Mathematics

Projective geometry, and the Cayley-Klein geometries embedded into it, were originated in the 19th century.

The 2nd edition of this successful book has several new features.

"e;Serre's Conjecture"e;, for the most part of the second half of the 20th century, - ferred to the famous statement made by J.

At the QMath9 meeting, young scientists learn about the state of the art in the mathematical physics of quantum systems.

The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semi-algebraic set appear frequently in many areas of science and engineering.

The general theory of relativity, as formulated by Albert Einstein in 1915, provided an astoundingly original perspective on the physical nature of gr- itation, showing that it could be understood as a feature of a curvature in the four-dimensional continuum of space-time.

Cyclotomic fields have always occupied a central place in number theory, and the so called "e;main conjecture"e; on cyclotomic fields is arguably the deepest and most beautiful theorem known about them.

A mathematically consistent formulation of relativistic quantum electrodynamics (QED) has still to be found.

Since the late 1980s, Toeplitz operators and matrices have remained a ?

Malliavin calculus provides an infinite-dimensional differential calculus in the context of continuous paths stochastic processes.

This volume contains two of the three lectures that were given at the 33rd Probability Summer School in Saint-Flour (July 6-23, 2003).

The fascinating theory of error-correcting codes is a rather new addition to the list of mathematical disciplines.

One of the most remarkable and beautiful theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory.

From the reviews: "e;The huge literature in risk theory has been carefully selected and supplemented by personal contributions of the author, many of which appear here for the first time.

The present text is an introduction to the theory of association schemes.

Yet that weakness is also its greatest strength.

For the most part, this book is the translation from Japanese of the earlier book written jointly by Koji Doi and the author who revised it substantially for the English edition.

Absolute values and their completions -like the p-adic number fields- play an important role in number theory.

Spontaneous pattern formation in nonlinear dissipative systems far from equilibrium is a paradigmatic case of emergent behaviour associated with complex systems.

Nonlinear analysis has developed rapidly in the last three decades.

From the reviews of the hardcover edition: .

Finite model theory, the model theory of finite structures, has roots in clas- sical model theory; however, its systematic development was strongly influ- enced by research and questions of complexity theory and of database theory.

Singularity theory is a field of intensive study in modern mathematics with fascinating relations to algebraic geometry, complex analysis, commutative algebra, representation theory, theory of Lie groups, topology, dynamical systems, and many more, and with numerous applications in the natural and technical sciences.

A new starting-point and a new method are requisite, to insure a complete [classi?

This encyclopedic, detailed exposition spans all the steps of one-period allocation from the foundations to the most advanced developments.

This book is an outgrowth of notes compiled by the author while teaching courses for undergraduate and masters/MBA ?

Author's Note: The material of this book has been reworked and expanded with a lot more detail and published in the author's 2014 book "e;Upper and Lower Bounds for Stochastic Processes"e; (Ergebnisse Vol.

The theory of groups and Lie algebras is interesting for many reasons.

The subject of this book is the solution of polynomial equations, that is, s- tems of (generally) non-linear algebraic equations.

This book offers the opportunity to study and experience advanced empi- cal techniques in finance and in general financial economics.

Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective studies the mathematical issues that arise in modeling the interest rate term structure.

To some extent, it would be accurate to summarize the contents of this book as an intolerably protracted description of what happens when either one raises a transition probability matrix P (i.

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