Roman, Steven
Overview
Works:  70 works in 521 publications in 6 languages and 16,030 library holdings 

Genres:  Textbooks 
Roles:  Author 
Publication Timeline
.
Most widely held works by
Steven Roman
Advanced linear algebra by
Steven Roman(
Book
)
67 editions published between 1965 and 2011 in 3 languages and held by 1,251 WorldCat member libraries worldwide
"This is a graduate textbook covering an especially broad range of topics. The new edition has been thoroughly rewritten, both in the text and exercise sets, and contains new chapters on convexity and separation, positive solutions to linear systems, singular values and QR decompostion. Treatments of tensor products and the umbral calculus have been greatly expanded and discussions of determinants, complexification of a real vector space, Schur's lemma and Gersgorin disks have been added."Jacket
67 editions published between 1965 and 2011 in 3 languages and held by 1,251 WorldCat member libraries worldwide
"This is a graduate textbook covering an especially broad range of topics. The new edition has been thoroughly rewritten, both in the text and exercise sets, and contains new chapters on convexity and separation, positive solutions to linear systems, singular values and QR decompostion. Treatments of tensor products and the umbral calculus have been greatly expanded and discussions of determinants, complexification of a real vector space, Schur's lemma and Gersgorin disks have been added."Jacket
Access database design and programming by
Steven Roman(
Book
)
41 editions published between 1997 and 2002 in 4 languages and held by 890 WorldCat member libraries worldwide
The third edition of Steven Roman's introduction to Access Database covers design and programming and is suitable for both beginners and programmers who wish to acquire a more indepth understanding of the subject
41 editions published between 1997 and 2002 in 4 languages and held by 890 WorldCat member libraries worldwide
The third edition of Steven Roman's introduction to Access Database covers design and programming and is suitable for both beginners and programmers who wish to acquire a more indepth understanding of the subject
Field theory by
Steven Roman(
Book
)
41 editions published between 1995 and 2011 in English and Undetermined and held by 770 WorldCat member libraries worldwide
213<br>9.4 The Multiplicative Structure of a Finite Field................................. 214<br>9.5 The Galois Group of a Finite Field......................................... ......215<br>9.6 Irreducible Polynomials over Finite Fields............. ..... .............215<br>"*9.7 Normal Bases................................................ ..... ...................... 218<br>"*9.8 The Algebraic Closure of a Finite Field................................... 219<br>Exercises.............................................. ........................................ . . ... 223<br>10 Finite Fields II: Additional Properties............................. .. 225<br>10.1 Finite Field Arithmetic.......................... ......... .................... ... 225<br>*10.2 The Number of Irreducible Polynomials..................................... 232<br>"*10.3 Polynomial Functions................................................................... 234<br>* 10.4 Linearized Polynomials.............................................................. 236<br>Exercises.................................................................................................238<br>11 The Roots of Unity.... .......... ............................... ....... .... .... 239<br>11.1 Roots of Unity.......................................................... ........... .. 239<br>11.2 Cyclotomic Extensions.................................................................... 241<br>"* 11.3 Normal Bases and Roots of Unity .............................................. 250<br>*11.4 Wedderburn’s Theorem............................................ ..... .......... 251<br>*11.5 Realizing Groups as Galois Groups.......................................... 253<br>E xercises.......................................................................................... . .... 257<br>12 Cyclic Extensions ............................................................261<br>12.1 Cyclic Extensions................................................................ ... 261<br>12.2 Extensions of Degree Char(F) ........................................................ 265<br>E xercises ........................................................................................... .... . . 266<br>13 Solvable Extensions................................................................ .. 269<br>13.1 Solvable Groups............................................................................ 269<br>13.2 Solvable Extensions......................... ........................... ........270<br>13.3 Radical Extensions.............................................................................. 273<br>13.4 Solvability by Radicals..................................................................274<br>13.5 Solvable Equivalent to Solvable by Radicals................................. 