Introductory Logic and Sets for Computer Scientists (International Computer Science Series)

Book Description

This text provides a practical, modern approach to teaching logic and
set theory, equipping students with the necessary mathematical
understanding and skills required for the mathematical specification
of software. It covers all the areas of mathematics that are
considered essential to computer science including logic, set theory,
modern algebra (group theory), graph theory and combinatorics, whilst
taking into account the diverse mathematical background of the
students taking the course. In line with current undergraduate
curricula this book uses logic extensively, together with set theory,
in mathematical specification of software. Languages such as Z and VDM
are used for this purpose.

Features
Particular emphasis is placed on the application of logic in the fields of software engineering, artificial intelligence and natural language processing

Customer Reviews:

Catches the Misconceptions Before They Happen.......2003-03-13

This book not only covers discrete mathematics well, but shows real professionalism in education. I have over twenty years of software experience and this book was arranged to allow me to refresh or learn for the first time precisely the material I wanted.

Not only this, but Dr Nissanke is well aware of common misconceptions and misunderstandings that students may have in learning discrete mathematics. Examples are the differences between bound and free variables, unknowns and genuine variables, what to guard against in building proofs, and more. For me, I had missed in my education the material from the entire chapters on Interpretation of Formulae and Proofs in Predicate Logic, and never had the time and patience to piece this together from textbooks where this material was learned by osmosis or "between-the-lines".

Another big plus for me was the introductory material to Z, formal specification, functional programming, and lambda calculus. These were done very straightforwardly and user-friendly.

The book also spends more than a tenth of its 400 pages on giving solutions to its exercises.

Finally, it is reasonably priced, especially considering that other introductory textbooks in discrete mathematics run $100 to $125 but are still short on the educational know-how.

My only regrets are that it does not cover posets and graphs. However, this may be a good division of labor between this and a follow-on course.

a good sophomore-level book.......2001-09-15

a nice sophomore-level book. it introduces basic set theory and logic concepts, but at "gentle" pace. the type of book that would be used at a liberal arts college, but not at a "real" engineering school. has a nice examples and does a decent job in explaining the basics.

Great Book for Understanding Logic.......1999-05-08

I like this book very much. It's very clearly written and a delight to read. I especially like the chapters on transformational proofs and propositional logic. The author makes the topics easy for students to grasp the theory and understand the fundamentals of what may seem to be a difficult subject.

Graphs: An Introductory Approach--A First Course in Discrete Mathematics

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Graphs: An Introductory Approach--A First Course in Discrete Mathematics
Robin J. Wilson , and John J. Watkins
Manufacturer: Wiley
ProductGroup: Book
Binding: Hardcover

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ASIN: 0471615544

Book Description

The only text available on graph theory at the freshman/sophomore level, it covers properties of graphs, presents numerous algorithms, and describes actual applications to chemistry, genetics, music, linguistics, control theory and the social sciences. Illustrated.

Introductory Combinatorics (3rd Edition)

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nice accessable text
Interesting Problems, Too Many Mistakes

Introductory Combinatorics (3rd Edition)
Richard A. Brualdi
Manufacturer: Prentice Hall
ProductGroup: Book
Binding: Hardcover

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ASIN: 0131814885

Book Description

Introductory Combinatorics emphasizes combinatorial ideas, including the pigeon-hole principle, counting techniques, permutations and combinations, Polya counting, binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, and combinatortial structures (matchings, designs, graphs). Written to be entertaining and readable, this book's lively style reflects the author's joy for teaching the subject. It presents an excellent treatment of Polya's Counting Theorem that doesn't assume the student is familiar with group theory. It also includes problems that offer good practice of the principles it presents. The third edition of Introductory Combinatorics has been updated to include new material on partially ordered sets, Dilworth's Theorem, partitions of integers and generating functions. In addition, the chapters on graph theory have been completely revised. A valuable book for any reader interested in learning more about combinatorics.

Customer Reviews:

nice accessable text.......2007-04-15

Most (but not all) of the copious errors in earlier editions have been fixed.
(Brualdi maintains an errata list on his website.) I like this book a lot,
it has a nice, relaxed style of exposition and the choice of topics is good
for an introductory course.

Interesting Problems, Too Many Mistakes.......1999-01-04

I used the book to guide me through a Combinatorics class I took in the summer of 1998. The author has presented some very interesting problems like prove that of any 10 points chosen withen an equlateral triangle of side length 1, there are 2 whose distance apart is at most 1/3 that use some interesting techniques such as the pigeonhole principal. The book, however contained too many mistakes. My professor said on average there is one mistake per page and he wasn't exagerating either. Luckily with his help, we corrected the many mistakes and then were successfully able to use the book. I notice that the author has written a new edition. I hope most of the mistakes have been corrected because when I pay a good sum of money for a book I expect it to be good book without errors.

