WorldCat Identities

Roman, Steven

Overview
Works: 70 works in 520 publications in 6 languages and 16,041 library holdings
Genres: Textbooks 
Roles: Author
Classifications: QA268, 512.5
Publication Timeline
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Most widely held works by Steven Roman
Advanced linear algebra by Steven Roman( Book )

65 editions published between 1965 and 2011 in 3 languages and held by 1,229 WorldCat member libraries worldwide

For the third edition, the author has added a new chapter on associative algebras that includes the well known characterizations of the finite-dimensional division algebras over the real field (a theorem of Frobenius) and over a finite field (Wedderburn's theorem); polished and refined some arguments (such as the discussion of reflexivity, the rational canonical form, best approximations and the definitions of tensor products); upgraded some proofs that were originally done only for finite-dimensional/rank cases; added new theorems, including the spectral mapping theorem; considerably expanded the reference section with over a hundred references to books on linear algebra. From the reviews of the second edition: "In this 2nd edition, the author has rewritten the entire book and has added more than 100 pages of new materials ... As in the previous edition, the text is well written and gives a thorough discussion of many topics of linear algebra and related fields ... the exercises are rewritten and expanded ... Overall, I found the book a very useful one ... It is a suitable choice as a graduate text or as a reference book." Ali-Akbar Jafarian, ZentralblattMATH "This is a formidable volume, a compendium of linear algebra theory, classical and modern ... The development of the subject is elegant ... The proofs are neat ... The exercise sets are good, with occasional hints given for the solution of trickier problems ... It represents linear algebra and does so comprehensively." Henry Ricardo, MAA Online
Access database design and programming by Steven Roman( Book )

39 editions published between 1997 and 2002 in 4 languages and held by 905 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 in-depth understanding of the subject
Field theory by Steven Roman( Book )

43 editions published between 1995 and 2011 in English and Undetermined and held by 765 WorldCat member libraries worldwide

0 Preliminaries ............................................................................. ..... 1<br>0.1 L attices.................................................................................. . . ....... ......<br>0.2 Groups .......................................................................................... 2<br>0.3 The Symmetric Group.......................................................... ... 10<br>0.4 Rings............................................................................................ 10<br>0.5 Integral Domains ............................................................. ..... ... 14<br>0.6 Unique Factorization Domains...................................... ...... .... 16<br>0.7 Principal Ideal Domains............................ ........................... ... 16<br>0.8 Euclidean Domains............................................ .................... .... 17<br>0.9 Tensor Products............................................... ...................... .... 17<br>E xercises......................................................................................... . . .. 19<br>Part I-Field Extensions<br>1 Polynomials.................................................................................. 23<br>1.1 Polynomials over a Ring................................................................ 23<br>1.2 Primitive Polynomials and Irreducibility..................................... 24<br>1.3 The Division Algorithm and Its Consequences............................. .... 27<br>1.4 Splitting Fields................................... ................ .........................32<br>1.5 The Minimal Polynomial ............................................................. .... 32<br>1.6 Multiple Roots................................... ........................................ 33<br>1.7 Testing for Irreducibility...................... ........... ........................ 35<br>Exercises............................................................................................. 38<br>2 Field Extensions....................................................................... .... 41<br>2.1 The Lattice of Subfields of a Field................................. .............. 41<br>2.2 Types of Field Extensions..................................... .............. .... 42<br>2.3 Finitely Generated Extensions................................................. ........ 46<br>2.4 Simple Extensions ............... ................. ................................. .. 47<br>2.5 Finite Extensions.............................................. ........................ 53<br>2.6 Algebraic Extensions......................................................... ..... 54<br>2.7 Algebraic Closures.............................. ................................ ..... 56<br>2.8 Embeddings and Their Extensions.......................................... ..... 58<br>2.9 Splitting Fields and Normal Extensions........................................... 63<br>Exercises.......... ................. ............................................................ 66<br>3 Embeddings and Separability..................................................... 73<br>3.1 Recap and a Useful Lemma........................................ .......... ..... 73<br>3.2 The Number of Extensions: Separable Degree............................. ....75<br>3.3 Separable Extensions............................ .....................................77<br>3.4 Perfect Fields.............................................................................. ..... 84<br>3.5 Pure Inseparability............................ .................................... ..... 85<br>*3.6 Separable and Purely Inseparable Closures.............................. ..... 88<br>Exercises............................................................ .......................... 91<br>4 Algebraic Independence................... ................... .........................93<br>4.1 Dependence Relations................................... ............... ............ .... 93<br>4.2 Algebraic Dependence......................... ........... ........................96<br>4.3 Transcendence Bases...................................................................... 100<br>"*4.4 Simple Transcendental Extensions........................................... ... 105<br>Exercises...................................... .................. ................................ 108<br>Part II-Galois Theory<br>5 Galois Theory I: An Historical Perspective............................ 113<br>5.1 The Quadratic Equation................................................................... 113<br>5.2 The Cubic and Quartic Equations........................................... ... 114<br>5.3 Higher-Degree Equations................................................................. 116<br>5.4 Newton’s Contribution: Symmetric Polynomials............................ 117<br>5.5 Vandermonde..................................................................................119<br>5.6 Lagrange................................................. ........................ .......... 121<br>5 .7 G au ss........................................................ ... .............................. .. 124<br>5.8 B ack to Lagrange................................................................................ 128<br>5 .9 G alois............................................................................................... 130<br>5.10 A Very Brief Look at the Life of Galois..................................... 135<br>6 Galois Theory II: The Theory.................................................. 137<br>6.1 G alois C onnections.......................................................................... 137<br>6.2 The Galois Correspondence............................................ ........143<br>6.3 W ho’s C losed?................................................................................. 148<br>6.4 Normal Subgroups and Normal Extensions.................................. 154<br>6.5 More on Galois Groups........................................................ .. 159<br>6.6 Abelian and Cyclic Extensions.................................... ............ ... 164<br>*6.7 Linear Disjointness.................................................................... 165<br>Exercises......................................................................................... 168<br>7 Galois Theory III: The Galois Group of a Polynomial........... 173<br>7.1 The Galois Group of a Polynomial................................................. 173<br>7.2 Symmetric Polynomials.................................................................. 174<br>7.3 The Fundamental Theorem of Algebra........................................... 179<br>7.4 The Discriminant of a Polynomial............................... ....... .......180<br>7.5 The Galois Groups of Some Small-Degree Polynomials.................182<br>Exercises............................................................... ............................ 193<br>8 A Field Extension as a Vector Space.................................. ..... 197<br>8.1 The Norm and the Trace................... .................................................. 197<br>*8.2 Characterizing Bases.................................................................... 202<br>"*8.3 The Normal Basis Theorem.........................................................206<br>Exercises.............................................................. .................... ...........208<br>9 Finite Fields I: Basic Properties............................................... 211<br>9.1 Finite Fields Redux..........................................................................211<br>9.2 Finite Fields as Splitting Fields................................................. . 212<br>9.3 The Subfields of a Finite Field
Introduction to coding and information theory by Steven Roman( Book )

