Book Description
Susanna Epp's DISCRETE MATHEMATICS, THIRD EDITION provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp's emphasis on reasoning provides students with a strong foundation for computer science and upper-level mathematics courses.
Customer Reviews:
Perfect book for its purpose.......2007-09-16
This book serves as a terrific introduction to concepts which are of paramount importance in upper-level math courses, most notably Probability Theory, Real Analysis, and Abstract Algebra. Moreover, it provides a solid basis for computer science majors who wish to write more logically sound and efficient programs. I regularly referred back to this in my Real Analysis and Probability courses, and I imagine others would do the same. Also, Dr. Epp's clear, conversational style doesn't hurt the student's confidence later in more rigorous academic enterprises, as well as a concise layout and reasonable pace. Highly recommended.
Good explainations........2007-08-15
This book explained concepts very well. The chapters were easy reads and I even referrred to this text for a Math Reasoning class. If you are a math genius and hate explainations then don't get this book. But if you like to fully understand what you are doing then I would suggest this book.
Great book.......2007-01-03
Wow, this is a great book. I bought this book as a secondary helper book to a really bad math textbook and this book helped me tons. It only seemed to help during the first half of the semester because by the end it wasn't covering the same material as the class was. But it covered the material that it did really really well.
It also has really good problems with good solutions that explain what's going on. Something that so many other math books seem to lack on Discrete math. Just a great book.
Great text on discrete mathematics especially for non-math majors.......2006-08-09
I used an earlier edition of this textbook in a discrete mathematics class that was required for those of us with a non-CS background enrolled in a MSCS program at Virginia Tech, and I found this to be an excellent and complete book on the subject. If you find yourself enrolled in a class using this book, you can be sure of two things - your instructor knows how to select good textbooks and also it won't matter if your instructor is a good teacher since this book does all of the work for him/her.
If you are enrolled in a class on discrete math and this textbook is not assigned, might I suggest you get a used copy of the previous edition. It is just as good as this current edition and used copies can easily be found dirt cheap. If you buy a copy of a previous edition the topics you'd be missing that are new to this edition would be expected value, conditional probability, Bayes' theorem, modular arithmetic, Fermat's little theorem and the Chinese remainder theorem, and RSA cryptography.
The author has included illuminating examples of all concepts throughout the textbook, defined all terms, and makes sure that each new concept introduced builds on previously explained material. Subjects covered include the logic of computation, including the predicate logic that is necessary for fully understanding artificial intelligence, methods of proof including the method of induction and also the terminology of sequences, number theory and combinatorics, O-notation and the calculation of the efficiency of algorithms, graph theory and discrete structures, and an introduction to concepts from the theory of computation. There are many exercises included, with the solutions to selected exercises in the back of the book.
This book only assumes mathematical maturity at the level of precalculus, excluding trigonometry. I highly recommend this text especially to students who are transitioning to computer science from some other discipline and need a firm foundation in the basics of that field. You'll find it useful as a foundational text for studying artificial intelligence, the theory of algorithms, mathematical models of computation, and the theory of computation. Another useful book on this subject is the "Schaum's Outline of Discrete Mathematics".
The table of contents are as follows:
1. The Logic of Compound Statements
2. The Logic of Quantified Statements
3. Elementary Number Theory and Methods of Proof
4. Sequences and Mathematical Induction
5. Set Theory
6. Counting
7. Functions
8. Recursion
9. O-Notation and the Efficiency of Algorithms
10. Relations
11. Graphs and Trees
12. Finite State Automata and Applications
Great Introductory Book.......2006-01-13
For a subject which has so much potential to be conveyed in complicated and esoteric ways, this book actually manages to present every single chapter in a clear and accessible way, even for those unfamiliar with formal logic.
It doesn't cover every single theorem you might come across in a first year class, but it comes close. I'd thoroughly recommend this book, even for self-study. I've used a couple of texts for this subject and while none of them are actually bad, this one is streets ahead for understandability and clarity.
