Product Description
A math model for the Bible, what for? The answer to this question is the same as the answer to the following question Christians should ask one another: "Whatever Happened to the Gospel?" Each concept of this Message has as many interpretations as there are faith denominations and members in each of them: Who are we to God: His adoptive or His natural born children? Is the purpose of our life the same or does God bring us to this world with tailored plan he calls each of us to discover through the illumination of the Holy Spirit? What sins did Christ come down to save us from: our own sins, Adam's, or both? To be saved, are good deeds enough? Is salvation through faith alone, through faith and works, or is it predestined? Are we once saved always saved? Is being born again the assurance of Eternal Life?Each of these denominations makes exclusive claims about the Truth. Each considers that only its teachings are grounded in Scripture. When you ask the question to know by what assurance an interpretation of the Scripture is exclusively true, each of these denominations claims the inward illumination of the Holy Spirit as the basis of its interpretation of the Scripture. If the Holy Spirit performs the functions of a teacher to all God's children, the multiplication of conflicting interpretations of the same Scripture cannot be explained; for the Holy Spirit cannot contradict Himself. Two interpretations of the same message cannot both be true when they oppose one another, unless the message is a contradiction: the Gospel is not a contradiction; who is true?Through Christ's identification of himself with the Word of God, the Truth and Fulfillment of the Law and the Prophets, he testifies to the Bible's math model that affixes the Gospel as its axioms, and to the view of these axioms as the basis of the interpretation of the Eternal Life knowledge the Bible conveys. The Lord's Prayer is the axioms of this math model that solves our questions on salvation. ... Read more

Customer Reviews (2)

Starts out a little rough
(1)The second inequality on page 3, while true, is apparently only accidentally so, because the set on the right is not a subset of the set on the left.Changing [0,1] to [0,2] fixes this.

(2)The first reference to "rotations" on page 5 needs to be "nontrivial rotations"; otherwise, Q is the entire sphere, rather than a countable subset.(If you insist that rotations are automatically nontrivial, then the claim on page 4 that they can form a group is false.)

(3)X^i on the fourth line of the proof of Lemma 1.5 needs to be X_1 instead.

(4)The proof of Theorem 1.2 uses S to stand for two different things: a sphere and a countable subset thereof.

(5)The point p is supposed to be an arbitrary point in S's cone but outside of C's cone.If the S here is supposed to be the uncountable S, then this doesn't guarantee that the right-hand side of (1.7) is a disjoint union as apparently intended, but if the S here is the countable S, then we're trying to choose p from an empty set.I'm guessing that the countable S is intended, and that p is supposed to be in C's cone but outside S's cone, not the other way around.

These errors occur in the first ten pages of this book.Based on this small sample size, I'm finding it difficult to motivate myself to read any further.

Sometimes buying an inexpensive, uncorrected Dover reprint isn't such a bargain.

Axiom of Choice
Good book if you are trying to understand where the field of Mathematics is going: from Set Theory (Cantor & Godel), to modern math going forward. High School and College math skills necessary to grasp hard concepts.However, a good read for lay Mathematicians. ... Read more

Product Description
The primary aim of this monograph is to clarify the undefined primitive concepts and the axioms which form the basis of Einstein's theory of special relativity. Minkowski space-time is developed from a set of independent axioms, stated in terms of a single relation of betweenness. It is shown that all models are isomorphic to the usual coordinate model, and the axioms are consistent relative to the reals. ... Read more

Product Description
Webster's bibliographic and event-based timelines are comprehensive in scope, covering virtually all topics, geographic locations and people. They do so from a linguistic point of view, and in the case of this book, the focus is on "Axiom," including when used in literature (e.g. all authors that might have Axiom in their name). As such, this book represents the largest compilation of timeline events associated with Axiom when it is used in proper noun form. Webster's timelines cover bibliographic citations, patented inventions, as well as non-conventional and alternative meanings which capture ambiguities in usage. These furthermore cover all parts of speech (possessive, institutional usage, geographic usage) and contexts, including pop culture, the arts, social sciences (linguistics, history, geography, economics, sociology, political science), business, computer science, literature, law, medicine, psychology, mathematics, chemistry, physics, biology and other physical sciences. This "data dump" results in a comprehensive set of entries for a bibliographic and/or event-based timeline on the proper name Axiom, since editorial decisions to include or exclude events is purely a linguistic process. The resulting entries are used under license or with permission, used under "fair use" conditions, used in agreement with the original authors, or are in the public domain. ... Read more

Product Description

Customer Reviews (4)

captured my son's attention
With honors geometry coming up in school this Fall, I had my son work through 2D Geometry over the summer break. Of course, he thought the idea of having to to do schoolwork over summer break was indication that he had been born of a Nazi father. However, once he caught the idea that this was going to happen, and that I'd be checking over his work each week, he gave the book a chance.

