No comments about Mathematics: Applications and Concepts, Course 3, Student Edition.

No comments about Guiding Children's Learning of Mathematics.

5 comments about Schaum's Outline of Theory and Problems of Linear Algebra (Schaum's Outlines).

1. There are several typing errors in the solutions to the solved problems in this book, and some are just wrong. There is a version in which most of these problems were fixed, I am relatively sure that this is not the corrected version.



2. A complex subject presented in the usual Schaum's way-made easy to grasp through correct language and well-explained steps.



3. As others have noted there are simple mistakes - I was suprised at the first few early ones I found (addition mistakes, mixing variables). I almost got another book based on other reviews to supplement my course text (Anton's which is pathetic), but overall the Schaum's Outlines have been very good for me and ultimately this one did have enough examples to be helpful.
   
   Not as helpful as many of the other Schaum Outlines but I'm not terribly disappointed as I feared based on other reviews.



4. Over my career as a college educator, I have occasionally taught linear algebra and have had students ask me if I knew of a resource they could use for additional help and practice. My answer has always been to refer them to this book. Even the most abstract mathematical theory is learned by seeing problems worked through and then doing some of them on your own. As every math teacher knows, mathematics is a participatory sport and participation is defined as being intellectually engaged in following logical reasoning.
   The problems in this book start at the very beginning and cover the fundamental principles of linear algebra. If there is a weakness, it is that there is nothing in the way of applications. Linear algebra and matrices forms one of the mathematical foundations of creating moving images via computer and that is one way to quickly pique the interest of the students (and instructors).



5. The Fourth Edition of this book is out. It should have corrected some typos that I saw in this edition. It's priced about the same, so I suggest you get that one instead. See link below.
   
   Schaum's Outline of Linear Algebra, 4ed (Schaum's Outlines)

No comments about Math Contests for Grades 4, 5, and 6.

No comments about How Students Learn: Science in the Classroom.

2 comments about Homework Helpers: Basic Math And Pre-Algebra.

1. This book is for overview. It cannot be a main book. But it can be used for revision purpose.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   



2. If you are trying to refresh your basic math skills from high school, then this is the book for you. I have checked out several different basic math guides, including the "for Dummies" one, and this one is by far the best. It's small enough to fit in my bag, but still explains the problems well. I am doing so well with it that I am looking into the other topics that are covered by the series.

No comments about Math Contests For High School: School Years 2001-2002 Through 2005-2006 (Math Contests).

3 comments about The Math Behind the Music (Outlooks).

1. If one is familiar with the physics of sound, with its accompanying use of sophisticated mathematics, such as Fourier series, partial differential equations, and so on, it is not surprising to learn that some mathematicians have tried to give music theory a mathematical foundation. If one studies the historical record one will find that their efforts go back for centuries, and musicians have used their results to varying degrees of success. Philosophers of aesthetics have also attempted to find formal or mathematical theories of art, and in a few cases have completely embarrassed themselves in doing this, primarily because of their misunderstanding of the mathematics. Mathematics can be a powerful tool, and it continues its domination in science, technology, business, and industry, but it must be used where it is relevant, and not distorted to make it fit a particular scenario. This is not to say that a successful theory of mathematical aesthetics could not be developed. Indeed, it is belief of this reviewer that such a theory could be developed and would encompass music, art, and dance, and would add much to the appreciation of all these areas.
   
   In general this short book gives a good overview of what is and has been done in the systematization and composition of music using mathematics. The author has given enough to wet the reader's appetite for more in-depth coverage by perusing the many references at the end of the book. The mathematics is kept at a very elementary level, making the book more accessible to a general readership (elementary group theory plays a central role). Therefore readers with a more sophisticated mathematical background may be disappointed. Musicians, both amateur and professional, would definitely gain an appreciation of just how mathematics can encapsulate musical compositions, and how indeed these compositions can be created using various mathematical constructions. The accompanying CD is of course helpful since it music must be heard in order to be fully appreciated. The book could also be of assistance to those who are interested in fully automated musical composition such as now being done in some research programs in artificial intelligence (some of this research is discussed briefly in the book). Of course, a machine that was able to use the same reasoning patterns to do mathematics as to compose music would signal a major advance in machine intelligence.
   
   Although the book is not one on music theory, the author realizes the importance of understanding the elementary physics behind musical sounds, as well as the various tonal systems, such as the Pythagorean `circle of fifths'. He discusses these concepts early in the book, making it more self-contained. This is followed by a somewhat detailed overview of how to use group theory to create musical compositions. Towards the end of the book one finds an interesting application of L-systems to musical compositions. The book ends with the author's views on how various approaches to mathematical music have failed or have been too ad hoc to be useful.



2. Has a lot of good math theory behind the numbers, and is not that difficult to read, assuming you've had a physics class. Very interesting in some parts, too.



3. It is no coincidence that the three areas of human endeavor where there are child prodigies are mathematics, music and chess. Success in each requires a similar form of mental reasoning, with music and mathematics being the two that are most related.
   Harkleroad has written an amazing book, after the base introduction in chapter one, chapter two covers the concept of pitch, in other words the fundamentals of how sounds are different. Chapter three then uses this idea to describe how different sounds can either clash or reinforce each other. In chapter four, you learn how to vary a theme mathematically; it is here where group and subgroup operations are used to alter tunes to make new ones that still sound pleasing. Chapter five covers bell-ringing, where groups and their cosets are used to describe the permutations in the order of bell-ringing. Creating music by using random processes is the topic of chapter six, while it seems odd to think of random processes creating noise having a pleasing structure; some composers have been able to do it. Chapter seven deals with some of the patterns found in music, chapter eight, which is called "Sight Meets Sound", starts with an explanation of "millimetrization." This is the process where the rises and falls of a tune are used to trace out a graph and vice-versa. Composer Heitor Villa-Lobos used photographs of scenes such as mountains and skylines to construct the graph, from which he would compose his music. The ninth and last chapter has the title "How Not to Mix Mathematics and Music." In it, attempts to do things like using numeric sequences such as the Fibonacci numbers to compose music are explored and the reasons why they failed explained. A CD containing the musical pieces referenced in the text is included with the book.
   Although I played the saxophone in elementary school and am a regular attendee at the local symphony, I make no claim to being knowledgeable in music. Yet, I was able to read and follow this entire book and truly came away with an appreciation for how mathematics can be used to explain the structure of musical pieces.

3 comments about Schaum's Outline of Understanding Calculus Concepts.

1. This book explains the theory of differential and some integral calculus. There are worked problems, but I mostly ignored them in favor of the raw concept discussion.

   I read the book in the summer before my university Calc I class, and it seemed to make everything fit together much more quickly for me than most other students in the class. The book may not be as valuable as others for review, however.

   Highly recommended reading before you start a calculus adventure. One of the clearest explanations of calculus theory that I've ever seen. A few hours a week with this book in the summer will save you months of frustration during a hectic semester.




2. Understanding Calculus is a esay and quick way to review and learn the hard topics in that course. The author uses a simply manner to explain the exercises and the theorems discuss.



3. This book won't make you want to learn calculus because it's more boring than most textbooks. Extra explanations of concepts are always helpful, but you get explanations with every calculus book, so don't think that this book is something special.

No comments about Passing the City University of New York Mathematics Skills Assessment Test.