Book Description
The book is a concise, self-contained and up-to-date introduction to extremal combinatorics for non-specialists. Strong emphasis is made on theorems with particularly elegant and informative proofs which may be called gems of the theory. A wide spectrum of most powerful combinatorial tools is presented: methods of extremal set theory, the linear algebra method, the probabilistic method and fragments of Ramsey theory. A throughout discussion of some recent applications to computer science motivates the liveliness and inherent usefulness of these methods to approach problems outside combinatorics. No special combinatorial or algebraic background is assumed. All necessary elements of linear algebra and discrete probability are introduced before their combinatorial applications. Aimed primarily as an introductory text for graduates, it provides also a compact source of modern extremal combinatorics for researchers in computer science and other fields of discrete mathematics.
Average customer rating:
- Somewhat dated...but still helpful
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Computational Economics and Finance: Modeling and Analysis with Mathematica (Economic & Financial Modeling with Mathematica)
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Mathematica for Microeconomics
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Computational Financial Mathematics using Mathematica
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Schaum's Outline of Mathematica
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An Introduction to Programming with Mathematica, Third Edition
ASIN: 0387945180 |
Book Description
As with the first volume, Volume Two of
Economic and
Financial Modeling with Mathematica is edited by Hal Varian, and its contributors are carefully selected by him to assure a high quality, practical work reflecting the efforts and expertise of an international cadre of Mathematica users from the economic, financial, investments, quantitative business and operations research communities.
Customer Reviews:
Somewhat dated...but still helpful.......2002-01-19
For the reader well-versed in Mathematica and in economic theory, this book gives a fairly good overview of how Mathematica can be used to study mathematical economics and finance. It is also assumed in the articles in the book that the reader has a strong background in mathematics. Since the book was published in 1993, Mathematica has considerably expanded, with many new features that make some of the accompanying code in the book somewhat dated, but the notebooks can still be used beneficially.In addition, economic theory is currently making more use of symbolic programming, and financial analysis has exploded as an area which is now making heavy use of high-performance computing. Although Mathematica cannot compete from a performance standpoint with the needs of financial engineering, it still has an advantage from a didactic standpoint. I did not read all of the articles in the book, so my comments will be limited to the ones that I did.
The article on "Mathematica and Diffusions" is an overview of how to use Mathematica to do stochastic calculus. The Ito calculus is reviewed briefly, and the authors begin with constructing a Weiner process. The Mathematica package they employ and on the disk accompanying the book is not discussed in detail, but is merely used to simulate realizations of the process. Readers who want a more in-depth view will have to go over the code themselves. The authors use the package to generate realizations of Weiner processes that are correlated with each other, and show this correlation via Mathematica graphics. The Black-Scholes formula is derived using the standard self-financing trading strategy and ignoring transaction costs and dividends. The algebraic manipulations are done with Mathematica, and this obscures (a little) the underlying concepts behind the derivation of this important formula. Since data structures in Mathematica are essentially lists, the authors outline the construction of the data structure that could be used to represent a diffusion, namely a list consisting of five terms: the diffusion, Weiner process name, expression for the drift and dispersion, and the initial value. For the reader familiar with OO-programming, accessor functions are used to extract the components of this data structure. This is a nice move by the authors, for it is an example of how Mathematica can be used to emulate OO-programming.
The article "Itovsn3: Doing Stochastic Calculus with Mathematica" is an overview of how to use the Itovsn3 package that is on the disk to implement Ito calculus. It is assumed that the reader has a background in stochastic calculus, since the author does not give a review. However, semimartingales, so important to those working in financial engineering, are discussed and their statistical behavior described using Mathematica. The Ito formula is presented as a semimartingale-type decomposition for smooth function of Brownian motion and the author shows using Mathematica plots how the higher order terms in the second-order Taylor expansion vanish asymptotically. This article is not merely Mathematica code for Ito calculus, for the author gives an example of how to use the package in a hedging problem.
