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An Introduction to Discrete Mathematics

Intended for a one-term course in discrete mathematics, to prepare freshmen and sophomores for further work in computer science as well as mathematics. Sets, proof techniques, logic, combinatorics, and graph theory are covered in concise form. All topics are motivated by concrete examples, often emphasizing the interplay between computer science and mathematics. Examples also illustrate all definitions. Applications and references cover a wide variety of realistic situations. Coverage of mathematical induction includes the stroung form of induction, and new sections have been added on nonhomogeneous recurrence relations and the essentials of probability.

Intended for a one-term course in discrete mathematics, to prepare freshmen and sophomores for further work in computer science as well as mathematics.

Implementing Discrete Mathematics

Combinatorics and Graphy Theory With Mathematica

This book concentrates on two distinct areas in discrete mathematics. The first section deals with combinatorics, loosely defined as the study of counting. We provide functions for generating combinatorial objects such as permutations, partitions, and Young tableaux, as well as for studying various aspects of these structures.The second section considers graph theory, which can be defined equally loosely as the study of binary relations. We consider a wide variety of graphs, provide functions to create them, and functions to show what special properties they have, Although graphs are combinatorial structures, understanding them requires pictures or embeddings. Thus we provide functions to create a variety of graph embeddings, so the same structure can be viewed in several different ways. Algorithmic graph theory is an important interface between mathematics and computer science, and so we study a variety of polynominal and exponential time problems.

This book concentrates on two distinct areas in discrete mathematics.

Computational Discrete Mathematics

Combinatorics and Graph Theory with Mathematica ®

This book was first published in 2003. Combinatorica, an extension to the popular computer algebra system Mathematica®, is the most comprehensive software available for teaching and research applications of discrete mathematics, particularly combinatorics and graph theory. This book is the definitive reference/user's guide to Combinatorica, with examples of all 450 Combinatorica functions in action, along with the associated mathematical and algorithmic theory. The authors cover classical and advanced topics on the most important combinatorial objects: permutations, subsets, partitions, and Young tableaux, as well as all important areas of graph theory: graph construction operations, invariants, embeddings, and algorithmic graph theory. In addition to being a research tool, Combinatorica makes discrete mathematics accessible in new and exciting ways to a wide variety of people, by encouraging computational experimentation and visualization. The book contains no formal proofs, but enough discussion to understand and appreciate all the algorithms and theorems it contains.

This book was first published in 2003.

A Comparison of Three Approaches to Teaching English as a Second Language

Language Teaching, (Mass: Newbury House Publishers, 1971), p. 46. Also see,
Edward M. Anthony and William E. Norris, "Method in Language Teaching,"
Readings on English as a Second Language, ed. Kenneth Croft (Cambridge,
Mass: Winthrop Publishers, Inc., 1972), p. 47. 10 Charles C. Fries, "A New
Approach to Language Learning," Teaching English as a Second Language, ed.
Harold B. Allen, (New York: McGraw-Hill Book Co., 1965), p. 85. Wilga Rivers,
Speaking in Many ...

Usage-Based Approaches to Language Acquisition and Language Teaching

Although usage-based approaches have been successfully applied to the study of both first and second language acquisition, to monolingual and bilingual development, and to naturalistic and instructed settings, it is not common to consider these different kinds of acquisition in tandem. The present volume takes an integrative approach and shows that usage-based theories provide a much needed unified framework for the study of first, second and foreign language acquisition, in monolingual and bilingual contexts. The contributions target the acquisition of a wide range of linguistic phenomena and critically assess the applicability and explanatory power of the usage-based paradigm. The book also systematically examines a range of cognitive and linguistic factors involved in the process of language development and relates relevant findings to language teaching. Finally, this volume contributes to the assessment and refinement of empirical methods currently employed in usage-based acquisition research. This book is of interest to scholars of language acquisition, language pedagogy, developmental psychology, as well as Cognitive Linguistics and Construction Grammar.

This volume presents state-of-the-art research on language acquisition from the perspective of usage-based approaches.

Experiences with community action projects

new research in the prevention of alcohol and other drug problems

Educational Action Research

Becoming Practically Critical

Action research is "about taking everyday things in the life of education and unpacking them for their historical and ideological baggage" (5). It recognizes tenets of education with a focus on the interplay between student outcomes, intuitive teaching, and the continuing collaborative development of educational pedagogy.

Action research is "about taking everyday things in the life of education and unpacking them for their historical and ideological baggage" (5).