Series: Sources and Studies in the History of Mathematics and
Physical Sciences
2007, Approx. 560 p., 259 illus., Hardcover
ISBN: 0-387-34543-4
Due: January 2007
About this book
The book analyzes the mathematical tablets which are in the
possession of a private collector, Martin Schoyen. This
collection contains all sorts of tablets, some similar to
classical ones but also others with fascinating new material.
Here the author translates their mathematical content, compares
it with previous known material, then evaluates the period of the
tablet and its purpose. This allows the author to provide new
insights into the interpretation of some classical tablets, as
for example Plimpton 322 which has an exclusive appendix.
What makes this book so unique is the light being shed on
Babylonian mathematics. For instance, new evidence of Babylonian
familiarity with sophisticated mathematical objects is provided,
including the knowledge of the three dimensional Pythagorean
equation and the familiarity with the geometry of the icosahedron
is new and unexpected. The author is a master of analysis of the
errors found in the tablets. It is well known that computational
errors in the tablets are revealing of the algorithms employed in
the computations. The author exploits with mastery this clever
technique to gain new insight in the mathematical reasoning
behind the content of the tablets. From the analysis it becomes
increasingly clear that Babylonians were outstanding calculators,
probably only comparable in modern times with exhibition genius
calculators. For example, it appears that schoolboys were
familiar with the multiplication tables at least up to 25!. He
also gives numerous geometrical possible explanations and
interpretations of the tablets. Another very important finding is
the use of the zero notation in novel contexts and periods.
The book is very carefully written and organized, the tablets are
classified according to their mathematical content and purpose,
while useful drawings and pictures are provided for the most
interesting tablets. The author makes a great effort to make the
material accessible to both assyriologists and mathematicians.
There is an introduction with basic background on babylonian
mathematics and on numerous occasions the author reviews basic
mathematical material
Table of contents
Acknowledgements.- Introduction.- Documentation of Provenance.-
Abbreviations.- How to Get a Better Understanding of Mathematical
Cuneiform Texts.- Old Babylonian Arithmetical Hand Tablets.- Old
Babylonian Arithmetical Table Texts.- Old Babylonian Metrological
Table Texts.- Mesopotamian Weight Stones.- Neo-Sumerian Field
Maps (Ur III).- An Old Sumerian Metro-Mathematical Table Text (Early
Dynastic IIIa).- Old Babylonian Hand Tablets with Practical
Mathematics.- Old Babylonian Hand Tablets with Geometric
Exercises.- The Beginning and the End of the Sumerian King List.-
Three Old Babylonian Mathematical Problem Texts from Uruk.- Three
Problem Texts Not Belonging to Any Known Group of Texts.- App. 1.
Subtractive Notations for Numbers in Mathematical Cuneiform Texts.-
App. 2. The Old Babylonian Combined Multiplication Table.- App. 3.
An Old Babylonian Combined Arithmetical Algorithm.- App. 4.
Cuneiform Systems of Notations for Numbers and Measures.- App. 5.
Old Babylonian Complete Metrological Tables.- App. 6. Metro-Mathematical
Cuneiform Texts from the Third Millennium BC.- App. 7. CUNES 50-08-001.
A Combined Metro-Mathematical Table Text (ED IIIb).- App. 8.
Plimpton 322, a Table of Parameters for igi?igi.bi Problems.- App.
9. Many-Place Squares of Squares in Late Babylonian Mathematical
Texts.- App. 10. Color Photos of Selected Texts.- Vocabulary for
the MS Texts.- Index of Subjects.- Index of Texts.- References.
2007, Approx. 295 p., Hardcover
ISBN: 0-387-34432-2
Online version available
Due: January 2007
About this textbook
This book is an introduction to the mathematics of finance. Part
I focuses on analysis of deterministic cash flows, such as those
generated by riskless bonds and annuities. Part II focuses on the
analysis of risky securities, such as stocks and options. This
book is suitable for undergraduates in mathematics, economics and
business programmes. It contains examples and exercises
throughout. This book uses investing as a vehicle to introduce
ideas, techniques and applications that might not be encountered
other mathematics courses. These include proofs by induction,
recurrence relations, inequalities (in particular, the Arithmetic-Geometric
Mean inequality and the Cauchy-Schwarz inequality), and the
elements of probability and statistics. The book introduces the
reader to the elements of investing that are of life-long
practical use. This book targets students at the sophomore/junior
level, without assuming a background or any experience in
investing.
