5 comments about Essentials of Statistics (2nd Edition) (Triola Series).

1. I teach statistics at 2 colleges. I use this book. It is outstanding in its clarity and mathematical depth. Students with strong math backgrounds will appreciate the fine logic developed by this book as it explains statistics. The word problems are outstanding and relevant to applications across broad fields of interests. The examples are explained thoroughly. This book is very well priced for the student who is struggling to pay tuition, fees, etc. Highly recommend this book to all serious students.



2. Triola's book is, for the most part, an excellent choice for an intro stats course. As an instructor, I find it relatively easy to work with, and the included STATDISK gives students many opportunities to analyze large sets of data without having to enter hundreds of values into calculators or computers. It also contains a lot of examples taken from actual data sets; this is the text that will deflect that ubiquitous "what's this useful for in real life" question from students. A few issues, though, dog the book. In order of importance:
   
   1 - Chapter 3-6, on counting methods is either underdeveloped or overdeveloped, depending on perspective. The short section gives an everything-but-the-kitchen-sink survey of the topic - permutations and combinations and such are dealt with in one fell swoop and followed up with only a smattering of problems, giving students little oportunity to fully digest the most mathematically-intense part of the course. If you're teaching this course to math majors, you'll need additional time and material for this section (I recommend Sullivan and Mizrahi's _Finite Mathematics_); if you're teaching humanities/social science majors, who are more concerned with data collecting and analysis, I'd recommend skipping this chapter entirely.
   
   2 - The book makes such frequent references to the TI-83+ calculator that one is inclined to wonder if Triola is receiving kickbacks from Texas Instruments. Contrary to what the book would have you believe, it's not necessary to invest in this beast (retail price: >$100) in order to compute standard deviations and correlation coefficients; my students are managing just fine with their $15 calculators with statistical functions.
   
   3 - In Chapter 4, there's some mention of the principle that if, under certain assumptions, the probability of an *observed event* is very low, then the assumptions are probably incorrect. There's some merit to that, to be sure (if all 1000 of my coin flips came up heads, it's natural to question the original assumption that my coin was fair), but Triola would do well to apply the critical thinking procedures exalted in Chapter 1 to elaborate on this. For instance: it's highly unlikely that Betty Terwilliger would have won the jackpot in the Lotto 6-49 if the contest wasn't rigged (probability: 1/14000000 or thereabouts), and yet, she did. (Similar arguments can be - and have been - used to defend intelligent design and astrology.) It's a subtle concept, one that deserves more attention than the cursory "this is the law, and it's important" treatment that Triola gives it.
   
   4 - Some of the later chapters (Chapter 7 in particular) complicate matters unnecessarily. Chapter 7 expands on ideas presented in Chapter 5 and developed in Chapter 6; these connections are not exploited as much as they could be.
   
   These flaws aside, _Essentials_ is a sound survey of the subject, one that's very nicely designed with its audience of humanities and social science majors in mind. The examples are timely, and the anecdotes are interesting and relevant. The book justifies the subject matter without getting bogged down in formality, which is an ideal balance for its intended audience. In the hands of a knowledgeable and experienced instructor with sufficient prep time, it provides very good support to a statistics course for non-majors, but it's not self-contained.



3. I had this book for my Statistics I class. I've read every bit of the instruction on the book (I read everything not just what's on homework). At the end I realised I learned nothing I was still confused. Unless you have a good instructor to follow you through every step, you should skip it. This is NOT something for at home students.



4. Wow! Got the book in just 2 days! Very good condition.



5. I don't know what the hell these people are talking about, but this text is garbage... and that is an overstatement. I absolutely LOATHE this textbook. The examples are fragmented to the point you can barely connect them to the problems at the end of the chapter.... it's just a worthless waste of perfectly good money and paper.
   
   My other statistics book for psychological statistics puts this book to such shame, it's sad. So sad that I damn near cried. It's unfortunate that I couldn't use my psych stats book to go along with the current class I am taking which is utilizing this junk.
   
   Perfect text... well organized... please.
   
   F -

2 comments about Algebra 1, Practice Workbook.

1. Excellent transaction! Communication with seller was excellent and fast shipping. Highly recommended.
   
   Thanks!