Graphs and Applications: An Introductory Approach (with CD-ROM)

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Graphs and Applications: An Introductory Approach (with CD-ROM)
Joan M. Aldous , and Robin J. Wilson
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 185233259X

Book Description

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.
Accompanying the book is a CD-ROM comprising a Graphs Database, containing all the simple unlabelled graphs with up to seven vertices, and a Graphs Editor that enables students to construct and manipulate graphs. Both the Database and Editor are simple to use and allow students to investigate graphs with ease. Computing Notes and suggested activities are provided.

Computer Algebra Recipes: An Introductory Guide to the Mathematical Models of Science

Average customer rating:

cd format mac incompatibility fixed (for me)

Computer Algebra Recipes: An Introductory Guide to the Mathematical Models of Science
Richard H. Enns , and George C. McGuire
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 0387257675

Book Description

Computer algebra systems are revolutionizing the teaching, the learning, and the exploration of science. Not only can students and researchers work through mathematical models more efficiently and with fewer errors than with pencil and paper, they can also easily explore, both analytically and numerically, more complex and computationally intensive models.

Aimed at science and engineering undergraduates at the sophomore/junior level, this introductory guide to the mathematical models of science is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, mathematics, physics, and chemistry. The topics are organized into the Appetizers dealing with graphical aspects, the Entrees concentrating on symbolic computation, and the Desserts illustrating numerical simulation.

The heart of the text is a large number of computer algebra recipes based on the Maple 10 software system. These have been designed not only to provide tools for problem solving, but also to stimulate the reader’s imagination. Associated with each recipe is a scientific model or method and an interesting or amusing story (accompanied with a thought-provoking quote) that leads the reader through the various steps of the recipe. The recipes are also included on the CD-ROM enclosed with the book. Each section of recipes is followed by a set of problems that readers can use to check their understanding or to develop the topic further.

This text is the first of two volumes, the advanced guide, aimed at junior/senior/graduate level students, dealing with more advanced differential equation models.

Customer Reviews:

cd format mac incompatibility fixed (for me).......2002-02-27

Contacted Springer who manufactured cd in microsoft format incompatible to mac today (26Feb2002).

... These authors are masters. Each author, I find from surfing on the web, has a computer learning lab. The early reading introduces the fact that without the constraints of paper, undergraduates can learn to compose solutions to more realistic problems, eg. golf balls do not go on parabolas but do depend on your irons and crosswinds.

Book Description

Concise, undergraduate-level text focuses on combinatorics, graph theory with applications to some standard network optimization problems, and algorithms to solve these problems. Applications are emphasized and more than 200 exercises help students test their grasp of the material. Appendix. Bibliography. Answers to Selected Exercises.

Customer Reviews:

Avoid this book, droogs.......2002-02-16

I've taken a first semester Discrete Math course, and am currently taking the second semester of it. I bought this book on a whim, hoping it might supplement my text, or at least clarify a few points. It fails at both of those things. Here's why:

1) Abundant errors: I read the first 15 pages and found at least one *serious* typo per page (i.e. a typo that could impede learning). Plus, the grammar ranges from illegal to ambiguous. Thankfully, I was familiar with all of the material that I was reading -- were I not, severe confusion and discouragement would have been the result.

2) Poor examples: They're too abstract or too simple -- and there aren't even very many of them. Oftentimes, he contradicts what he's trying to illustrate due to a small oversight or typo. It's truly bad.

3) Gratuitous brevity (yes I know that may sound paradoxical): The author uses compound sentences in his definitions; sometimes going as far as to define two or three concepts IN THE SAME SENTENCE! It's infuriating.

4) Chapter Zero: This deserves its own rant section. Chapter zero contains nearly all of the material from the first four chapters of my current textbook: Logic, Set theory, Induction, Relations, etc. Somehow the author crams all of it into about 24 pages (plus 4 or 5 pages of exercises). He fails at clarity or lucidity. It's an ambomination -- it reads like lecture notes (you know, the ones only the professor looks at).

OK -- I WANTED to like this book. It's kind of cute, I'll admit it. And the price is sweet. But friends, you get what you pay for. Even after I came across the first 5 or so serious typos I was willing to forgive. Eventually, the sheer amount of contradictory examples and ambiguous sentences riled me up so much that I considered tearing the book in half. Really. I doubt I'll ever open the thing again.

Excellent Text.......2000-12-04

As with any Dover text, it is important to remember that this text is designed to teach the material, not to coddle the reader. This text provides broad and deep coverage of the various topics that fall under discrete mathematics (set theory, boolean logic, graph theory, etc.) with clarity and simplicity. This book is not designed to help you pass a test, but is instead designed to help you grasp and understand the topic, which it does very well. Easily the best book I own on this topic (I often joke that the author covered my first semester course on discrete math in the first chapter!).

Too succinct for the discrete novice.......2000-08-30

I learned much more from the Schaum's Outline (ISBN: 0070380457 -Schaum's Outline of Theory and Problems of Discrete Mathematics (Schaum's Outline Series) by Seymour Lipschutz, Marc Lipson (Contributor), Seymour Lipschultz ).

