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Isbn: 0852740379
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Isbn: 0486600815
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Isbn: 0521588073
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Isbn: 0195092023
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Isbn: 0521480582
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Reviews (39)

Great job
Kudos to the author on his well researched story. Read this to get an insight into early 20th century mathematics at Cambridge and of course, the life of the genius Ramanujam. A must buy.

Outstanding Biography
An exemplary piece of biographical writing.Kanigel brings Ramanujan, his times, and his contemporaries vividly to life.I wish even more of Ramanujan's mathematical contributions had been treated, but appreciate that a biographer has many priorities.Kanigel handles them all deftly.One of the finest (most informative and engaging) biographies I've ever read.

Reviews (12)

Good Secondary Resource
This book should seriously be used ONLY with another text. A good one (in my opinion) is Griffiths. It goes into great depth (sometimes too much) conceptually and is very weak with the mathematics. Another reviewer said somethings about not giving many applications, and i agree. It gets the idea down, but no more than that. Griffiths along side this is awesome, and if you have time after those two, take a look at Shakars book; its a little harder mathematically, but if you hit those three together, youll prolly have a good idea of what QM is about. Feynman Lectures also help.
Point being: Dont use this book alone, very good otherwise.

Better than most
Although I would agree that this is probably the best book to begin your study of quantum mechanics with, there are still serious flaws with the book.I just finished taking a class that used this text and I found that a major problem is that it never actually 'get's to the point.'Instead of telling you how to apply a technique to solving problems, the text simply assumes that you'll be able to figure that out yourself.So much of the notation goes unexplained and important points go unemphasized.I would suggest using this book if you're a first time student of quantum mechanics but supplement it with another book that explains how to do problems (Liboff or Griffiths).

Great treatment of basic topics
Several of the other reviews here express my general, very positive feelings about this book, so I'll concentrate on two specific examples which illustrate the teaching emphasis of the book's authors.

Chapters 6 and 7 introduce quantum states with a brilliant discussion of Dirac's bracket notation using polarization of light as the driving example.The student at this level typically already knows what to expect when, for example, linearly polarized light passes through a linear analyzer oriented at an angle with respect to the polarization axis.The authors develop a set of projection amplitudes for linear and circular polarization which reproduce the results familiar to the student.This makes state vectors easy to understand and, in turn, it's much easier to learn and accept the less intuitive results which come from solving more complex problems later on.I would recommend this book for these two chapters alone.

In Chapter 9 the authors in just a few pages develop a simple but quantitative theory of alpha decay which is easy to follow and relates half-life (or decay constant) to alpha-particle energy with no adjustable parameters.They then compare their result to experiment and show agreement over 24 orders of magnitude of half-life.This example wonderfully illustrates the power of simple, clear reasoning to achieve a widely applicable result.Fantastic job!

Reviews (24)

Exceptionally pretty complex analysis book
This is a very exciting introduction to complex analysis. Its most striking feature is the many excellent illustrations; pictures are used to explain things whenever possible. Needham is always eager to explain, and also to show meaning. Thus Möbius transformations are not just charming quirks; instead Needham gives a self-contained introduction to non-Euclidean geometry to show them in action. And when one needs to understand analytic functions as flows, then Needham gives a self-contained introduction to the ideas of vector analysis. Because the book always spills over on other topics like this, I keep my copy within reach at all times, as a treasure mine of beautiful, visual explanations of topics even outside of complex analysis proper. This wide scope works very well most of the time but it should be said that there are probably too many minor side topics than are appropriate in a first textbook. Sometimes Needham seems to include results not because they fit in or add something important, but because he has thought of such a pretty proof. But we quickly forgive him, for the book is so extremely loveable, and it is still by far my first choice as a first textbook of complex analysis.

essential
It is possible to memorize definitions, master proofs and work endless exercises and still feel that you don't understand what's going on.This is especially true in complex analysis.This book emphasizes the visual/geometric aspect of analytic functions at the expense of some loss of rigor.These insights are priceless.

Needham employs a wider range of mathematical tools than other books aimed at the upper level undergraduate, e.g., Palka and Brown/Churchill.This would include simple group theory, linear algebra, vector calculus and obviously geometry.Often this works very well at the expense of some digression. At other times, the more traditional algebraic approach is better.

This book is unique and fills an important need.

Reviews (1)

Great piece of Mathematical History!
This is a great book on the life and Complex Variable Analysis work of Augustine Cauchy.

Smithies brings many of the quaint, yet pertinent pieces that comprise the rich field called Complex Variables together into a mathematical jigsaw. I for one was fascinated to see the link between the CR Equations and Green's Theorem.

Using copious examples, directly from Cauchy's published as well as unpublished notes, Smithies enlightens the reader of the genius of Cauchy. To the reader versed in modern representation of Complex Variable theory, Smithies insistence on sticking to Cauchy's formulation of complex functions in real terms and then using his method of separation may seem laborious at first, but it rewards the reader by giving deep insight into Cauchy's thought processes.

