early Exercise.- Change 

of Numeraire.- Term Structure Models.- Introduction to Jump Processes.



ISBN: 9788184892727

Page:  XVI, 187 p. 33 

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ISBN: 9788184892864

Page:  XIX, 550 p. 28 

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The Mathematical Theory of Finite Element Methods, 3e

Susanne C. Brenner,  Louisiana State University, Baton Rouge, LA, USA

Ridgway Scott,  University of Chicago, IL, USA

About the Book

This book develops the basic mathematical theory of the finite element method, the most widely used 

technique for engineering design and analysis. It formalizes basic tools that are commonly used by 

researchers in the field but not previously published. The book will be useful to mathematicians as well 

as engineers and physical scientists. It can be used for a course that provides an introduction to basic 

functional analysis, approximation theory, and numerical analysis, while building upon and applying basic 

techniques of real variable theory. Different course paths can be chosen, allowing the book to be used 

for courses designed for students with different interests. For example, courses can emphasize physical 

applications, or algorithmic efficiency and code development issues, or the more difficult convergence 

theorems of the subject. This new edition is substantially updated with additional exercises throughout 

and new chapters on Additive Schwarz Preconditioners and Adaptive Meshes. Review of earlier edition: 

“This book represents an important contribution to the mathematical literature of finite elements. It is 

both a well-done text and a good reference.”  Mathematical Reviews, 1995.

Contents

Preface(3rdEd) - Preface(2ndEd) - Preface(1stED) - Basic Concepts - Sobolev Spaces - Variational Formulation 

of Elliptic Boundary Value Problems - The Construction of a Finite Element of Space - Polynomial 

Approximation Theory in Sobolev Spaces - n-Dimensional Variational Problems - Finite Element Multigrid 

Methods - Additive Schwarz Preconditioners - Max-norm Estimates - Adaptive Meshes - Variational Crimes 

- Applications to Planar Elasticity - Mixed Methods - Iterative Techniques for Mixed Methods - Applications 

of Operator-Interpolation Theory - References - Index.

ISBN: 9788132204756

Page:  XVIII, 402 p. 50 

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Price: ` 

459.00


Market: Open

Reprint Year: Nov-11

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Algebraic Graph Theory

Chris Godsil,  University of Waterloo, ON, Canada

Gordon F. Royle,  University of Western Australia, Nedlands, WA, Australia

About the Book

Algebraic graph theory is a combination of two strands. The first is the study of algebraic objects associated 

with graphs. The second is the use of tools from algebra to derive properties of graphs. The authors' goal 

has been to present and illustrate the main tools and ideas of algebraic graph theory, with an emphasis 

on current rather than classical topics. While placing a strong emphasis on concrete examples, the authors 

tried to keep the treatment self-contained.



Contents

Graphs -  Groups -  Transitive Graphs -  Arc-Transitive Graphs -  Generalized Polygons and Moore Graphs 

-  Homomorphisms -  Kneser Graphs -  Matrix Theory -  Interlacing -  Strongly Regular Graphs -  Two-Graphs 

-  Line Graphs and Eigenvalues -  The Laplacian of a Graph -  Cuts and Flows -  The Rank Polynomial -  Knots 

-  Knots and Eulerian Cycles -  Glossary of Symbols -  Index.

Graph Theory

Adrian Bondy,  Université Claude-Bernard Lyon, France

U.S.R. Murty,  University of Waterloo, ON, Canada

About the Book

"Graph theory is a flourishing discipline containing a body of beautiful and powerful theorems of 

wide applicability. Its explosive growth in recent years is mainly due to its role as an essential structure 

underpinning modern applied mathematics – computer science, combinatorial optimization, and 

operations research in particular – but also to its increasing application in the more applied sciences. 

The versatility of graphs makes them indispensable tools in the design and analysis of communication 

networks, for instance.

The primary aim of this book is to present a coherent introduction to the subject, suitable as a textbook 

for advanced undergraduate and beginning graduate students in mathematics and computer science. 