That book overcomes the two shortcomings of this one: for a self-proclaimed introductory work on discrete mathematics, this text contains too few worked out in-chapter examples, and too many omitted steps in the reasoning. On this latter point, there were many times my reading brought me to the phrase "It follows from the definition that..." or "obviously..." when, for me, it didn't follow, or it wasn't obvious. Contrary to another reviewer's assessment, I found quite a lot of typos, but none too serious. To its credit, the book does contain a lot of end-of-chapter problems with solutions, and it is inexpensive.

The author of the text I review here wrote another in this field, the Schaum's outline series offering with ISBN 007003575X, which is not the Schaum's text I recommend above. I express no opinion on this other work of his.

Near-Useless Garbage.......1999-12-09

This is an unreadable, low quality text. The theorems and proofs are explained in a ridiculously formal and boring style. I challenge you to read and understand a full page of this book on your first try. Avoid at all costs, and if your professor is using this text, avoid the course at all costs, and try talking some sense into your professor.

Near-Useless Garbage.......1999-12-09

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Introduction to Computer Mathematics!?

Introductory Computer Mathematics
Nigel P. Cook
Manufacturer: Prentice Hall
ProductGroup: Book
Binding: Paperback

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ASIN: 0130131512

Book Description

Best-selling author Nigel Cook's new second edition of Introductory Computers Mathematics provides a complete math course for those learning computer technology. Employing an “integrated math applications” approach, this book reinforces all math topics with extensive applications to show readers the value of math as a tool. Specific chapters in the section on Basic Math discuss fractions; decimal numbers; positive and negative numbers; exponents and the metric system; algebra, equations and formulas; geometry and trigonometry; and logarithms and graphs. Computer Math topics cover analog to digital, number systems and codes, logic gates, Boolean expressions and algebra, binary arithmetic, and an introduction to computers and programming. For individuals preparing for a career in computer technology.

Customer Reviews:

Introduction to Computer Mathematics!?.......2007-04-18

I got this book as an assistant for programming and additional mathematics. The book is written more like an introduction to mathematics. It starts with basic fractions, multiplication, and exponents. It briefly covers advanced algebraic expressions and trig. Though the good side of it is that it covers logic gates pretty good. I would suggest buying a series of books instead of one brief one. Whether you are going into computer science or information technology, get something more in depth.

Introductory Concepts for Abstract Mathematics

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Worth the price!

Introductory Concepts for Abstract Mathematics
Kenneth E. Hummel
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Hardcover

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An Introduction to Mathematical Reasoning: Numbers, Sets and Functions

ASIN: 1584881348

Book Description

Beyond calculus, the world of mathematics grows increasingly abstract and places new and challenging demands on those venturing into that realm. As the focus of calculus instruction has become increasingly computational, it leaves many students ill prepared for more advanced work that requires the ability to understand and construct proofs. Introductory Concepts for Abstract Mathematics helps readers bridge that gap. It teaches them to work with abstract ideas and develop a facility with definitions, theorems, and proofs. They learn logical principles, and to justify arguments not by what seems right, but by strict adherence to principles of logic and proven mathematical assertions - and they learn to write clearly in the language of mathematics The author achieves these goals through a methodical treatment of set theory, relations and functions, and number systems, from the natural to the real. He introduces topics not usually addressed at this level, including the remarkable concepts of infinite sets and transfinite cardinal numbers Introductory Concepts for Abstract Mathematics takes readers into the world beyond calculus and ensures their voyage to that world is successful. It imparts a feeling for the beauty of mathematics and its internal harmony, and inspires an eagerness and increased enthusiasm for moving forward in the study of mathematics.

Customer Reviews:

Worth the price!.......2002-07-28

I have used this text for a Foundations in Mathematics course, and have subsequently found this book among the best that I have read. It would also be good for self-study, as most of the answers are included in the back--which is essential for a good self-study book at this level of Mathematics. Other books I would recommend are: Morash's "Bridge to Abstract mathematics"; "200% of nothing", "An introduction to mathematical reasoning";and "A transition to higher mathematics". Books I would recommend you don't use for self-study are: How to prove it: a structured approach, and any book which doesn't include solutions. (Once one is comfortable with writing and reading proofs, and with higher math in general, then solutions are not always needed.) This book will introduce the reader to many of the topics that one will find in Abstract Algebra and Real analysis: upper and lower bounds, least upper bound, real number system, epsilon-delta proofs, a little number theory, the uncountability of the reals, trans-finite cardinal arithmetic; also has a nice section on the controversial axiom of choice . On the whole, I would recommed this book.

Introductory Discrete Structures With Applications

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Introductory Discrete Structures With Applications

Manufacturer: Prentice Hall College Div
ProductGroup: Book
Binding: Hardcover

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ASIN: 0135007941

Introductory Programming for Discrete Mathematics

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Introductory Programming for Discrete Mathematics
Kenneth P. Bogart
Manufacturer: D C Heath & Co
ProductGroup: Book
Binding: Paperback

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