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Algebra, an Elementary Text-book for the Higher Classes of Secondary Schools and for Colleges

In addition to the standard topics, this volume contains many topics not often found in an algebra book, such as inequalities, and the elements of substitution theory. Especially extensive is Chrystal's treatment of the infinite series, infinite products, and (finite and infinite) continued fractions.

Theory of Interest and Annuities Certain. § 1.] Since the mathematical theory of
interest and annuities affords the best illustration of the principles we have been
discussing in the last two chapters, we devote the present chapter to a few of the
more elementary propositions of this important practical subject. What we shall
give will be sufficient to enable the reader to form a general idea of the principles
involved. Those whose business requires a detailed knowledge of the matter
must ...

Randomization Methods in Algorithm Design

DIMACS Workshop, December 12-14, 1997

Five Papers on Logic and Foundations

99, 1972 A METHOD OF PRESENTING THE THEORY OF ALGORITHMS AND
ENUMERABLE SETS* G. S. CEfllN §1. The purpose of this article is to describe a
mathematical formalism which for certain applications of the theory of algorithms
may be more convenient than normal algorithms, Turing machines, etc. For
example, in constructive analysis one often needs to prove the existence of
algorithms which operate in a prescribed manner. In many cases, the very
description of the ...

Handbook of Demonstrations and Activities in the Teaching of Psychology: Personality, abnormal, clinical-counseling, and social

For those who teach students in psychology, education, and the social sciences, the Handbook of Demonstrations and Activities in the Teaching of Psychology, Second Edition provides practical applications and rich sources of ideas. Revised to include a wealth of new material (56% of the articles are new), these invaluable reference books contain the collective experience of teachers who have successfully dealt with students' difficulty in mastering important concepts about human behavior. Each volume features a table that lists the articles and identifies the primary and secondary courses in which readers can use each demonstration. Additionally, the subject index facilitates retrieval of articles according to topical headings, and the appendix notes the source as it originally appeared in Teaching of Psychology--especially useful for users needing to cite information. The official journal of the Society for the Teaching of Psychology, Division Two of the American Psychological Association, Teaching of Psychology is a highly respected publication devoted to improving teaching and learning at all educational levels. Volume III consists of 95 articles about teaching personality, abnormal, clinical-counseling, and social psychology. Divided into four sections (one for each specialty), the book suggests ways to work with case studies, advocate a research perspective, use the arts and literature as teaching tools, and otherwise facilitate understanding of theoretical concepts.

For those who teach students in psychology, education, and the social sciences, the Handbook of Demonstrations and Activities in the Teaching of Psychology, Second Editionprovides practical applications and rich sources of ideas.

Techniques of Problem Solving

The purpose of this book is to teach the basic principles of problem solving, including both mathematical and nonmathematical problems. This book will help students to ... translate verbal discussions into analytical data. learn problem-solving methods for attacking collections of analytical questions or data. build a personal arsenal of internalized problem-solving techniques and solutions. become ``armed problem solvers'', ready to do battle with a variety of puzzles in different areas of life. Taking a direct and practical approach to the subject matter, Krantz's book stands apart from others like it in that it incorporates exercises throughout the text. After many solved problems are given, a ``Challenge Problem'' is presented. Additional problems are included for readers to tackle at the end of each chapter. There are more than 350 problems in all. This book won the CHOICE Outstanding Academic Book Award for 1997. A Solutions Manual to most end-of-chapter exercises is available.

[POL1] G. Polya, How to Solve It, Princeton University Press, Princeton, 1988. [
POL2] G. Polya, Mathematics and Plausible Reasoning, in two volumes.
Princeton University Press, Princeton, 1954. [POK] G. Polya and J. Kilpatrick, The
Stanford ...

Geometri?eskie svojstva krivyh vtorogo porâdka

"Geometry Of Conics deals with the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, this book moves to less trivial results, both classical and contemporary. It demonstrates the advantage of purely geometric methods of studying conics."--Publisher's website.

Starting with the well-known optical properties of conics, this book moves to less trivial results, both classical and contemporary. It demonstrates the advantage of purely geometric methods of studying conics."--Publisher's website.