It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic 

appeal. Commonly used proof techniques are described and illustrated, and a wealth of exercises - of 

varying levels of difficulty - are provided to help the reader master the techniques and reinforce their 

grasp of the material.

A second objective is to serve as an introduction to research in graph theory. To this end, sections on more 

advanced topics are included, and a number of interesting and challenging open problems are highlighted 

and discussed in some detail. Despite this more advanced material, the book has been organized in such 

a way that an introductory course on graph theory can be based on the first few sections of selected 

chapters."



Contents

Graphs - Subgraphs - Connected Graphs - Trees - Nonseparable Graphs - Tree-Search Algorithms - Flows 

in Networks - Complexity of Algorithms - Connectivity - Planar Graphs - The Four-Colour Problem - Stable 

Sets and Cliques - The Probabilistic Method - Vertex Colourings - Colourings of Maps - Matchings - Edge 

Colourings - Hamilton Cycles - Coverings and Packings in Directed Graphs - Electrical Networks - Integer 

Flows and Coverings - Unsolved Problems - References - General Mathematical Notation - Graph Parameters 

- Operations and Relations - Families of Graphs - Structures - Other Notation - Index.

ISBN: 9788181282620

Page:  XIX, 439 p. 120 

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Reprint Year: Mar-05

ISBN: 9788132210740

Page:  XII, 654 p. 235 

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Price: ` 

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Market: ANE

Reprint Year: Dec-12

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Graphs and Applications: An Introductory Approach 

Joan M. Aldous,  The Open University, Milton Keynes, UK

Robin J. Wilson,  The Open University, Milton Keynes, UK

About the Book

Discrete Mathematics is one of the fastest growing areas in mathematics today with an ever-increasing 

number of courses in schools and universities. Graphs and Applications is based on a highly successful 

Open University course and the authors have paid particular attention to the presentation, clarity and 

arrangement of the material, making it ideally suited for independent study and classroom use. An 

important part of learning graph theory is problem solving; for this reason large numbers of examples, 

problems (with full solutions) and exercises (without solutions) are included.

Contents

1. Introduction.- 2. Graphs.- 3. Eulerian and Hamiltonian Graphs.- 4. Digraphs.- 5. Matrix Representations.- 

6. Tree Structures.- 7. Counting Trees.- 8. Greedy Algorithms.- 9. Path Algorithms.- 10. Connectivity.- 11. 

Planarity.- 12. Vertex Colourings and Decompositions.- 13. Edge Colourings and Decompositions.- 14. 

Conclusion.- Suggestions for Further Reading.- Appendix: Methods of Proof.- Solutions to the Problems.- 

Computer Notes.- Index.



Modern Graph Theory

Bela Bollobas,  University of Memphis, TN, USA



About the Book

The time has now come when graph theory should be part of the education of every serious student of 

mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics 

as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects 

the current state of the subject and emphasizes connections with other branches of pure mathematics. 

The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length 

is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the 

subject. Recognizing that graph theory is one of several courses competing for the attention of a student, 

the book contains extensive descriptive passages designed to convey the flavor of the subject and to 

arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, 

matching, extremal theory, and algebraic graph theory, the book presents a detailed account of newer 

topics, including Szemer'edi's Regularity Lemma and its use, Shelah's extension of the Hales-Jewett 

Theorem, the precise nature of the phase transition in a random graph process, the connection between 

electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. 

In no other branch of mathematics is it as vital to tackle and solve challenging exercises in order to master 

the subject. To this end, the book contains an unusually large number of well thought-out exercises: over 

600 in total. Although some are straightforward, most of them are substantial, and others will stretch even 

the most able reader.



Contents

Fundamentals - Electrical Networks - Flows, Connectivity and Matching - Extremal Problems - Colouring 

- Ramsey Theory - Random Graphs - Graphs, Groups and Matrices - Random Walks on Graphs - The Tutte 

Polynomial.