276<br>13.6 Natural and Accessory Irrationalities........................................ .. 278<br>13.7 Polynomial Equations............................................................... 280<br>E xercises........................................................................................... 2 82<br>Part IllThe Theory of Binomials<br>14 Binomials ..................................................................................... 289<br>14.1 Irreducibility...................................................................... 289<br>14.2 The Galois Group of a Binomial............................................... .. 296<br>*14.3 The Independence of Irrational Numbers.................................. 304<br>E xercises......................................................................................... . . 307<br>15 Families of Binomials............................. ............................... 309<br>15.1 The Splitting Field..................................................................... 309<br>15.2 Dual Groups and Pairings ............................................................ 310<br>15.3 Kummer Theory.......................................................................... ...312<br>Exercises...................................................... ...................................316<br>Appendix: M dbius Inversion ............................................................ 319<br>Partially Ordered Sets........................................................................... 319<br>The Incidence Algebra of a Partially Ordered Set.............................. 320<br>Classical M6bius Inversion............................................................ . .324<br>Multiplicative Version of M6bius Inversion...................................... .. 325<br><br>
41 editions published between 1995 and 2011 in English and Undetermined and held by 770 WorldCat member libraries worldwide
213<br>9.4 The Multiplicative Structure of a Finite Field................................. 214<br>9.5 The Galois Group of a Finite Field......................................... ......215<br>9.6 Irreducible Polynomials over Finite Fields............. ..... .............215<br>"*9.7 Normal Bases................................................ ..... ...................... 218<br>"*9.8 The Algebraic Closure of a Finite Field................................... 219<br>Exercises.............................................. ........................................ . . ... 223<br>10 Finite Fields II: Additional Properties............................. .. 225<br>10.1 Finite Field Arithmetic.......................... ......... .................... ... 225<br>*10.2 The Number of Irreducible Polynomials..................................... 232<br>"*10.3 Polynomial Functions................................................................... 234<br>* 10.4 Linearized Polynomials.............................................................. 236<br>Exercises.................................................................................................238<br>11 The Roots of Unity.... .......... ............................... ....... .... .... 239<br>11.1 Roots of Unity.......................................................... ........... .. 239<br>11.2 Cyclotomic Extensions.................................................................... 241<br>"* 11.3 Normal Bases and Roots of Unity .............................................. 250<br>*11.4 Wedderburn’s Theorem............................................ ..... .......... 251<br>*11.5 Realizing Groups as Galois Groups.......................................... 253<br>E xercises.......................................................................................... . .... 257<br>12 Cyclic Extensions ............................................................261<br>12.1 Cyclic Extensions................................................................ ... 261<br>12.2 Extensions of Degree Char(F) ........................................................ 265<br>E xercises ........................................................................................... .... . . 266<br>13 Solvable Extensions................................................................ .. 269<br>13.1 Solvable Groups............................................................................ 269<br>13.2 Solvable Extensions......................... ........................... ........270<br>13.3 Radical Extensions.............................................................................. 273<br>13.4 Solvability by Radicals..................................................................274<br>13.5 Solvable Equivalent to Solvable by Radicals................................. 276<br>13.6 Natural and Accessory Irrationalities........................................ .. 278<br>13.7 Polynomial Equations............................................................... 280<br>E xercises........................................................................................... 