The article "Option Valuation" is a more detailed overview of how to use Mathematica in the context of the Black-Scholes model to perform options valuation and risk management. Heavy use is made of the graphics capability of Mathematica to illustrate how option values change as a function of stock price and time of expiration. The author also shows how Mathematica can be used as a OO-language to treat options as self-contained objects with accessor functions. He does however state that Mathematica does not live up to the OO toolkits available elsewhere, contrary to my experience. He closes the article with a consideration of how to use Mathematica to value options that can be exercised before expiry, the binomial model playing the central role in the discussion. It is here in particular that the performance of Mathematica is readily felt. The numerical number-crunching needed to do the calculations in these types of models cannot be done in Mathematica efficiently and profitably.
The article "Time Series Models and Mathematica" gives a general treatment on how Mathematica can be used to study ARIMA models for time series. Mathematica is used more interactively than the other articles and the visualization obtained is quite nice in giving the reader insight into such concepts as the moving average and the spectral density function. The author shows how to estimate the spectral density function and why periodogram techniques fall short in this estimation. I would have liked to see other techniques for studying time series discussed, such as neural networks and hidden Markov models, but the author does do a fairly good job with the ARIMA models.
Book Description
Advanced Mathematical Concepts, ©2006 provides comprehensive coverage of all the topics covered in a full-year Precalculus course. Its unique unit organization readily allows for semester courses in Trigonometry, Discrete Mathematics, Analytic Geometry, and Algebra and Elementary Functions. Pacing and Chapter Charts for Semester Courses are conveniently located in the Teacher Wraparound Edition.
Advanced Mathematical Concepts lessons develop mathematics using numerous examples, real-world applications, and an engaging narrative. Graphs, diagrams, and illustrations are used throughout to help students visualize concepts. Directions clearly indicate which problems may require the use of a graphing calculator.
Customer Reviews:
Excellent transaction.......2005-09-06
Books was in great condition, as advertised, and arrived in a timely manner.
Average customer rating:
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Applications of Abstract Algebra with Maple and MATLAB, Second Edition (Discrete Mathematics and Its Applications)
Richard E. Klima ,
Neil Sigmon , and
Ernest Stitzinger
Manufacturer: Chapman & Hall/CRC
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Book Description
Eliminating the need for heavy number-crunching, sophisticated mathematical software packages open the door to areas like cryptography, coding theory, and combinatorics that are dependent on abstract algebra. Applications of Abstract Algebra with Maple and MATLAB®, Second Edition explores these topics and shows how to apply the software programs to abstract algebra and its related fields. Carefully integrating Maple™ and MATLAB®, this book provides an in-depth introduction to real-world abstract algebraic problems. The first chapter offers a concise and comprehensive review of prerequisite advanced mathematics. The next several chapters examine block designs, coding theory, and cryptography while the final chapters cover counting techniques, including Pólya's and Burnside's theorems. Other topics discussed include the Rivest, Shamir, and Adleman (RSA) cryptosystem, digital signatures, primes for security, and elliptic curve cryptosystems. New to the Second Edition · Three new chapters on Vigenère ciphers, the Advanced Encryption Standard (AES), and graph theory as well as new MATLAB and Maple sections · Expanded exercises and additional research exercises · Maple and MATLAB files and functions available for download online and from a CD-ROM With the incorporation of MATLAB, this second edition further illuminates the topics discussed by eliminating extensive computations of abstract algebraic techniques. The clear organization of the book as well as the inclusion of two of the most respected mathematical software packages available make the book a useful tool for students, mathematicians, and computer scientists.
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Advanced Engineering Mathematics with Mathematica and Matlab, Vol. 1
Reza Malek-Madani
Manufacturer: Addison Wesley
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Advanced Engineering Mathematics With Mathematica and Matlab, Vol. 2
ASIN: 0201598817 |
Average customer rating:
- Fantastic book for beginner.
- A book with lots of examples, but...