2. This workbook was a big disappointment" The title Alegra 1 Study Guide and Intervention Workbook." Where are the answers? The answers should be with the study guide. I purchased the workbook so my child could reinforce mathematical skills. Let me make it clear, there are no answers in the book.

5 comments about A Course in Number Theory and Cryptography (Graduate Texts in Mathematics).

1. This is an excellent book fot those, who are interested in the theoretical background of cryptography. It was also my first book in number theory, and I had no trouble following most of the text ( except the chapter on Elliptic curves, which -as I realize now- IS difficult)

   Highly recommendable! A pleasant surprise is, that there are virtually no typos.




2. This book is an outstanding introduction to cryptographic techniques and algorithms Although it's labelled as a "graduate text in mathematics", most of it should be accessible to anyone who knows a little linear algebra. For readers just interested in the how-to of the algorithms, not even that is needed. Koblitz does a thorough job of leading up to each algorithm and proving its formal properties. He also presents the algorithms themselves, unencumbered by denser material of interest to mathematicians.

   The book covers a variety of topics - public-key encryption, primality testing, factoring, and cryptographic protocols. It introduces zero-knowledge proofs and blind transfer, techniques that offer real hope of personal privacy in a world where data transfer is mandatory. I was a little disappointed by the chapters on elliptic cryptography, however. I hoped that Koblitz would bring is explanatory powers to bear on the algorithms. Somehow, I never quite connected with his descriptions of elliptic curves - perhaps I'm just thick, or perhaps a bit more introductory material would have helped.

   The rest of the book is a very fine example of clear, readable math writing. Its clarity its range of topics earn it a place with anyone interested in cryptography, factoring, and prime numbers.




3. Chapters 1 and 2 give some elementary background material on number theory and finite fields. Chapter 3 discusses some old and naive cryptosystems. Chapter 4 discusses public key cryptosystems. In the RSA system, the receiver chooses two large primes p,q and makes public their product pq=n and some integer e relatively prime to phi(n). The sender then sends his message to the power e reduced mod n. To invert this operation one must know phi(n), i.e. one must know the factorisation n=pq. Since factoring big numbers is hard, only the intended receiver will be able to decipher the message instantly. RSA thus uses the fact that multiplying is easy but inverting it is hard; similarly, one can employ other such "trapdoor functions", such as exponentiation in Z/nZ, to create other public key cryptosystems. In chapter 5 we look at various algorithms and tricks for factorisation and primality testing. As for the cryptosystems, classical number theory that is hundreds of years old still provides the best tools (modulo arithmetic, quadratic residues, continued fractions, etc.), and in chapter 6 we see how another classical theory--elliptic curves--also proves to be fruitful in cryptography. The points of an elliptic curve over a finite field form a finite group, which we can use as the basis for new cryptosystems, analogous to how we made cryptosystems out of Z/nZ for instance. And starting with an integer and constructing corresponding finite field elliptic curves we can employ these groups and elliptic curve techniques to give improved algorithms for primality testing and factorisation.



4. How Neal Koblitz manages to squeeze the amount of material he presents into this slim volume is a miracle of nature. It even includes what most authors of graduate works leave out as a matter of course: answers to exercises. More amazing still is that far from being terse and unreadable the text is a delight.
   
   My advice to anyone interested in this field is to have this book by their side at all times. Then if the need arises to find out what makes an algorithm tick or to refresh one's mind about a well known concept it's just the flick of a page away.



5. This book is a real gem - very clearly written and covering the subject matter concisely but comprehensively. Particularly welcome are the exercises which are ingenious and extend the subject matter rather than just test knowledge of the chapter. It is extremely helpful too (and rare in a graduate text book) that solutions to all of the problems are provided at the back of the book. Exceptionally, and again very helpfully, there seem to be zero errors/typos in the text.
   
   Strongly recommended as the best introduction to this fascinating and important field

No comments about Precalculus: Graphs and Models.

4 comments about Student Solutions Manual for Stewart/Redlin/Watson's Algebra and Trigonometry, 2nd.

1. This book helps when you miss a class session. I was able to keep up when I read the text on days missed.



2. This math book helped me get into calculus without much of a mathematical background. I messed around in high school too much :p. For three months I intensely studied this book - I nearly answered all the question. I bought the answer guide to help me see what I was doing wrong. The book is easy to read and understand; all the steps are explained in an orderly manner. If you get stuck, try reading the chapter again, you might have missed a critical part of the puzzle.
   
