No comments about The Implicit Function Theorem: History, Theory, and Applications.

2 comments about Matroid Theory (Oxford Science Publications).

1. The author clearly explains the topic. My only complaint is that some of the problems are rather difficult, and there isn't a solution key.



2. This is a great text on matroid theory. This book is far easier to read than other matroid book I have seen (Welsh). Second priting from 2006 fixes some of the errors in the first printing and is cheaper to boot(being a paperback).
   
   Caveat: Amazon points to wrong book as the paperback of first edition.

No comments about Connections: A World History, Combined Volume, VangoBooks (MyHistoryKit Series).

2 comments about The Theory of the Riemann Zeta-Function (Oxford Science Publications).

1. Titchmarch is well known in the theory of functions, in this book, he described the Riemann's Zeta function in the most comprehensive way. ( e. g. in the topic of functional equation, he quoted 7 methods) I cannot find any other book more comprehensive than this one. ( though in order the theories, you must have some background knowledge and patience ! )



2. This is the true encyclopaedia of the zeta function. Although I prefer Ivic, I always have the feeling that Titchmarsh wants to appear brilliant.

   This book cannot be criticized because of the amount of time and effort that must have been spent on it. It was update in 1986 by Heath Brown.
   It is useless to summarize the contents because it mainly has everything, and most theorems have several proofs and very long comments.
   One thing that is missing is more stuff about prime number distributions (for this, check Ingham, Edward's, and a bit of Ivic's).

   It never becomes redundant, and it can either be used a source for additional information, as dictionary, or it can be used in a linear way.

1 comments about Great Moments in Mathematics After 1650 (Dolciani Mathematical Expositions).

1. This book, a sequel to the one with the same title with "Before" replacing "After", is just as good as the "predecessor." Eves has no peer in exploring the development of mathematics by identifying and describing some of the "inflection points" of mathematical progress. That is a term made famous by businessman Andrew Grove and is used to refer to a time when dramatic change is occurring.
   Mathematicians, despite many conceptions to the contrary, work in a field where astonishing results sometimes occur. Eves, through his set of great moments selected from his series of lectures on the topic, ably describes some of those moments of astonishment. He also explains why the result was significant in a manner that almost everyone, including mathematically sophisticated high school students, can understand. Eves also includes problems at the end of each section, and these are excellent. They are well written and serve to solidify and expand the main points of the section. He also includes solution hints for most of the exercises.
   A partial list of the topics includes the birth of probability, the invention of the calculus, the discovery of non-Euclidean geometry, the creation of group theory, the organization of set theory, and my favorite, transfinite numbers.
   There is no better set of books available for courses in mathematical history than the two in this short series. Mathematics occasionally progresses in great bounds rather than small leaps and Eves gives detailed, understandable explanations of some of those of greatest length.

No comments about Transcendental Numbers. (AM-16) (Annals of Mathematics Studies).

No comments about Brahmagupta, Man who found zero, addition, subtraction, multiplication and division (1).

1 comments about The Ancient Tradition of Geometric Problems.

1. This is a history of Greek mathematics from the point of view of problems and problem solving, not least the three classical problems: cube duplication, circle quadrature, angle trisection. Knorr argues that this restriction is not arbitrary: "One seems typically to assume that metamathematical concerns were the effective motivating force underlying efforts of geometers ... In general, I will find most convincing the 'internalist' position that technical research is directed toward the solution of problems arising from previous and current research efforts", mathematics thus being "on the whole autonomous in setting the directions of research". So the focus on problems is a way to understand the development of Greek mathematics by exposing the mindsets of the mathematicians. This aspect is naturally very interesting, and the mere presence of such perspectives sets this book apart from the bare bones histories of Heath et al. However, grand programs and pretty pots on the cover is not everything. Our fragmented knowledge of Greek mathematics does not allow Knorr's program to be carried out in a completely satisfactory manner; neither is the big picture one of Knorr's main concerns. Instead much of the book amounts to quite specialised scholarly analysis of sources and critique of other scholarly interpretations. In the end, one is not entirely convinced that Knorr has unveiled the key to understanding Greek mathematics. His criticism of other interpretative schemes is convincing but sometimes suspiciously convenient. So, for instance, Knorr rather enjoys arguing that philosophy never had a major influence on mathematics (thus supporting his point of view) while the more interesting and relevant questions of the influences of astronomy, mechanics and optics are largely silenced.

1 comments about Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals.

1. Part of the Mathematics Across the Curriculum series, Foundations of Diatonic Theory IS mathematically based, but only requires basic math skills. While it claims to serve as a intro or basic music theory text, the first few chapters do not introduce interval names and thus require prior knowledge. On the other hand, it introduces relatively little mathematical skills such as greatest common divisor and coprime, avoiding modulo 12.
   
   This instructional text is based on the latest papers in diatonic set theory. For people who took a music theory intro class and left with more questions than they began, this book is likely what they want. Why major and minor? Why the modes? Why the diatonic scale? Why the diatonic triads and seventh chords? The book leads readers through the discovery of properties of these collections which help explain their general, and some specific, uses and qualities.

1 comments about Piero della Francesca: A Mathematician's Art.

1. It is quite amazing to stop and consider that in today's world almost anything - and I mean literally anything - if marketed properly and able to be sold for profit in a gallery (regardless of quality or creator's intelligence) is too often pawned off as fine art. Once sold those one trick ponies are ultimately meaningless, and worthless. There was a time when art meant something. Having either a context of social or political meaning, an item of spirituality and beauty or even ugliness, art once stood for solid ideological principles which could always be backed by the creator's talent of hand, eye, and certainly mind. One of the greatest artists of the early Italian Renaissance, an accomplished mathematician, Piero della Francesca painted religious works that are marked by their simple serenity and clarity and by the pure virtue of his genius; he certainly ranks among one of the greatest men who ever created fine art.
   
   Often in great works there are interesting connections between mathematics and art and Piero della Francesca - A Mathematician's Art clearly outlines that the work of della Francesca shows no exception to that connection. The book leaves the reader with an enhanced and enlightened understanding of his paintings and writings. A painter of the fifteenth century, della Francesca`s skills and talents are explored in this the first combined study of his career as both a mathematician, and as a painter.
   
   Author J. V. Field is an honorary visiting research fellow at Birkbeck College, University of London. Field has done a stunning job of describing della Francesca's background as well as the artists interests and constant ability to create outstanding works of lasting artistic significance. Field goes in-depth into della Francesca's training as an artist and examines the powerful sense of his 3D forms, his abstraction abilities, and the often-solid geometry of his writings. Field also outlines della Francesca's treatise on perspective and paintings examining the all-important optical "rules" the artist followed in his pictorial placement. The book concludes with an important consideration of the historical significance of della Francesca's tradition and connections to the Scientific Revolution. Through the art and Field's text Piero della Francesca is rightfully described as a man of intellectual strength. The book at 420 pages is beautifully illustrated with 32 color illustrations and 50 black and white.
   
   Highly recommended.