Mutually Catalytic Super Branching Random Walks: Large Finite Systems and Renormalization Analysis

Large Finite Systems and Renormalization Analysis

We study features of the longtime behavior and the spatial continuum limit for the diffusion limit of the following particle model. Consider populations consisting of two types of particles located on sites labeled by a countable group. The populations of each of the types evolve as follows: Each particle performs a random walk and dies or splits in two with probability $\frac{1}{2}$ and the branching rates of a particle of each type at a site $x$ at time $t$ is proportional to the size of the population at $x$ at time $t$ of the other type. The diffusion limit of ``small mass, large number of initial particles'' is a pair of two coupled countable collections of interacting diffusions, the mutually catalytic super branching random walk. Consider now increasing sequences of finite subsets of sites and define the corresponding finite versions of the process. We study the evolution of these large finite spatial systems in size-dependent time scales and compare them with the behavior of the infinite systems, which amounts to establishing the so-called finite system scheme. A dichotomy is known between transient and recurrent symmetrized migrations for the infinite system, namely, between convergence to equilibria allowing for coexistence in the first case and concentration on monotype configurations in the second case. Correspondingly we show (i) in the recurrent case both large finite and infinite systems behave similar in all time scales, (ii) in the transient case we see for small time scales a behavior resembling the one of the infinite system, whereas for large time scales the system behaves as in the finite case with fixed size and finally in intermediate scales interesting behavior is exhibited, the system diffuses through the equilibria of the infinite system which are indexed by the pair of intensities and this diffusion process can be described as mutually catalytic diffusion on $(\mathbb{R}^+)^2$. At the same time, the above finite system asymptotics can be applied to mean-field systems of $N$ exchangeable mutually catalytic diffusions. This is the building block for a renormalization analysis of the spatially infinite hierarchical model and leads to an association of this system with the so-called interaction chain, which reflects the behavior of the process on large space-time scales. Similarly we introduce the concept of a continuum limit in the hierarchical mean field limit and show that this limit always exists and that the small-scale properties are described by another Markov chain called small scale characteristics. Both chains are analyzed in detail and exhibit the following interesting effects. The small scale properties of the continuum limit exhibit the dichotomy, overlap or segregation of densities of the two populations, as a function of the underlying random walk kernel. A corresponding concept to study hot spots is presented. Next we look in the transient regime for global equilibria and their equilibrium fluctuations and in the recurrent regime on the formation of monotype regions. For particular migration kernels in the recurrent regime we exhibit diffusive clustering, which means that the sizes (suitably defined) of monotype regions have a random order of magnitude as time proceeds and its distribution is explicitly identifiable. On the other hand in the regime of very large clusters we identify the deterministic order of magnitude of monotype regions and determine the law of the random size. These two regimes occur for different migration kernels than for the cases of ordinary branching or Fisher-Wright diffusion. Finally we find a third regime of very rapid deterministic spatial cluster growth which is not present in other models just mentioned. A further consequence of the analysis is that mutually catalytic branching has a fixed point property under renormalization and gives a natural example different from the trivial case of multitype models consisting of two independent versions of the fixed points for the one type case.

[DF1] [DF2 [DG1] [DG2 [DG3) [DG4] [DG5] (DGV [DGW] [DM) [FG [FK] D.A.
Dawson, K. Fleischmann, A continuous super-Brownian motion in a super-
Brownian medium, J. Theoret. Probab., 10(1), 213-276 (1997). D.A. Dawson, K.
Fleischmann, ...

An Introduction to Superprocesses

Over the past 20 years, the study of superprocesses has expanded into a major industry and can now be regarded as a central theme in modern probability theory. This book is intended as a rapid introduction to the subject, geared toward graduate students and researchers in stochastic analysis. A variety of different approaches to the superprocesses emerged over the last ten years. Yet no one approach superseded any others. In this book, readers are exposed to a number of different ways of thinking about the processes, and each is used to motivate some key results. The emphasis is on why results are true rather than on rigorous proof. Specific results are given, including extensive references to current literature for their general form.

This book is intended as a rapid introduction to the subject, geared toward graduate students and researchers in stochastic analysis. A variety of different approaches to the superprocesses emerged over the last ten years.