   Many wonderful long night hours with this book. It's hard enough to keep your attention and make you want to strive to improve.



3. I'm using this book in an online trig class. Despite the lack of class instruction I'm able to move along by reading the text and doing the problems. It's a little wordy at times, but, as I'm learning in the online class, math can be a difficult subject to express in words alone.



4. I had this textbook for my precalculus class, almost never attended the clas, but got all A's on the test and A final grade -- all thanks to this book. You literally don't need a teacher, or any other sources, even if you not a science person, you will be able to understand the concepts. It has a lot of sample problems solved in each section, and then at the end of each section, the problems are listed from very simple to moderate to high difficulty. So once you will solve the simple problems, that will give you ability to solve moderate problems, and then difficult ones from there...

5 comments about Linear Algebra and Its Applications (3rd Edition).

1. This was the textbook that my school has been using for its first and second year Linear Algebra courses. I found it somewhat terse. It seems like it could be a great book for someone already familiar with linear algebra or the logic aspect of mathematics; I don't recommend it for anyone who is not very familiar with proofs. Fortunately, it doesn't lack examples of how to solve computation problems and solutions to the odd-numbered problems are provided in the back of the book. Unfortunately, when it comes to the proof problems, instead of just providing the reader with the answer like most other texts, the author will either mention a hint or refer the reader to the study guide (mine came with a disk which has to be installed on a computer), which could be a problem for readers not familiar with how to do proofs. Serving as a somewhat of a mediator between these two extremes are true/false questions which accompany each chapter in each section of the text. While those start out somewhat fun in the beginning, they can also get tiresome and repetive very quickly. The solutions to these, like the proofs, are not provided, but fortunately, all one has to do is read the text carefully in order to determine the appropriate response.



2. The organization and the treatment given to most subjects are well below what one would expect for a Wikipedia entry on each respective topic.
   
   Anyone who uses this book for any kind of self-study is unlikely to get more out of it more than a few examples on multiplying matrices, row reduction, and some poetry about eigen-spaces and vector spaces.
   
   Take a look at ``Linear Algebra Done Right'' by Alxr.



3. covers 75% of the detail and leaves the 25% up to you. it lacks clear explition is vector space secotion (row col vector nul basis etc). it seems like you do the first coumple of sections not understanding what you are getting at but when you get to chapter 6 or so the past stuff finaly makes sense. I found the book hard to understand when it was talking about maping, one to one on too. i suggest a TI-83 or higher and the solutions manual. The book also lacks pictures showing dimention row col nul basis etc.



4. I used this book to teach myself linear algebra using a lesson plan developed by a teacher. A few things I found really helpful:
   
   Lay constantly admonishes the reader to carefully study the text, by reading and re-reading. He understands that students learning linear algebra are likely to to be embarking on more abstract/advanced mathematics in the future--and he cares enough to teach good study skills as well as math. I've followed his advice, and found that with proper effort, I am able to teach myself.
   
   Many of the questions are conceptual or True/False, which helps me to retain new concepts.
   
   The study guide (sold separately, but very important if you're self-teaching) only includes answers to odd-numbered exercises. However, the answers are nicely detailed.
   
   I especially appreciate that Lay refuses to flat-out offer answers to conceptual and True/False questions. Instead, there are hints and references to page numbers where helpful information can be found. This is important, not only because it (again) helps reinforce good study skills, but it encourages students to really try a problem before giving up and looking up the answer.
   
   The introduction of new concepts is always followed by one or more examples, which helps to link theory to practice. In general, there are many examples that illustrate good problem-solving techniques. Proofs are detailed and well-justified, and there are some simple proofs that are left as problems in the book. These proofs are simple enough to not be terribly daunting to the student who is new to more abstract mathematical ideas.
   
   For the student who would ask, "well what is it good for?" there are plenty of sections dedicated purely to applications of material learned in previous sections.
   
   Detail-oriented methodical learners like myself should benefit from this book.



