No comments about The Mathematics of Great Amateurs.

No comments about Corrections: A Comprehensive View.

No comments about Convex Polytopes (Graduate Texts in Mathematics).

No comments about Spline Regression Models (Quantitative Applications in the Social Sciences).

1 comments about Mathematical Olympiads, 2000-2001: Problems and Solutions from Around the World (MAA Problem Book Series).

1. This book contains a selection of very interesting problems proposed to various mathematical olympiads from USA and other countries in 2000 and 2001. The solutions are well presented and they contain very informative remarks and references, as well as cross-references to other problems proposed to mathematical competitions. All in all, this book is VERY WELL written, full of interesting problems and I WARMLY recommend it to anyone interested in mathematical competitions, or just in solving nice problems.

No comments about Mathematics, Matter and Method (Philosophical Papers, Vol. 1).

No comments about Applied Data Analytic Technique for Turning Points Research (Multivariate Applications Series).

No comments about Roots to Research.

2 comments about Numerical Analysis and Scientific Computation.

1. Leader has written this book to reflect several trends in maths during the last 20 years. One has been the rise of symbolic algebra, as exemplified by the success of such packages as Mathematica and Maple. A student who uses those to get analytic solutions to problems might simply fail to appreciate any compelling need for numerical analysis. Thus Leader offers examples of when such symbolic algebra methods fail, and numerical methods are necessary. His examples are good, but I'm not sure they will suffice for some students. Because if a maths student does not appreciate numerical analysis, even before taking any course in it, then is this merely inexperience, which Leader addresses in the book. Or it is that the student is simply not very bright? If the latter, then the book's efforts might be futile.
   
   Another trend which the book reflects is the ready availability of powerful maths packages that can perform numerical analysis. He chooses to use Matlab. Indeed, if you are already facile in this field, but need to thoroughly learn the capabilities of Matlab, you can use the book as a field guide.
   
   It is this which is the main qualitative difference between the book and those of the 70s and 80s, from which I learned the subject. There is now less need to give examples of source code for, say, applying Newton's Method of root finding. Because Matlab (or equivalent packages) already implement the method. So you can concentrate on higher level issues.
   
   The order in which he presents various subjects seems logical enough. Though you should not necessarily feel bound by this. Most chapters can be read in any order. One apparent curiosity is how the first chapter is on nonlinear systems. While the second and third chapters are on linear systems. Most texts reverse the order, since linear systems are typically considered simpler, and their analysis can usually be taken much further.
   
   It should be said that the nonlinear equations in chapter 1 are actually quite simple. And they let Leader easily introduce such ideas as the above mentioned Newton's Method.



2. I took Numerical Analysis from Professor Leader before he published this book. He gave all his students in the class his latest draft free of charge. (Which I thought was rather kind of him). I was only a sophmore at the time and a lot of the analysis went over my head, but the Matlab sections were great and have set me up for a lot of Matlab programming that has come my way ever since.
   
   As they say Practice and theory are the same in theory, but in practice they aren't. This is all too true for numerical analysis. Leader approaches theory and practice, making both clear. (Though, reader here be warned, some theoritical parts are somewhat thick especially without proper analysis background.)
   
   I am currently taking a slightly higher level Numerical Analysis class than the one Leader taught. The book required for the course is "Numerical Analysis," which isn't well written (essential steps are missing, things are skipped, theory isn't well explained, and the "practice" is practically non-existant in the book), so I pulled out Leader's book and found the information I needed to understand for the course and do the homework. (And the programming for the course isn't that difficult since I already have that down from Leader's book.) Leader's book has been a great reference.
   
   Another good book in the field is Numerical Methods for Unconstrained Optimization and Nonlinear Equations by J.E. Dennis Jr, and Rober B. Schnabel. (A classic in Applied Mathematics.)
   
   In short, Leader's book is good, and Leader is a good guy.
   
   I highly recommend the book.

1 comments about How Many Subjects?: Statistical Power Analysis in Research.

1. Helen Kraemer is a Stanford Professor with a subspecialty in statistics. She wrote this delightful book with the simple title "How many subjects." Along with Jacob Cohen's book this was one of the first statistical textbooks devoted to the determination of power and sample size in hypothesis testing situations. It is a great reference book on the topic. With the appearance of statistical software to handle the problems addressed in these books and more, the book now serve the purpose of providing a deeper understanding of the issues and an aid to help the user understand what the parameters (e.g. effect size, subject to subject variance) mean.