2 82<br>Part IllThe Theory of Binomials<br>14 Binomials ..................................................................................... 289<br>14.1 Irreducibility...................................................................... 289<br>14.2 The Galois Group of a Binomial............................................... .. 296<br>*14.3 The Independence of Irrational Numbers.................................. 304<br>E xercises......................................................................................... . . 307<br>15 Families of Binomials............................. ............................... 309<br>15.1 The Splitting Field..................................................................... 309<br>15.2 Dual Groups and Pairings ............................................................ 310<br>15.3 Kummer Theory.......................................................................... ...312<br>Exercises...................................................... ...................................316<br>Appendix: M dbius Inversion ............................................................ 319<br>Partially Ordered Sets........................................................................... 319<br>The Incidence Algebra of a Partially Ordered Set.............................. 320<br>Classical M6bius Inversion............................................................ . .324<br>Multiplicative Version of M6bius Inversion...................................... .. 325<br><br>
Introduction to coding and information theory by
Steven Roman(
Book
)
13 editions published between 1996 and 1997 in English and held by 611 WorldCat member libraries worldwide
This book is an introduction to coding and information theory, with an emphasis on coding theory. It is suitable for undergraduates with a modest mathematical background. While some previous knowledge of elementary linear algebra is helpful, it is not essential. All of the needed elementary discrete probability is developed in a preliminary chapter. After a preliminary chapter, there follows an introductory chapter on variablelength codes that culminates in Kraft's Theorem. Two chapters on Information Theory follow  the first on Huffman encoding and the second on the concept of the entropy of an information source, culminating in a discussion of Shannon's Noiseless Coding Theorem. The remaining four chapters cover the theory of errorcorrecting block codes. The first chapter covers communication channels, decision rules, nearest neighbor decoding, perfect codes, the main coding theory problem, the spherepacking, Singleton and Plotkin bounds, and a brief discussion of the Noisy Coding Theorem. There follows a chapter on linear codes that begins with a discussion of vector spaces over the field [actual symbol not reproducible]. The penultimate chapter is devoted to a study of the Hamming, Golay, and ReedMuller families of codes, along with some decimal codes and some codes obtained from Latin squares. The final chapter contains a brief introduction to cyclic codes
13 editions published between 1996 and 1997 in English and held by 611 WorldCat member libraries worldwide
This book is an introduction to coding and information theory, with an emphasis on coding theory. It is suitable for undergraduates with a modest mathematical background. While some previous knowledge of elementary linear algebra is helpful, it is not essential. All of the needed elementary discrete probability is developed in a preliminary chapter. After a preliminary chapter, there follows an introductory chapter on variablelength codes that culminates in Kraft's Theorem. Two chapters on Information Theory follow  the first on Huffman encoding and the second on the concept of the entropy of an information source, culminating in a discussion of Shannon's Noiseless Coding Theorem. The remaining four chapters cover the theory of errorcorrecting block codes. The first chapter covers communication channels, decision rules, nearest neighbor decoding, perfect codes, the main coding theory problem, the spherepacking, Singleton and Plotkin bounds, and a brief discussion of the Noisy Coding Theorem. There follows a chapter on linear codes that begins with a discussion of vector spaces over the field [actual symbol not reproducible]. The penultimate chapter is devoted to a study of the Hamming, Golay, and ReedMuller families of codes, along with some decimal codes and some codes obtained from Latin squares. The final chapter contains a brief introduction to cyclic codes
Coding and information theory by
Steven Roman(
Book
)
17 editions published between 1992 and 2011 in 3 languages and held by 515 WorldCat member libraries worldwide
17 editions published between 1992 and 2011 in 3 languages and held by 515 WorldCat member libraries worldwide
The umbral calculus by
Steven Roman(
Book
)
23 editions published between 1978 and 2013 in English and held by 397 WorldCat member libraries worldwide