And once he did, he was thoroughly engaged. Instead of a formal, class-like approach, the book showed him how human being get their brains to work solving problems... and oh, by the way, you learn some geometry principles as well.

Each chapter's project connected him to something real, something he could imagine. Then, with very little prompting from me (mostly about showing his work line by line), he was off. The pacing was very accessible for him, the explanations both thorough and clear, and the visual layout appealing enough that the summer became HIS project, not mine.

I'd recommend this treatment of geometry without hesitation.

Head First 2D Geometry
Fiction meets textbook as kids are ushered into a realm of crime-solving, economic problems and rock venue planning... armed only with protractors, pencils and a ton of scratch paper. The folks at Head First Labs certainly had fun with this piece.The slightly corny `crime scenes' notwithstanding, the problems presented actually provoked a bit of interest with this reader's family, including the adults.

After initially scoffing at the rather silly names and cartoony appearance of the pages, the actual language of the various problems proved quite easy to decipher, as well as the simple manner in which one invariably retains the axioms and rules presented.A far cry from the droning, dull and hefty volumes--which hover ominously in the mind's eye at the mention of the word `geometry'--the lessons in //Head First 2D Geometry//proved rather fun, conceptually helpful and quickly shanghaied one's hands into measuring angles and scribbling calculations. This book is a must-have for middle school students, but happily it can be read and understood by far younger (and older) audiences.

Reviewed by Meredith Greene

A quick note from one of the authors
Just to pick up on the previous review, the reviewer is correct that this book isn't focussed on geometry proofs in the formal sense.

Instead, it aims to be a stepping stone for learners, moving them across that big scary jump between simply learning formulas and plugging your numbers in, and creating formal geometry proofs.

In Head First 2D Geometry, the learner - not the author - creates the formulas that they need to solve challenging problems. By going through the process of discovering those formulas for themselves we believe learners develop a deeper and more confident understanding of how geometry works, putting them in the right place to move on to formal proofs.

If you're one of those students who didn't struggle until you hit geometry proofs, this book should help you over that hurdle. If you were already confused by the time you hit 'Pi' or if you're new to circle formulas, quads and polygons then Head First 2D Geometry is waiting to be your guide.If you need geometry to apply to your programming or design work, you're our learner too.

Like all Head First books, this is a book that will help you to think differently, and targets your brain rather than focussing directly on your exam grade. Head First 3D Geometry (which includes Trig) and Head First Geometry Proofs will both be coming out in 2010. If you're a Head First 2D Geometry reader and you're moving your new skills into proofs, please do come and talk to us at[...] - the more we know about what you find difficult the better our books become.

[Hmm... I can't submit unless I rate the item - so obviously I'm giving it 5 stars - but I don't expect anyone to take my rating at face value!]

This book is not about proofs
Since the average student of geometry is having problems performing the proofs which make up the largest portion of any geometry course, I'd say that most high school and college geometry students will not get that much out of this book. Most geometry students easily grasp how to make geometric calculations, what they can't do is formally prove why those calculations are correct.

However, if you are a technician and you need to learn how to solve problems using geometry and think geometrically, this is a very good book, and that is why I give it five stars. The table of contents are:

Chapter 1. Finding Missing Angles
Chapter 2. Similarity and Congruence
Chapter 3. The Pythagorean Theorem
Chapter 4. Triangle Properties
Chapter 5. Circles
Chapter 6. Quadrilaterals
Chapter 7. Regular Polygons

O'Reilly plans to publish a similar practitioner's book on 3D geometry and eventually print still another Head First book on those who need to learn how to perform proofs in geometry.