Table of contents
Preface.- Interest - Simple.- Interest - Compound.- Inflation and
Taxes.- Annuities.- Loans and Risks.- Amortization.- Credit Cards.-
Bonds.- Stocks and Stock Markets.- Stock Market Indexes, Pricing,
and Risk.- Options.- Appendix: Induction, Recurrence Relations,
Inequalities.- Appendix: Statistics.- Answers.- References.-
Index.
2007, Approx. 550 p., 350 illus., Softcover
ISBN: 0-8176-4482-2
Due: April 2007
About this textbook
Dynamical Systems with Applications Using MathematicaR provides
an introduction to the theory of dynamical systems with the aid
of the Mathematica computer algebra package. The book has a very
hands-on approach and takes the reader from basic theory to
recently published research material. Emphasized throughout are
numerous applications to biology, chemical kinetics, economics,
electronics, epidemiology, nonlinear optics, mechanics,
population dynamics, and neural networks.
Throughout the book, the author has focused on breadth of
coverage rather than fine detail, with theorems and proofs being
kept to a minimum. The first part of the book deals with
continuous systems using ordinary differential equations, while
the second part is devoted to the study of discrete dynamical
systems. Exercises are included at the end of every chapter. Both
textbooks and research papers are presented in the list of
references
Table of contents
Preface.- A tutorial introduction to Mathematica.- Differential
equations.- Planar systems.- Interacting species.- Limit cycles.-
Hamiltonian systems, Lyapunov functions, and stability.-
Bifurcation theory.- Three-dimensional autonomous systems and
chaos.- Poincare maps and nonautonomous systems in the plane.-
Local and global bifurcations.- The second part of David
Hilbert's sixteenth problem.- Linear discrete dynamical systems.-
Nonlinear discrete dynamical systems.- Complex iterative maps.-
Electromagnetic waves and optical resonators.- Fractals and
multifractals.- Chaos control and synchronization.- Neural
networks.- Examination-type questions.- Solutions to exercises.-
References.- Mathematica program file index.- Index
2007, X, 390 p., Hardcover
ISBN: 0-387-36034-4
Due: June 2007
About this book
Differential forms satisfying the A-harmonic equations have found
wide applications in fields such as general relativity, theory of
elasticity, quasiconformal analysis, differential geometry, and
nonlinear differential equations in domains on manifolds.
This monograph is the first one to systematically present a
series of local and global estimates and inequalities for such
differential forms in particular. It concentrates on the Hardy-Littlewood,
Poincare, Cacciooli, imbedded and reverse Holder inequalities.
Integral estimates for operators, such as homotopy operator, the
Laplace-Beltrami operator, and the gradient operator are also
presented. Additionally, some related topics such as BMO
inequalities, Lipschitz classes, Orlicz spaces and inequalities
in Carnot groups are discussed in the concluding chapter. An
abundance of bibliographical references and historical material
supplement the text throughout.
This book will serve as an invaluable reference for researchers,
instructors and graduate students in analysis and partial
differential equations and could be used as additional material
for specific courses in these fields.
Table of contents
Hardy-Littlewood Inequalities.- Norm Comparison Theorems.-
Poincare-type inequalities.- Caccioppoli Inequalities.- Imbedding
Inequalities.- Reverse Holder Inequaltiies.- Estimates for
Jacobians.- Inequalities for Operators.- Some related topics.-
Bibliography.- Index
2006, 130 p., Hardcover
ISBN: 4-431-34341-5
About this book
A lot of economic problems can formulated as constrained
optimizations and equilibration of their solutions. Various
mathematical theories have been supplying economists with
indispensable machineries for these problems arising in economic
theory. Conversely, mathematicians have been stimulated by
various mathematical difficulties raised by economic theories.
The series is designed to bring together those mathematicians who
were seriously interested in getting new challenging stimuli from
economic theories with those economists who are seeking for
effective mathematical tools for their researchers.
Table of contents
Takashi Adachi: Option on a unit-type closed-end investment fund.-
Takahiko Fujita, Ryozo Miura: The distribution of continuous time
rank processes.- Hirotaka Fushiya: Asymptotic expansion for a
filtering problem and a short term rate model.- Elyes Jouini,
Walter Schachermayer, and Nizar Touzi: Law invariant risk
measures have the Fatou property.- Mikio Nakayama: The dawn of
modern theory of games.- Manabu Toda: Approximation of excess
demand on the boundary and equilibrium price set.- Yuji Umezawa:
The minimal risk of hedging with a convex risk measure.- Na Zhang:
The distribution of firm size.