Title Page; Copyright Page; Dedication; Table of Contents; PREFACE; CHAPTER 1  INTRODUCTION; 1. A DEFINITION OF THE CLASSICAL UMBRAL CALCULUS; 2. PRELIMINARIES; CHAPTER 2  SHEFFER SEQUENCES; 1. THE UMBRAL ALGEBRA; 2. LINEAR OPERATORS; 3. SHEFFER SEQUENCES; 4. ASSOCIATED SEQUENCES; 5. APPELL SEQUENCES; 6. A FEW EXAMPLES; CHAPTER 3  OPERATORS AND THEIR ADJOINTS; 1. CONTINUOUS OPERATORS ON P*; 2. AUTOMORPHISMS AND DERIVATIONS ON P*; 3. ADJOINTS; 4. UMBRAL OPERATORS AND UMBRAL COMPOSITION; 5. SHEFFER OPERATORS AND UMBRAL COMPOSITION
23 editions published between 1978 and 2013 in English and held by 397 WorldCat member libraries worldwide
Title Page; Copyright Page; Dedication; Table of Contents; PREFACE; CHAPTER 1  INTRODUCTION; 1. A DEFINITION OF THE CLASSICAL UMBRAL CALCULUS; 2. PRELIMINARIES; CHAPTER 2  SHEFFER SEQUENCES; 1. THE UMBRAL ALGEBRA; 2. LINEAR OPERATORS; 3. SHEFFER SEQUENCES; 4. ASSOCIATED SEQUENCES; 5. APPELL SEQUENCES; 6. A FEW EXAMPLES; CHAPTER 3  OPERATORS AND THEIR ADJOINTS; 1. CONTINUOUS OPERATORS ON P*; 2. AUTOMORPHISMS AND DERIVATIONS ON P*; 3. ADJOINTS; 4. UMBRAL OPERATORS AND UMBRAL COMPOSITION; 5. SHEFFER OPERATORS AND UMBRAL COMPOSITION
Introduction to the mathematics of finance : from risk management to options pricing by
Steven Roman(
Book
)
14 editions published between 2004 and 2012 in English and held by 353 WorldCat member libraries worldwide
"This book is specifically written for upperdivision undergraduate or beginning graduate students in mathematics, finance, or economics. With the exception of an optional chapter on the Capital Asset Pricing Model, the book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the BlackScholes option pricing formula as a limiting case of the CoxRossRubinstein discrete model. The final chapter is devoted to American options."Jacket
14 editions published between 2004 and 2012 in English and held by 353 WorldCat member libraries worldwide
"This book is specifically written for upperdivision undergraduate or beginning graduate students in mathematics, finance, or economics. With the exception of an optional chapter on the Capital Asset Pricing Model, the book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the BlackScholes option pricing formula as a limiting case of the CoxRossRubinstein discrete model. The final chapter is devoted to American options."Jacket
VB.NET language in a nutshell : a desktop quick reference by
Steven Roman(
Book
)
36 editions published between 2001 and 2002 in English and Undetermined and held by 351 WorldCat member libraries worldwide
VB .NET Language in a Nutshell introduces the important aspects of the language and explains the .NET framework. An alphabetical reference covers the functions, statements, directives, objects, and object members that make up the VB .NET language. To ease the transition, each language element includes a "VB .NET/VB 6 Differences" section
36 editions published between 2001 and 2002 in English and Undetermined and held by 351 WorldCat member libraries worldwide
VB .NET Language in a Nutshell introduces the important aspects of the language and explains the .NET framework. An alphabetical reference covers the functions, statements, directives, objects, and object members that make up the VB .NET language. To ease the transition, each language element includes a "VB .NET/VB 6 Differences" section
An introduction to discrete mathematics by
Steven Roman(
Book
)
13 editions published between 1986 and 2004 in English and held by 310 WorldCat member libraries worldwide
13 editions published between 1986 and 2004 in English and held by 310 WorldCat member libraries worldwide
Writing Excel macros by
Steven Roman(
Book
)
13 editions published in 1999 in English and German and held by 221 WorldCat member libraries worldwide
13 editions published in 1999 in English and German and held by 221 WorldCat member libraries worldwide
Concepts of objectoriented programming with Visual Basic by
Steven Roman(
Book
)
12 editions published between 1997 and 1998 in 3 languages and held by 203 WorldCat member libraries worldwide
This book is about objectoriented programming and how it is implemented in Microsoft Visual Basic. Accordingly, the book has two separate, though intertwined, goals: to describe the general concepts of objectorientation, and to describe how to do objectoriented programming in Visual Basic. Readers are assumed to have a familiarity with Visual Basic and some rudimentary knowledge of programming. On this foundation, Steve Roman introduces the abstract concepts of object orientation, such as class, abstraction, encapsulation, and others and then shows how each are implemented in a meaningful and useful application. Throughout the style is handson: plenty of code is given and discussed, including errorhandling. As a result, Visual Basic programmers and students will find this an invaluable introduction to this topic
12 editions published between 1997 and 1998 in 3 languages and held by 203 WorldCat member libraries worldwide