The book covers a wide field of Complex Variables from the formulation of Cauchy's Theorem, Cauchy's Integral Formula, the Residue Theorem and Integrals between imaginary limits.

Remarkable though his work was, the book shows the almost insular nature of Cauchy - by sometimes never publishing his results and being either unaware or disdainful of other results, e.g. d':Alembert, Gauss, Euler, etc.

Editorial Review

Reviews (3)

Readable, Enjoyable! Like Physics ought to be!
The text is lucid in its presentation of what is often viewed as a difficult subject.

Starting with no more than a sound understanding of sixth form (high school) Mathematics and Physics, the authors proceed to underpin elementary concepts of electrostatics, simple circuits, and magnetism with the rigour and completeness demanded at University level. New mathematical ideas are introduced gently (so naturally, in fact, that the reader does not feel that (s)he is being asked to learn some new things!) and blended into the key Physical concepts.

The book accelerates through a whole lot of material and tacitly introduces the reader to Maxwell's Equations without calling them so. Only after all of the core physical concepts - Dielectrics, Steady Currents and Magnetic Fields, Ferromagnetism, Electromagnetism/Induction - have been covered, do the authors venture to integrate the mathematics into Maxwell's equations. This emphasis on the Physics (with the Mathematics working merely as a tool) works really well and is central to the readability of this book.

The latter chapters explore Transmission Lines, Electromagnetic Waves (which the mathematically inclined texts like to boast about as solutions of Maxwell's Equations), and the beginnings of Relativistic Electrodynamics.

All in all, an excellent, enjoyable book - highly recommended! Makes Physics fun!

Lastly, I might add that I was one of the "guinea pigs" at Manchester who benefited directly from the materials in this book and others in the Manchester Physics Series.

Excellent, Readable! Like Physics ought to be!
The text is lucid in its presentation of what is often viewed as a difficult subject.

Starting with no more than a sound understanding of sixth form (high school) Mathematics and Physics, the authors proceed to underpin elementary concepts of electrostatics, simple circuits, and magnetism with the rigour and completeness demanded at University level. New mathematical ideas are introduced gently (so naturally, in fact, that the reader does not feel that (s)he is being asked to learn some new things!) and blended into the key Physical concepts.

The book accelerates through a whole lot of material and tacitly introduces the reader to Maxwell's Equations without calling them so. Only after all of the core physical concepts - Dielectrics, Steady Currents and Magnetic Fields, Ferromagnetism, Electromagnetism/Induction - have been covered, do the authors venture to integrate the mathematics into Maxwell's equations. This emphasis on the Physics (with the Mathematics working merely as a tool) works really well and is central to the readability of this book.

The latter chapters explore Transmission Lines, Electromagnetic Waves (which the mathematically inclined texts like to boast about as solutions of Maxwell's Equations), and the beginnings of Relativistic Electrodynamics.

All in all, an excellent, enjoyable book - highly recommended! Makes Physics fun!

Lastly, I might add that I was one of the "guinea pigs" at Manchester who benefited directly from the materials in this book and others in the Manchester Physics Series.

Reviews (5)

A great history book!
Edna Kramer's is perhaps the best of the genre of books on the History of Mathematics.

The most pleasing feature about this book is that it is a fine balance between the mathematical ideas and the lives of the mathematicians. Best of all, it paints a sympathetic history of the times in which the discoveries were made. The use of anecdotes and "little" events in the lives of the men and women really brings to life both the subjects and their work.

Although my particular favourite sections are on the achievements of Euler, Gauss, Lagrange, d'Alambert, Ricci, Levi Civita, and Riemann, the book is truly an expansive landscape - there is coverage of virtually all the greats from the 16th century onwards. There are numerous examples from which to learn the basics of the mathematics. For instance, the sections on the history of the calculus are interwoven with simple, yet lucid examples. Equally, the more complex ideas like integral equations and partial differential equations are illustrated by examples drawn from the physical world.

All this makes the book worthwhile - it DOES NOT skirt over the Mathematics, but rather, makes an active attempt at imparting knowledge and understanding. This makes the book ideal for both the Maths specialist who is interested in history and for the generalist seeking a broad understanding without being daunted by the Maths. Kramer has done a marvellous job in meeting this tough challenge.

If this book has one failing, it is the way it skims over mathematical contributions from non-western societies, but it balances this somewhat by not overplaying the "Greek card". Some books do go on about Euclid as if he was the Newton of the ancients! Having said this, it can be excused since the book is quite old and much new knowledge has been gained on contributions from India and China in the last couple of decades. The interested reader may also wish to look up George Joseph's book, "The flight of the Peacock" for this.

An ideal book for both history and mathematics. I have had my copy for 20 years and it keeps my interest, still. Thoroughly recommended!

Thirty Years and Still the Best
I first read "The Nature and Growth of Modern Mathematics" in1970 as an engineering student with minors in math and physics. This book,over the course of a summer, provided me with the history of mathematicaldevelopment at the same time leaving me with the elementals of math areasin which I had not submerged myself. The effect was a tremendous weavingtogether of mathematical knowledge - both the rudiments of theory andsimple examples of applications - which has served me well in the decadessince.