5. This book is good for a basic introduction, that is for people who have never really seen much linear algebra and who haven't taken a proof-based course before. I used it in my first linear algebra course as an undergrad, and also when I taught an introductory course over the summer.
   
   I especially like that it has some options, such as details of R^n being presented at the end of chapter two as an alternative to covering those facts in the more general context of "vector spaces" in chapter 4. It is not especially rigorous as far as proving things, and does not get too in depth as far as computations though there are some good sections on dynamical systems. So if you are teaching a class that is half engineers and half math majors, it strikes a decent balance.
   
   For anyone who uses linear algebra, you will not be able to get away with having this as your only book, try Strang or Axler for more computational or theoretical (respectively) treatments. It is definitely a good intro though, it gives a decent overview of the main ideas.

3 comments about Calculus: Concepts and Applications.

1. This book made a difficult subject (calculus) easy to understand through its effective use of diagrams, examples, and word problems. I would not have been able to survive Calculus BC AP without it.



2. This is a great book, I used it in my Pre-Cal and BC Cal class. It's very easy to understand, and easy to get into Calculus class!



3. This was the main textbook used for my Calculus AB class. Its explanations are clear, though sometimes difficult steps in algebraic manipulation are skipped (which may initially confuse but can be figured out after some additional work). The text progresses within each chapter, relying initially on an exploratory section where concepts are not directly stated but figured out through a little guidance with the questions. This first section introduces the readers to the concept being studied in each respective chapter. Then, the information is given in ensuing sections of the chapter. The best part of this text is the "green boxes" which sum up concepts learned, definitions, formulas, etc., which make reviewing for a final exam a much simpler task. It has a simple presentation with few colors, sticking mainly to a light olive green and gray for the pictures and other illustrations. This textbook is a very good tool for calculus students, relying on varied methods of learning and some self-discovery of the subject matter.

5 comments about Mathematical Mysteries: The Beauty and Magic of Numbers (Helix Books).

1. Clawson writes with refreshing enthusiasm and really conveys how much fun it can be to explore the nature of mathematics. Although there are many equations in the book, Clawson uses them not only to help the readers understand the mathematical ideas, but also to show how truly great mathematicians can come up with extremely elegant expressions to describe what at first would seem to be completely unmanageable concepts.



2. Clawson does an excellent job of introducing the reader to a variety of number theory topics. With each topic, he provides enough information to understand the idea and appreciate its implications without being overly technical or tedious. Suprisingly, an advanced understanding of math is not required to enjoy this book. If you have an interst in number theory and need a starting point, this is the book.



3. This book is superbly written by a highly intuitive author. The author knows how to connect to his intended readers. Book is highly informative and the equations are well defined and explained. Once you read a few pages, you are hooked. I just hope that Mr. Calvin C. Clawson will write more books on Mathematics, he will be doing a great service to would-be-mathematicians like me. More power to you sir!



4. I was a student of Mr. Clawson's, and highly recommend any student of his to use this book as a study guide.



5. This book is a gentle introduction to number theory. The material covered here is absolutely fascinating. Once you get into the text you will be hooked. Although I have read other stuff in this genre what is different about this book is that the author does not shun from giving you equations that explain the IDEA and BEAUTY behind the numbers.
   
   This book will give you hours of absolute delight. Excellent work.

2 comments about Study Guide for Stewart's Single Variable Calculus, 6th.

1. This book really helps out when you have to learn on your own. It gives a detailed work out of each problem. Helps by showing the steps and process of working the problems. Definitely worth having.



2. I have YET to receive this book requested over a month ago. I would like a full refund. I would NEVER do business this this vendor again.

1 comments about Mastering Essential Math Skills PRE-ALGEBRA CONCEPTS (Mastering Essential Math Skills).

1. I reviewed all six of the new Mastering Essential Math Skills titles at the 2008 NCTM conference. As a math consultant, I was impressed by all of them. This particular title addresses a very important need. So many students enter their first algebra class with huge gaps in their foundational skills. This book does an excellent job of introducing the pre-algebra skills which are essential to success in algebra. Just like Fisher's original books, each lesson contains review, new material, with instruction, and problem solving. After having gone through this book, students will have the necessary skills to be successful in algebra and beyond. Excellent also for students who are struggling in their pre-algebra or algebra class. Highly recommended. An excellent summer refresher.