This book is about objectoriented programming and how it is implemented in Microsoft Visual Basic. Accordingly, the book has two separate, though intertwined, goals: to describe the general concepts of objectorientation, and to describe how to do objectoriented programming in Visual Basic. Readers are assumed to have a familiarity with Visual Basic and some rudimentary knowledge of programming. On this foundation, Steve Roman introduces the abstract concepts of object orientation, such as class, abstraction, encapsulation, and others and then shows how each are implemented in a meaningful and useful application. Throughout the style is handson: plenty of code is given and discussed, including errorhandling. As a result, Visual Basic programmers and students will find this an invaluable introduction to this topic
Writing Excel macros with VBA by
Steven Roman(
Book
)
19 editions published between 2001 and 2007 in English and held by 195 WorldCat member libraries worldwide
Updated for Excel 2002, this text offers Excel powerusers, as well as programmers who are unfamiliar with the Excel object model, with an introduction to writing Visual Basic for Applications (VBA) macros and programs for Excel
19 editions published between 2001 and 2007 in English and held by 195 WorldCat member libraries worldwide
Updated for Excel 2002, this text offers Excel powerusers, as well as programmers who are unfamiliar with the Excel object model, with an introduction to writing Visual Basic for Applications (VBA) macros and programs for Excel
Win32 API programming with Visual Basic by
Steven Roman(
Book
)
9 editions published in 2000 in English and held by 148 WorldCat member libraries worldwide
9 editions published in 2000 in English and held by 148 WorldCat member libraries worldwide
Writing Word macros by
Steven Roman(
Book
)
14 editions published between 1999 and 2000 in English and Czech and held by 135 WorldCat member libraries worldwide
Many Microsoft Word users and VBA programmers don't realize the extensive opportunities that exist when Word's Object Model is accessed using Visual Basic for Applications (VBA), which replaced WordBasic in conjunction with the release of Word 97. By creating what is commonly called a "Word Macro" you can automate many features available in Word. Writing Word Macros (previously titled Learning Word Programming is the introduction to Word VBA that allows you to do these things and more, including: Create custom popup menus Automatically create tables from lists Append one document to the end (or beginning) of another Create a toggle switch to change a document from draft to final copy by adding or removing a watermark in the header Generate reports using data from other applications Not intended to be an encyclopedia of Word programming, Writing Word Macros provides Word users, as well as programmers who are not familiar with the Word object model with a solid introduction to writing VBA macros and programs. In particular, the book focuses on: The Visual Basic Editor and the Word VBA programming environment. Word features a complete and very powerful integrated development environment for writing, running, testing, and debugging VBA macros. The VBA programming language (which is the same programming language used by Microsoft Excel, Access, and PowerPoint, as well as the retail editions of Visual Basic). The Word object model. Word exposes nearly all of its functionality through its object model, which allows Word to be controlled programmatically using VBA. While the Word object model, with almost 200 objects, is the largest among the Office applications, readers need be familiar with only a handful of objects. Writing Word Macros focuses on these essential objects, but includes a discussion of a great many more objects as well. Writing Word Macros is written in a terse, nononsense manner that is characteristic of Steven Roman's straightforward, practical approach. Instead of a slowpaced tutorial with a lot of handholding, Roman offers the essential information about Word VBA that you must master to program effectively. This tutorial is reinforced by interesting and useful examples that solve practical programming problems, like generating tables of a particular format, managing shortcut keys, creating fax cover sheets, and reformatting documents. Writing Word Macros is the book you need to dive into the basics of Word VBA programming, enabling you to increase your power and productivity when using Microsoft Word
14 editions published between 1999 and 2000 in English and Czech and held by 135 WorldCat member libraries worldwide
Many Microsoft Word users and VBA programmers don't realize the extensive opportunities that exist when Word's Object Model is accessed using Visual Basic for Applications (VBA), which replaced WordBasic in conjunction with the release of Word 97. By creating what is commonly called a "Word Macro" you can automate many features available in Word. Writing Word Macros (previously titled Learning Word Programming is the introduction to Word VBA that allows you to do these things and more, including: Create custom popup menus Automatically create tables from lists Append one document to the end (or beginning) of another Create a toggle switch to change a document from draft to final copy by adding or removing a watermark in the header Generate reports using data from other