13 editions published between 1996 and 1997 in English and held by 614 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 variable-length 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 error-correcting block codes. The first chapter covers communication channels, decision rules, nearest neighbor decoding, perfect codes, the main coding theory problem, the sphere-packing, 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 Reed-Muller 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 512 WorldCat member libraries worldwide

The umbral calculus by Steven Roman( Book )

24 editions published between 1978 and 2013 in English and held by 398 WorldCat member libraries worldwide

Geared toward upper-level undergraduates and graduate students, this elementary introduction to classical umbral calculus requires only an acquaintance with the basic notions of algebra and a bit of applied mathematics (such as differential equations) to help put the theory in mathematical perspective. Subjects include Sheffer sequences and operators and their adjoints, with numerous examples of associated and other sequences. Related topics encompass the connection constants problem and duplication formulas, the Lagrange inversion formula, operational formulas, inverse relations, and binomial
VB.NET language in a nutshell : a desktop quick reference by Steven Roman( Book )

41 editions published between 2001 and 2002 in 3 languages and held by 365 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
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 350 WorldCat member libraries worldwide

"This book is specifically written for upper-division 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 Black-Scholes option pricing formula as a limiting case of the Cox-Ross-Rubinstein discrete model. The final chapter is devoted to American options."--Jacket
An introduction to discrete mathematics by Steven Roman( Book )

13 editions published between 1986 and 2004 in English and held by 313 WorldCat member libraries worldwide

Writing Excel macros by Steven Roman( Book )

13 editions published in 1999 in English and German and held by 232 WorldCat member libraries worldwide

Concepts of object-oriented programming with Visual Basic by Steven Roman( Book )

12 editions published between 1997 and 1998 in 3 languages and held by 207 WorldCat member libraries worldwide

This book is about object-oriented 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 object-orientation, and to describe how to do object-oriented 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 hands-on: plenty of code is given and discussed, including error-handling. 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 199 WorldCat member libraries worldwide

Updated for Excel 2002, this text offers Excel power-users, 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 )

8 editions published in 2000 in English and held by 147 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 136 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 pop-up 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, no-nonsense manner that is characteristic of Steven Roman's straightforward, practical approach. Instead of a slow-paced tutorial with a lot of hand-holding, 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 113 WorldCat member libraries worldwide

The Mathematics of Finance has been a hot topic ever since the discovery of the Black-Scholes 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 Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein 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 "need-to-know" basis. No background in finance is required, since the book contains a chapter on options
Lattices and ordered sets by Steven Roman( Book )

17 editions published in 2008 in English and Undetermined and held by 110 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, fixed-point theorems, duality theory and more ..."
Developing Visual Basic add-ins by Steven Roman( Book )

9 editions published in 1999 in English and held by 104 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 89 WorldCat member libraries worldwide

VB.NET language pocket reference by Steven Roman( Book )

11 editions published between 2002 and 2009 in English and French and held by 54 WorldCat member libraries worldwide

Visual Basic .NET is a radically new version of Microsoft Visual Basic, the world's most widely used rapid application development (RAD) package. Whether you are just beginning application development with Visual Basic .NET or are already deep in code, you will appreciate just how easy and valuable the VB.NET Language Pocket Reference is. VB.NET Language Pocket Reference contains a concise description of all language elements by category. These include language elements implemented by the Visual Basic compiler, as well as all procedures and functions implemented in the Microsoft. VisualBasic nam
An introduction to Catalan numbers by Steven Roman( Book )

10 editions published in 2015 in English and held by 41 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
 
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Advanced linear algebra
Alternative Names
Roman, Steve.

Roman, Steven

Roman, Steven A.

Steven Roman Amerikaans wiskundige

Steven Roman matemático estadounidense

Steven Roman matematico statunitense

Steven Roman mathématicien américain

Роман, Стивен

استیون رومن

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Languages
English (394)

German (5)

Spanish (5)

French (4)

Dutch (1)

Czech (1)

Covers
Access database design and programmingField theoryIntroduction to coding and information theoryCoding and information theoryThe umbral calculusVB.NET language in a nutshell : a desktop quick referenceIntroduction to the mathematics of finance : from risk management to options pricingAn introduction to discrete mathematics