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Elements of Computer Algebra With Applications
Alkiviadis G. Akritas
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ASIN: 0471611638 |
Book Description
Numerical Modeling in Science and Engineering Myron B. Allen, George F. Pinder, and Ismael Herrera Emphasizing applications, this treatment combines three traditionally distinct disciplines—continuum mechanics, differential equations, and numerical analysis—to provide a unified treatment of numerical modeling of physical systems. Covers basic equations of macroscopic systems, numerical methods, steady state systems, dissipative systems, nondissipative systems, and high order, nonlinear, and coupled systems. 1988 (0 471-80635-8) 418 pp. Mathematical Modeling and Digital Simulation for Engineers and Scientists Second Edition Jon M. Smith Totally updated, this Second Edition reflects the many developments in simulation and computer modeling theory and practice that have occurred over the past decade. It includes a new section on the use of modern numerical methods for generating chaos and simulating random processes, a section on simulator verification, and provides applications of these methods for personal computers. Readers will find a wealth of practical fault detection and isolation techniques for simulator verification, fast functions evaluation techniques, and nested parenthetical forms and Chebyshev economization techniques. 1987 (0 471-08599-5) 430 pp. Numerical Analysis 1987 David F. Griffiths and George Alistair Watson An invaluable guide to the direction of current research in many areas of numerical analysis, this volume will be of great interest to anyone involved in software design, curve and surface fitting, the numerical solution of ordinary, partial, and integro-differential equations, and the real-world application of numerical techniques. 1988 (0 470-21012-5) 300 pp.
Customer Reviews:
Fantastic book for beginner........2007-05-05
Great book. I strongly recommend it before reading an advanced book on Computer Algebra.
A book with lots of examples, but..........2000-06-02
This book covers mainly the elementary topics in the algorithms of computer algebra. The book has a lot of examples which make it much easier to read. However, comparing to existing algorithmic algebra texts, this book is not really covering many topics. For example, Grobner Basis is not in the book.
Book Description
Discrete Mathematics and its Applications is a focused introduction to the primary themes in a discrete mathematics course, as introduced through extensive applications, expansive discussion, and detailed exercise sets. These themes include mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and enhanced problem-solving skills through modeling. Its intent is to demonstrate the relevance and practicality of discrete mathematics to all students. The Fifth Edition includes a more thorough and linear presentation of logic, proof types and proof writing, and mathematical reasoning. This enhanced coverage will provide students with a solid understanding of the material as it relates to their immediate field of study and other relevant subjects. The inclusion of applications and examples to key topics has been significantly addressed to add clarity to every subject.
True to the Fourth Edition, the text-specific web site supplements the subject matter in meaningful ways, offering additional material for students and instructors. Discrete math is an active subject with new discoveries made every year. The continual growth and updates to the web site reflect the active nature of the topics being discussed.
The book is appropriate for a one- or two-term introductory discrete mathematics course to be taken by students in a wide variety of majors, including computer science, mathematics, and engineering. College Algebra is the only explicit prerequisite.
Customer Reviews:
Great buy.......2007-03-15
Purchased for computer science course since it was required. Great price, good book.
A good book .......2006-05-20
I like this book and use it for teaching my students. As a teacher, you have the opportunity to select similar problems for class activity and homework assignment. Also, you can find not only simple and middle-level problems but also high-level problems to provide a good source for active students. Unfortunately, the author uses the letters "F" and "T" in the truth tables instead of much easier and perspective "0" and "1", which correspond to the real needs, e.g., in computer science. That's the most essential lack, which I've found by this time.
This book is interesting.......2006-04-11
I like the exclamations and the concepts/problem solving this book teaches. Maybe I am being swayed by the subject because I enjoy it, however, in comparison to other math books, this one livens it up and is a higher then the average mathematics book.
Very, very helpful..........2006-03-17
This manual was the only reason I got through discrete mathematics for computer science! It's awesome. Now if they only had one for the even solutions...
:-)
The best book on Discrete Math.......2006-03-16
This is the best book I have come across in Discrete Mathematics. It is fun to read and very easy to follow. The subject was taught as a very theoretical way in my course in college, but this book gave a whole new practical dimension to the topics, mainly in the chapters on Graph Theory.
It is a must buy for anybody who wants to know about the fun side of mathematics. That is not to say that this book is not suitable for the serious study program. It has everything that you may require in an Introductory Discrete Math course.
The problem sets are big and the answers to odd number questions are really helpful at times, when you are stuck. The author's detailing of almost every aspect in the book and coupled with the applications of the same idea make it easy to understand.