applications Not intended to be an encyclopedia of Word programming, Writing Word Macros provides Word users, as well as programmers who are not familiar with the Word object model with a solid introduction to writing VBA macros and programs. In particular, the book focuses on: The Visual Basic Editor and the Word VBA programming environment. Word features a complete and very powerful integrated development environment for writing, running, testing, and debugging VBA macros. The VBA programming language (which is the same programming language used by Microsoft Excel, Access, and PowerPoint, as well as the retail editions of Visual Basic). The Word object model. Word exposes nearly all of its functionality through its object model, which allows Word to be controlled programmatically using VBA. While the Word object model, with almost 200 objects, is the largest among the Office applications, readers need be familiar with only a handful of objects. Writing Word Macros focuses on these essential objects, but includes a discussion of a great many more objects as well. Writing Word Macros is written in a terse, nononsense manner that is characteristic of Steven Roman's straightforward, practical approach. Instead of a slowpaced tutorial with a lot of handholding, Roman offers the essential information about Word VBA that you must master to program effectively. This tutorial is reinforced by interesting and useful examples that solve practical programming problems, like generating tables of a particular format, managing shortcut keys, creating fax cover sheets, and reformatting documents. Writing Word Macros is the book you need to dive into the basics of Word VBA programming, enabling you to increase your power and productivity when using Microsoft Word
Introduction to the mathematics of finance : arbitrage and option pricing by
Steven Roman(
Book
)
20 editions published between 2012 and 2014 in English and Undetermined and held by 115 WorldCat member libraries worldwide
The Mathematics of Finance has been a hot topic ever since the discovery of the BlackScholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specifically written for advanced undergraduate or beginning graduate students in mathematics, finance or economics. This book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the BlackScholes option pricing formulas as a limiting case of the CoxRossRubinstein discrete model. This second edition is a complete rewrite of the first edition with significant changes to the topic organization, thus making the book flow much more smoothly. Several topics have been expanded such as the discussions of options, including the history of options, and pricing nonattainable alternatives. In this edition the material on probability has been condensed into fewer chapters, and the material on the capital asset pricing model has been removed. The mathematics is not watered down, but it is appropriate for the intended audience. Previous knowledge of measure theory is not needed and only a small amount of linear algebra is required. All necessary probability theory is developed throughout the book on a "needtoknow" basis. No background in finance is required, since the book contains a chapter on options
20 editions published between 2012 and 2014 in English and Undetermined and held by 115 WorldCat member libraries worldwide
The Mathematics of Finance has been a hot topic ever since the discovery of the BlackScholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specifically written for advanced undergraduate or beginning graduate students in mathematics, finance or economics. This book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the BlackScholes option pricing formulas as a limiting case of the CoxRossRubinstein discrete model. This second edition is a complete rewrite of the first edition with significant changes to the topic organization, thus making the book flow much more smoothly. Several topics have been expanded such as the discussions of options, including the history of options, and pricing nonattainable alternatives. In this edition the material on probability has been condensed into fewer chapters, and the material on the capital asset pricing model has been removed. The mathematics is not watered down, but it is appropriate for the intended audience. Previous knowledge of measure theory is not needed and only a small amount of linear algebra is required. All necessary probability theory is developed throughout the book on a "needtoknow" basis. No background in finance is required, since the book contains a chapter on options
Lattices and ordered sets by
Steven Roman(
Book
)
16 editions published in 2008 in English and Undetermined and held by 111 WorldCat member libraries worldwide
" ... A thorough introduction to the subject of ordered sets and lattices, with an emphasis on the latter. Topic coverage includes: modular, semimodular and distributive lattices, boolean algebras, representation of distributive lattices, algebraic lattices, congruence relations on lattices, free lattices, fixedpoint theorems, duality theory and more ..."
