This bookfs unique approach to the teaching of mathematics lies in its use of history to provide a framework for understanding algebra and related fields. With Algebra in Context, students will soon discover why mathematics is such a crucial part not only of civilization but also of everyday life. Even those who have avoided mathematics for years will find the historical stories both inviting and gripping.
The bookfs lessons begin with the creation and spread of number systems, from the mathematical development of early civilizations in Babylonia, Greece, China, Rome, Egypt, and Central America to the advancement of mathematics over time and the roles of famous figures such as Descartes and Leonardo of Pisa (Fibonacci). Before long, it becomes clear that the simple origins of algebra evolved into modern problem solving. Along the way, the language of mathematics becomes familiar, and students are gradually introduced to more challenging problems. Paced perfectly, Amy Shell-Gellasch and J. B. Thoofs chapters ease students from topic to topic until they reach the twenty-first century.
By the end of Algebra in Context, students using this textbook will be comfortable with most algebra concepts, including
* Different number bases * Algebraic notation * Methods of arithmetic calculation * Real numbers * Complex numbers * Divisors * Prime factorization * Variation * Factoring * Solving linear equations * False position * Solving quadratic equations * Solving cubic equations * nth roots * Set theory * One-to-one correspondence * Infinite sets * Figurate numbers * Logarithms * Exponential growth * Interest calculations
Amy Shell-Gellasch is an associate professor of mathematics at Montgomery College. She is the editor of Hands on History: A Resource for Teaching Mathematics, the author of In Service to Mathematics: The Life and Work of Mina Rees, and the coeditor of From Calculus to Computers: Using the Last 200 Years of Mathematics History in the Classroom. J. B. Thoo is a mathematics instructor at Yuba College.
Hardback, 552 pages
28 b&w illus., 12 line drawings, 9 maps
ISBN:9781421417288
September 2015
ISBN: 978-1-118-92313-9
512 pages
July 2015
The second edition enhanced with new chapters, figures, and appendices to cover the new developments in applied mathematical functions
This book examines the topics of applied mathematical functions to problems that engineers and researchers solve daily in the course of their work. The text covers set theory, combinatorics, random variables, discrete and continuous probability, distribution functions, convergence of random variables, computer generation of random variates, random processes and stationarity concepts with associated autocovariance and cross covariance functions, estimation theory and Wiener and Kalman filtering ending with two applications of probabilistic methods. Probability tables with nine decimal place accuracy and graphical Fourier transform tables are included for quick reference. The author facilitates understanding of probability concepts for both students and practitioners by presenting over 450 carefully detailed figures and illustrations, and over 350 examples with every step explained clearly and some with multiple solutions.
Additional features of the second edition of Probability and Random Processes are:
Updated chapters with new sections on Newton-Pepysf problem; Pearson, Spearman, and Kendal correlation coefficients; adaptive estimation techniques; birth and death processes; and renewal processes with generalizations
A new chapter on Probability Modeling in Teletraffic Engineering written by Kavitha Chandra
An eighth appendix examining the computation of the roots of discrete probability-generating functions
With new material on theory and applications of probability, Probability and Random Processes, Second Edition is a thorough and comprehensive reference for commonly occurring problems in probabilistic methods and their applications.
Venkatarama Krishnan, PhD., is Professor Emeritus in the Department of Electrical and Computer Engineering at the University of Massachusetts at Lowell. He has served as a consultant to the Dynamics Research Corporation, the U.S. Department of Transportation, and Bell Laboratories. Dr. Krishnanfs research includes estimation of steady-state queue distribution, tomographic imaging, aerospace, control, communications, and stochastic systems. Dr. Krishnan is a senior member of the IEEE and listed in Who is Who in America.
Series: Research Perspectives CRM Barcelona
2015, X, 90 p.
Printed book
Softcover
ISBN 978-3-319-21283-8
The two parts of the present volume contain extended conference abstracts
corresponding to selected talks given by participants at the "Conference on Geometric
Analysis" (thirteen abstracts) and at the "Conference on Type Theory, Homotopy Theory
and Univalent Foundations" (seven abstracts), both held at the Centre de Recerca
Matematica (CRM) in Barcelona from July 1st to 5th, 2013, and from September 23th
to 27th, 2013, respectively. Most of them are brief articles, containing preliminary
presentations of new results not yet published in regular research journals. The articles are
the result of a direct collaboration between active researchers in the area after working in
a dynamic and productive atmosphere.
The first part is about Geometric Analysis and Conformal Geometry; this modern field lies
at the intersection of many branches of mathematics (Riemannian, Conformal, Complex or
Algebraic Geometry, Calculus of Variations, PDE's, etc) and relates directly to the physical
world, since many natural phenomena posses an intrinsic geometric content. The second
part is about Type Theory, Homotopy Theory and Univalent Foundations.
The book is intended for established researchers, as well as for PhD and postdoctoral
students who want to learn more about the latest advances in these highly active areas of
research.
Series: Springer Monographs in Mathematics
2015, IX, 196 p. 5 illus.
Printed book
Hardcover
ISBN 978-4-431-55746-3
* Presents quite recent research works, all of very high standard, in the
field of several complex variables
* Selects only extremely important materials from the conventional
basic theory of complex analysis and manifold theory
* Requires no more than a one-semester introductory course in
complex analysis as a prerequisite for understanding
The purpose of this monograph is to present the current status of a rapidly developing
part of several complex variables, motivated by the applicability of effective results to
algebraic geometry and differential geometry. Highlighted are the new precise results on
the L2 extension of holomorphic functions.
In Chapter 1, the classical questions of several complex variables motivating the
development of this field are reviewed after necessary preparations from the basic
notions of those variables and of complex manifolds such as holomorphic functions,
pseudoconvexity, differential forms, and cohomology. In Chapter 2, the L2 method of
solving the d-bar equation is presented emphasizing its differential geometric aspect.
In Chapter 3, a refinement of the Oka*Cartan theory is given by this method. The L2
extension theorem with an optimal constant is included, obtained recently by Z. B*ocki
and by Q.-A. Guan and X.-Y. Zhou separately. In Chapter 4, various results on the Bergman
kernel are presented, including recent works of Maitani*Yamaguchi, Berndtsson, and
Guan*Zhou. Most of these results are obtained by the L2 method. In the last chapter,
rather specific results are discussed on the existence and classification of certain
holomorphic foliations and Levi flat hypersurfaces as their stables sets. These are also
applications of the L2 method obtained during these 15 years.
Series: Fields Institute Communications, Vol. 75
2015, XII, 424 p. 47 illus., 19 illus. in color.
Printed book
Hardcover
ISBN 978-1-4939-2949-8
This book is a unique selection of work by world-class experts exploring the latest
developments in Hamiltonian partial differential equations and their applications. Topics
covered within are representative of the fieldfs wide scope, including KAM and normal
form theories, perturbation and variational methods, integrable systems, stability of
nonlinear solutions as well as applications to cosmology, fluid mechanics and water
waves.
The volume contains both surveys and original research papers and gives a concise
overview of the above topics, with results ranging from mathematical modeling to
rigorous analysis and numerical simulation. It will be of particular interest to graduate
students as well as researchers in mathematics and physics, who wish to learn more
about the powerful and elegant analytical techniques for Hamiltonian partial differential
equations.