There is a great deal of power in the present era from being ableto recognize the appropriate techniques from a more wide knowledge base, attimes, yes, to synthesize two or more techniques to solve a potent problemor develop an application. Edna Kramers book gave me a great deal, and itis written in a way that could assist people in all occupations and withall interests.

It is a fascinating and at times awe inspring overview ofmath.

Reviews (1)

A good little "bridge" from School Maths into University
It is amazing that, despite the changing fads in the curriculum, this book has the quality to remain a steadfast bridge from School Mathematics on the first steps into the realm of the Maths specialist for over 40 years now.

The recipe is simple: keep it short, keep it sweet, keep it simple! Mr Burkill has produced a fine little book that gently guides the new student embarking on a specialism in Maths. The author has struck a good balance between the problem solving so familiar at school and introducing the rigour of Mathematical Analysis.

Familiar concepts like differentiation and integration are brought into play right after a quick refresher on numbers and then introducing the notion of limit within the framework of sequences. The delta-epsilon construct is used to great effect to give meaning to the ideas of convergence of sequences and the continuity of functions.

These then lead naturally to the Differential calculus where previously learnt ideas like the rules of differentiation are placed in a rigorous setting and interesting elementary analytical results such as the Mean Value Theorem and Taylor's theorem are discussed. The chapter on Infinite series together with the elementary rules for testing for convergence is followed by a chapter on the special functions of analysis as defined in terms of series - e.g. exp, log, sin, cos, etc.

The chapter on the Integral Calculus makes a natural next step utilising the ideas of an integral as a limit and of infinite series. Specific techniques such as the integral to infinity and approximation methods are placed on a rigorous footing. The final chapter introduces functions of several variables.

The book has lots of worked examples within the text, which aid understanding of new material. As a bonus, there are also several end of section with notes/hints at the end of the book.

Reviews (4)

a good history book, a bad mathematics book
there have been glowing reviews for this text but i do not think they accurately reflect the book in its entirety. that is to say, that yes, as a history book, this is a good reference book with a lot of information. however, as a book to teach students about mathematics, it falls far from even being decent. the text is poorly laid out, often fudging the exactness of crucial definitions, with the finer details being left to the reader to figure out in each chapters example problems. the chapter problems in general require a much greater of mathematics than the book is willing to give and do not build very well upon one another. good for reading about the history, but if you're trying to learn the math behind it, you may just wind up very, very frustrated.

a brief opinion
As a phd student in economics, the study of mathematics is more than a parallel, it is a symmetrical relationship. In the study of mathematics, further appreciation of its tools and meaning can be better appreciated in an understanding of its roots and the needs of such tools.This book offers that and more.It is thorough yet comprehendible to even the casual student of mathematics.

It should be considered the premier text on the subject of mathematical history as well as a wonderfully written text of reference.A+++!

A super reference!
Katz's book is one of the best general works on the history of Mathematics around!

Its over-riding feature is that it is a TEXTBOOK - one that can be used for systematic study of the subject. Though tilted in favour of the mathematically inclined reader, the author has managed to connect the Maths to the History. The book has numerous topical exercises, sidebars and focus essays, which makes the subject easily accessible to the student. Yet, the structure and presentation are such that they also allow the book to be used simply as a reference or one that can be read purely for interest. Each chapter is followed by Exercises to assist the student to assess their learning and copious references that can be followed up for more details.

As with most good books of this genre, Mathematical developments from the last four centuries or so are most comprehensively presented. All the material is here: the "tussle" between Algebra and Geometry, the formal beginnings of the Calculus, the growth of Analysis, the development of new Mathematical techniques to tackle problems in Physics, and Probability mathematics.

The book places these developments within the socio-political context. Each chapter and main section starts with a preamble setting out the environment, the stimuli for the mathematical development to be discussed, etc. So, important events like the Renaissance, the French Revolution, etc. are discussed. In this regard, the use of Biography boxes for the main characters in the story of Mathematics helps to render the book more accessible to readers who may not be Mathematical. For instance, the chapter on Differential Equations would be inaccessible to the non-Mathematical reader were it not for such boxes retelling the lives and times of people like Bernoulli, Euler, Lagrange, and Laplace.

The early chapters deal with Babylonian and Greek developments, the latter with well presented biographies of Aristotle, Plato, and Euclid, among others. The chapters on the mathematics of the Arabs is well balanced, whilst that on India and China is possibly the best I have seen in a "mainstream" work of this type.

Where other authors like Morris Kline have almost totally ignored the contributions of these cultures to the subject, Katz has done a fine job. To note a couple of examples:

(1) India as the rightful source of the decimal place value system;
(2) Bhramagupta's research into what it usually known as Pell's equation, some 1000 years before Pell, and,
(3) Madhava's derivation of the power series for the arcsine and his appreciation of convergence over 200 years before Gregory.