16 editions published in 2008 in English and Undetermined and held by 111 WorldCat member libraries worldwide
" ... A thorough introduction to the subject of ordered sets and lattices, with an emphasis on the latter. Topic coverage includes: modular, semimodular and distributive lattices, boolean algebras, representation of distributive lattices, algebraic lattices, congruence relations on lattices, free lattices, fixedpoint theorems, duality theory and more ..."
Developing Visual Basic addins by
Steven Roman(
Book
)
10 editions published in 1999 in English and held by 103 WorldCat member libraries worldwide
10 editions published in 1999 in English and held by 103 WorldCat member libraries worldwide
Fundamentals of group theory : an advanced approach by
Steven Roman(
Book
)
15 editions published in 2012 in English and held by 88 WorldCat member libraries worldwide
15 editions published in 2012 in English and held by 88 WorldCat member libraries worldwide
An introduction to Catalan numbers by
Steven Roman(
Book
)
13 editions published between 2015 and 2016 in English and held by 49 WorldCat member libraries worldwide
This textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics. Intended to be accessible to students new to the subject, the book begins with more elementary topics before progressing to more mathematically sophisticated topics. Each chapter focuses on a specific combinatorial object counted by these numbers, including paths, trees, tilings of a staircase, null sums in Zn+1, interval structures, partitions, permutations, semiorders, and more. Exercises are included at the end of book, along with hints and solutions, to help students obtain a better grasp of the material. The text is ideal for undergraduate students studying combinatorics, but will also appeal to anyone with a mathematical background who has an interest in learning about the Catalan numbers. “Roman does an admirable job of providing an introduction to Catalan numbers of a different nature from the previous ones. He has made an excellent choice of topics in order to convey the flavor of Catalan combinatorics. [Readers] will acquire a good feeling for why so many mathematicians are enthralled by the remarkable ubiquity and elegance of Catalan numbers.”  From the foreword by Richard Stanley
13 editions published between 2015 and 2016 in English and held by 49 WorldCat member libraries worldwide
This textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics. Intended to be accessible to students new to the subject, the book begins with more elementary topics before progressing to more mathematically sophisticated topics. Each chapter focuses on a specific combinatorial object counted by these numbers, including paths, trees, tilings of a staircase, null sums in Zn+1, interval structures, partitions, permutations, semiorders, and more. Exercises are included at the end of book, along with hints and solutions, to help students obtain a better grasp of the material. The text is ideal for undergraduate students studying combinatorics, but will also appeal to anyone with a mathematical background who has an interest in learning about the Catalan numbers. “Roman does an admirable job of providing an introduction to Catalan numbers of a different nature from the previous ones. He has made an excellent choice of topics in order to convey the flavor of Catalan combinatorics. [Readers] will acquire a good feeling for why so many mathematicians are enthralled by the remarkable ubiquity and elegance of Catalan numbers.”  From the foreword by Richard Stanley
An introduction to the language of category theory by
Steven Roman(
Book
)
9 editions published in 2017 in English and German and held by 30 WorldCat member libraries worldwide