ISBN: 9788181284785

Page:  XI, 444 p. 644 

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Reprint Year: Jul-07

ISBN: 9788181283092

Page:  XIV, 394 p. 114 

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895.00


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Reprint Year: Mar-05

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A Basic Course in Algebraic Topology

W.S. Massey 



About the Book

This book is intended to serve as a textbook for a course in algebraic topology at the beginning graduate 

level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, 

covering spaces, singular homology theory, and singular cohomology theory. These topics are developed 

systematically, avoiding all unecessary definitions, terminology, and technical machinery. Wherever possible, 

the geometric motivation behind the various concepts is emphasized. The text consists of material from the 

first five chapters of the author's earlier book, ALGEBRAIC TOPOLOGY: AN INTRODUCTION (GTM 56), together 

with almost all of the now out-of- print SINGULAR HOMOLOGY THEORY (GTM 70). The material from the 

earlier books has been carefully revised, corrected, and brought up to date.

Contents

Preface - Notation and Terminology - CHAPTER I Two-Dimensional Manifolds - CHAPTER II The Fundamental 

Group - CHAPTER III Free Groups and Free Products of Groups - CHAPTER IV Seifert and Van Kampen 

Theorem on the Fundamental Group of the Union of Two Spaces. Applications - CHAPTER V Covering 

Spaces - CHAPTER VI Background and Motivation for Homology Theory - CHAPTER VII Definitions and Basic 

Properties of Homology Theory - CHAPTER VIII Determination of the Homology Groups of Certain Spaces: 

Applications and Further Properties of Homology Theory - CHAPTER IX Homology of CW-Complexes - 

CHAPTRR X Homology with Arbitrary Coefficient Groups - CHAPTER XI The Homology of Product Spaces 

- CHAPTER XII Cohomology Theory - CHAPTER XIII Products in Homology and Cohomology - CHAPTER XIV 

Duality Theorems for the Homology of Manifolds - CHAPTER XV Cup Products in Projective Spaces and 

Applications of Cup Products - APPENDIX A A Proof of De Rham's Theorem - APPENDIX B Permutation 

Groups or Transformation Groups - Index.



Elementary Differential Geometry

A.N. Pressley,  King's College, London, UK



About the Book

Elementary Differential Geometry presents the main results in the differential geometry of curves and 

surfaces while keeping the prerequisites to an absolute minimum. Nothing more than first courses in 

linear algebra and multivariate calculus are required, and the most direct and straightforward approach is 

used at all times. Numerous diagrams illustrate both the ideas in the text and the examples of curves and 

surfaces discussed there. The book will provide an invaluable resource to all those taking a first course in 

differential geometry, for their lecturers, and for all others interested in the subject.

Contents

Curves in the Plane and in Space - How Much Does a Curve Curve?- Global Properties of Curves - Surfaces 

in Three Dimensions - The First Fundamental Form - Curvature of Surfaces - Gaussian Curvature and the 

Gauss Map - Geodesics - Minimal Surfaces - Gauss's Theorema Egregium - The Gauss-Bonnet Theorem - 

Solutions - Index.

ISBN: 9788181286949

Page:  428 p.

Price: ` 

750.00


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Reprint Year: Jul-07

ISBN: 9788181281432

Page:  IX, 332 p. 185 

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Price: ` 

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Market: CBS

Reprint Year: Mar-04

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Proofs from The Book, 4e

Martin Aigner,  Freie Universität Berlin, Germany

Günter M. Ziegler,  Technische Universität Berlin, Germany

About the Book

This revised and enlarged fourth edition features five new chapters, which treat classical results such as 

the 'Fundamental Theorem of Algebra', problems about tilings, but also quite recent proofs, for example of 

the Kneser conjecture in graph theory. The new edition also presents further improvements and surprises, 

among them a new proof for 'Hilbert's Third Problem'. From the Reviews: '... Inside [this book] is indeed a 

glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and 

glorious ways. There is vast wealth within its pages, one gem after another. ..., but many [proofs] are new 

and brilliant proofs of classical results. ...Aigner and Ziegler... write: '... all we offer is the examples that we 

have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and 

wonderful observations.' I do. ... ' AMS Notices 1999 '... the level is close to elementary ... the proofs are 

brilliant. ...' LMS Newsletter 1999.


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