I have thoroughly enjoyed reading this book and I feel anybody who goes through this book, too will enjoy it immensely.
Book Description
Susanna Epp's Discrete Mathematics with Applications, Second Edition provides a clear introduction to discrete mathematics. Epp has always been recognized for her lucid, accessible prose that explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. The text is suitable for many course structures, including one-semester or full-year classes. Its emphasis on reasoning provides strong preparation for computer science or more advanced mathematics courses.
Customer Reviews:
This is when I fell in love with Math........2006-05-09
This book is well written, it contains good examples, and excellent exposition. This was my introduction to mathematical proofs, and after studying it well, I was able to approach more advanced courses, such as advanced calculus and modern algebra with a clear view of how to approach problems where a mathematical proof is needed. I highly recommend this book to undergraduate math majors.
Nice and Clear.......2005-06-25
I honestly can't see how you'd make a book explaining such topics as prime numbers and set theory any clearer than this one. I consider this to be a high quality book. It's easy to understand and reference. Its one drawback is that it covers only a limited number of topics, and none of them are heavy duty. If I found a book that explained graduate level math as well as this one explains undergraduate math, I'd consider it to be gold.
Good book IF you know how to use it........2005-05-04
This is a solid math book that covers every topic you'll need to know in the area. Make no mistake this is not a kid's book, and one must know how to study and read math in order to utilize it to the full potential. Many people that rate math books poorly do so because they have not developed adequate skills in studying math. If you take your time, work out the examples with the book, read and read again all of the concepts are about as clear as they can come from a math book. Most teachers/professors prefer to use their own examples, because that's how they abstract the problem in their own mind. It's easier to create a problem, than sit down and observe a premade example. Aside from some slightly screwy lesson organization it is a solid book. If you have patience, and try to do more than briefly skim over a lesson to understand it this book will be more than adequate for the topic.
Awful, even the prof said so.......2004-07-20
This book is horrible. I am a graduate software engineering student and took this course at a local university. The prof said that the book is horrible and used his own exaplainations and skipped the books explainations. If I was forced to use the book's explaination and examples I would be S.O.L. The only reason every discrete class uses this book is because there are no other discrete books in competition. If you are a comp sci student they should break discrete math classes apart to discrete for comp sci and discrete from math majors. They should also have comp sci teachers teaching this because math teachers don't usually have a clue how to relate discrete math to computer science.
Excellent Math Book.......2004-06-04
This is one of the best undergraduate math textbooks I have ever read. The concepts and examples provided by the author are very clear. Highly recommended for anyone who wants to learn Discrete Math.
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Learning and Generalization: With Applications to Neural Networks
Mathukumalli Vidyasagar
Manufacturer: Springer
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Pattern Recognition and Machine Learning (Information Science and Statistics)
ASIN: 1852333731 |
Book Description
Learning and Generalization provides a formal mathematical theory for addressing intuitive questions such as:
• How does a machine learn a new concept on the basis of examples?
• How can a neural network, after sufficient training, correctly predict the outcome of a previously unseen input?
• How much training is required to achieve a specified level of accuracy in the prediction?
• How can one identify the dynamical behaviour of a nonlinear control system by observing its input-output behaviour over a finite interval of time?
In its successful first edition,
A Theory of Learning and Generalization was the first book to treat the problem of machine learning in conjunction with the theory of empirical processes, the latter being a well-established branch of probability theory. The treatment of both topics side-by-side leads to new insights, as well as to new results in both topics.
This second edition extends and improves upon this material, covering new areas including:
• Support vector machines.
• Fat-shattering dimensions and applications to neural network learning.
• Learning with dependent samples generated by a beta-mixing process.
• Connections between system identification and learning theory.
• Probabilistic solution of 'intractable problems' in robust control and matrix theory using randomized algorithm.
Reflecting advancements in the field, solutions to some of the open problems posed in the first edition are presented, while new open problems have been added.
Learning and Generalization (second edition) is essential reading for control and system theorists, neural network researchers, theoretical computer scientists and probabilist.
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