This textbook provides an introduction to elementary category theory, with the aim of making what can be a confusing and sometimes overwhelming subject more accessible. In writing about this challenging subject, the author has brought to bear all of the experience he has gained in authoring over 30 books in universitylevel mathematics. The goal of this book is to present the five major ideas of category theory: categories, functors, natural transformations, universality, and adjoints in as friendly and relaxed a manner as possible while at the same time not sacrificing rigor. These topics are developed in a straightforward, stepbystep manner and are accompanied by numerous examples and exercises, most of which are drawn from abstract algebra. The first chapter of the book introduces the definitions of category and functor and discusses diagrams, duality, initial and terminal objects, special types of morphisms, and some special types of categories, particularly comma categories and homset categories. Chapter 2 is devoted to functors and natural transformations, concluding with Yoneda's lemma. Chapter 3 presents the concept of universality and Chapter 4 continues this discussion by exploring cones, limits, and the most common categorical constructions? products, equalizers, pullbacks and exponentials (along with their dual constructions). The chapter concludes with a theorem on the existence of limits. Finally, Chapter 5 covers adjoints and adjunctions. Graduate and advanced undergraduates students in mathematics, computer science, physics, or related fields who need to know or use category theory in their work will find An Introduction to Category Theory to be a concise and accessible resource. It will be particularly useful for those looking for a more elementary treatment of the topic before tackling more advanced texts
9 editions published in 2017 in English and German and held by 30 WorldCat member libraries worldwide
This textbook provides an introduction to elementary category theory, with the aim of making what can be a confusing and sometimes overwhelming subject more accessible. In writing about this challenging subject, the author has brought to bear all of the experience he has gained in authoring over 30 books in universitylevel mathematics. The goal of this book is to present the five major ideas of category theory: categories, functors, natural transformations, universality, and adjoints in as friendly and relaxed a manner as possible while at the same time not sacrificing rigor. These topics are developed in a straightforward, stepbystep manner and are accompanied by numerous examples and exercises, most of which are drawn from abstract algebra. The first chapter of the book introduces the definitions of category and functor and discusses diagrams, duality, initial and terminal objects, special types of morphisms, and some special types of categories, particularly comma categories and homset categories. Chapter 2 is devoted to functors and natural transformations, concluding with Yoneda's lemma. Chapter 3 presents the concept of universality and Chapter 4 continues this discussion by exploring cones, limits, and the most common categorical constructions? products, equalizers, pullbacks and exponentials (along with their dual constructions). The chapter concludes with a theorem on the existence of limits. Finally, Chapter 5 covers adjoints and adjunctions. Graduate and advanced undergraduates students in mathematics, computer science, physics, or related fields who need to know or use category theory in their work will find An Introduction to Category Theory to be a concise and accessible resource. It will be particularly useful for those looking for a more elementary treatment of the topic before tackling more advanced texts
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Associated Subjects
Algebra Algebra, Homological Algebraic fields Algebras, Linear Application software BASIC (Computer program language) Business mathematics Calculus Capital assets pricing model Catalan numbers (Mathematics) Categories (Mathematics) Class field theory Coding theory Combinatorial analysis Computer scienceMathematics Database design Database management Field theory (Physics) Galois theory Graph theory Group theory Information theory Internet programming InvestmentsMathematics Lattice theory Macro instructions (Electronic computers) Macroprogramming Mathematics Matrices Microsoft .NET Framework Microsoft Access Microsoft Excel (Computer file) Microsoft software Microsoft Visual Basic for applications Microsoft Win32 Microsoft Word Number theory Objectoriented programming (Computer science) Operating systems (Computers) Options (Finance)Mathematical models Options (Finance)Prices Ordered algebraic structures Ordered sets Polynomials Portfolio managementMathematical models Sequences (Mathematics) Systems programming (Computer science) Visual Basic (Computer program language) Visual programming languages (Computer science) Word processing