Showing papers in "The Mathematical Gazette in 1994"

Elementary differential equations (5th edition), by W.E. Boyce and R.C. DiPrima. Pp 553. £55.1992. ISBN 0-471-50997-3 (Wiley)

Abstract: First Order Differential Equations Second Order Linear Equations Higher Order Linear Equations Series Solutions of Second Order Linear Equations The Laplace Transform Systems of First Order Linear Equations Numerical Methods Nonlinear Differential Equations and Stability Answers to Problems Index.

An intuitive approach to calculus

Abstract: “A derivative is a linear transformation which approximates a function near to a point.” I heard this definition for the first time in 1964, in a lecture at Oxford on the calculus of several variables (the lecturer was D.A. Edwards). The words came as a revelation, and from then on I had a new conception of differential calculus. At school, I thought that I knew about calculus because I could write out proofs of differentiation ‘from first principles’. I enjoyed going through the hoops and proving that δy/δ tends to a limit, but somehow the idea of differentiation never became ‘part of me’.

The Search for E.T. Bell, also known as John Taine , by Constance Reid. Pp. 357. $35. 1993. ISBN 0-88385-508-9 (The Mathematical Association of America)

Abstract: Acknowledgments 1. The eloquence of facts 2. A habit of independent work 3. Imagination's other place 4. The prime years 5. The low road Index.

Mathematical morphology in image processing , edited by E R Dougherty. Pp530 $160. 1993. ISBN 0-8247-8724-2 (Marcel-Dekker)

Abstract: Follow up what we will offer in this article about mathematical morphology in image processing. You know really that this book is coming as the best seller book today. So, when you are really a good reader or you're fans of the author, it does will be funny if you don't have this book. It means that you have to get this book. For you who are starting to learn about something new and feel curious about this book, it's easy then. Just get this book and feel how this book will give you more exciting lessons.

Minimal Steiner trees for three dimensional networks

Abstract: I was intrigued by Brian Bolt’s note “The Home Stretch”, as it had not occurred to me to look at Steiner trees spanning networks in three dimensions before. Nor did I find any references to them in the (admittedly limited) literature I consulted, though plenty has been written about the two dimensional case (see, eg, Gardner, Wells, MacKinnon). I was quickly able to improve on Bolt's tree, and decided to investigate networks for other shapes.

A certain sense of the possibility of application 2: getting the maths-science relationship right

Abstract: The crisis in applicable maths for schools In the first paper in this series I remarked that there have been three successive paradigms which have dominated school mathematics since 1960: three “eras” of predominant pedagogy –“traditional” maths, “new” maths and “applicable” maths. The main theme of the first paper was, however, that the new degree of involvement of school mathematics with applications – which came about as a result of the third paradigm – can hardly be unlearned. It will be very difficult, if not impossible, to disengage from paradigm 3. Society is most unlikely ever to let school mathematics revert to a condition of explicit, high-academic, mandarinstyle leadership, whether of the traditional pure mathematics or the modem pure maths allegiance. Yes, the third paradigm looks as if it may be beginning to falter, but the reason, I suggest, is that we are not getting the full pedagogic benefit from the particular genre of applications we are using, and from the particular style of application-mindedness we are building into our teaching.

Runs of composite integers and the Chinese Remainder Theorem

Abstract: The distribution of the prime numbers is of course a well-trodden path. The casual enquirer, working with small numbers, soon finds that the distribution has no obvious regularities, and sees that the primes thin out. The Prime number theorem (which is not elementary) helps to firm up this observation: Prime number theorem: If π(n) is the number of primes no greater than n, then i.e. π(n)/(n/ln(n)) → 1 as n → ∞. Thus for the proportion of prime numbers upto to n, π(n)/n, we have that which tends slowly to 0.

The Penguin dictionary of information technology and computer science , by Tony Gunton. Pp 205. £5.99. 1992. ISBN 0-14-051240-3 (Penguin)

Abstract: This dictionary of information technology is aimed at managers, students and schools. Using technically precise definitions, this dictionary covers personal computing, key programming terms and concepts, common abbreviations, underlying technologies and many aspects of data processing.