If you've never seen the Head First series of books before, they are completely different from conventional textbooks. They use pictures, fake interview sessions, Q&A sessions, and even crossword puzzles to help you understand concepts. They'll even set you down the wrong path to solving a problem just to help you remember the right path better. This approach works particularly well for something as visual as geometry. Highly recommended for the practitioner and technician, but not the student of geometric proofs. ... Read more

Product Description
The fourth edition of Probability, Random Variables and Stochastic Processes has been updated significantly from the previous edition, and it now includes co-author S. Unnikrishna Pillai of Polytechnic University. The book is intended for a senior/graduate level course in probability and is aimed at students in electrical engineering, math, and physics departments. The authors' approach is to develop the subject of probability theory and stochastic processes as a deductive discipline and to illustrate the theory with basic applications of engineering interest. Approximately 1/3 of the text is new material--this material maintains the style and spirit of previous editions. In order to bridge the gap between concepts and applications, a number of additional examples have been added for further clarity, as well as several new topics.Amazon.com Review
This text is a classic in probability, statistics, andestimation and in the application of these fields to modern engineeringproblems. Probability, Random Variables, and StochasticProcesses assumes a strong college mathematics background. Thefirst half of the text develops the basic machinery of probability andstatistics from first principles while the second half developsapplications of the basic theory. Topics in the first section includeprobability distributions and densities, random variables and vectors,expectations, covariance, correlations, functions of random variablesand vectors, and conditional distributions and densities. In thisthird edition of the text, the second half of the book has beensubstantially updated and expanded to include new or reviseddiscussions of the following topics: mean square estimation,likelihood tests, maximum entropy methods, Monte Carlo techniques,spectral representations and estimation, sampling theory, bispectraand system identification, cyclostationary processes, deterministicsignals in noise, and the Wiener and Kalman filters. Probability,Random Variables, and Stochastic Processes covers a remarkabledensity of material and the clarity of both presentation and notationmake this book invaluable as a text and a reference. ... Read more

Customer Reviews (32)

Easily the most incomprenesible book written on the subject - EVER
This book should never have made it past an editor.All examples at the theoretical level, nothing is ever explained indepedently. Many cross references, even to chapters that follow the current one.The authors succeed in making relatively simple probability utterly impossible to follow.Rediculous math notations.If your professor uses this text, take another course.

Great book
I have used this book as a course for stochastic processes.This is the prerequisite for every comm. graduate class.Papoulis is an elegant writer and this style suits me well. I prefer the most elegant solution to a problem or proof.I find that this book is excellent for reference and self-teaching.I know that many disagree with me but after all this book is intended for graduate work.There are undergraduate type books that are easier to read but not as insightful.Steve Kay's book is pretty good but lacks the rigor that this book has that makes it difficult to cite as a reference in a publication.As a researcher and professional engineer, I always turn to Papoulis.And though I have many other probability books, I find that Papoulis has better coverage in applications to other fields.The chapter on queuing theory is excellent and was very useful in my networking class.I do believe that this fourth edition is the best in terms of coverage, though the other editions are good also.My only gripe about the fourth edition is the long errata for the 1st printing.Subsequent printings correct much of this but some errors still exist.And now it seem to be only offered on Amazon in softcover.Very unfortunate for this classic.

Not an INTRODUCTION!!!
I cannot believe that this book is used as a classic text book for probability and stochastic processes courses for engineering students.

You definitely shouldn't start learning about probability and random variables with Papoulis.

There are so many Greek symbols in this book that readingit was more like reading Plato's dialogues instead of a math book.

Maybe this book would make sense to someone with an Advanced Math degree or at the graduate level who also can read greek!

changing edition
you are not good becuase you changed my order last time. i ordered forth edition and you sent third edition

Adequate in many ways but falls short of being a classic.
The late Prof. Papoulis received degrees in electrical engineering and mathematics at the National Technical University in Athens and the University of Pennsylvania. This textbook was used in my graduate-level course on 'Probability and Stochastic Processes' as part of my MS in electrical engineering. During the course we managed to cover Chapters 1 - 7 (Probability and Random Variables), and Chapter 15 (Markov Chains). One of the strongest points of this book is the large number of solved examples provided per chapter, as well as end-of-chapter problems for which an electronic solutions manual is available.

WHO SHOULD USE THIS BOOK: From an engineering graduate student's perspective, this textbook is a solid reference tool if you wish to look up the mechanics of individual/joint probability density functions or introductory material on stochastic processes.
However, this book is unsuitable for self-study or for reading from cover-to-cover. Part II of the book which deals with stochastic processes and estimation theory is again somewhat incoherently presented and other textbooks are recommended for an in-depth study of these topics.
... Read more