Arnold, Vladimir I.
Yesterday and Long Ago
Original Russian edition published by PHASIS, Moscow, Russia,
2006. English edition jointly published with PHASIS.
2007, XIV, 229 p., 43 illus., Hardcover
ISBN-10: 3-540-28734-5
About this book
This is a charming collection of essays on life and science, by
one of the leading mathematicians of our day. Vladimir Igorevich
Arnold is renowned for his achievements in mathematics, and
nearly as famous for his informal teaching style, and for the
clarity and accessibility of his writing. The chapter headings
convey Arnold’s humor and restless imagination. A few examples:
My first recollections; The combinatorics of Plutarch; The
topology of surfaces according to Alexander of Macedon; Catching
a pike in Cambridge. Yesterday and Long Ago offers a rare
opportunity to appreciate the life and work of one of the world’s
outstanding living mathematicians.
Table of contents
Preface.- My first recollections.- The North-West direction.-
Vera Stepanovna Arnold (nee Zhitkova).- First scientific
reminiscences.- The Arnold family.-A household library.- The
axiomatic method.- The color of a meridian.- School years.- It is
not easy to keep a secret.- The temple of science.- Who is the
winner?- State examination on Marxism.- Goodwill.- The thermal
conductivity equation.- Lavoisier and French mathematics during
the Revolution.- Queen Eleanor, Rosamund, and labyrinth theory.-
Place de Vogueses.- "Champel Sea".- Neutrinos,
neutrons, and Bruno Pontecorvo.- From Pareto to Arzamas.- How to
distinguish good and bad mathematical works.- The combinatorics
of Plutarch.- Galilei.- The topology of surfaces according to
Alexander of Macedon.- Snake-hunting.- Suputinskii nature reserve.-
Pheasants of the Vincent forest.- The guillotine and Marie-Antoinette.-
Damiens’s sufferings.- Queen Marguerite and the kingdom of law.-
Jeanne d’Arc as a witch and as a saint.- Ravailliac, French
cuisine, and traffic jams.- Anne Yaroslavna, Princess of Russia.-
Gennady of Novgorod and education in Russia under Ivan III.-
Catherine I and the Prut river campaign.- Catherine II and I.I.Betskoi.-
An order of Catherine II.- Radishchev.- The Crimean war.-
Princess Dashkova and parachutes.- The desecrated host and
abstract algebra.- France ? Guinea ? India.- Julius Caesar and
Gallians: protecting Rome from Germans.- A planning department.-
Mountain lions over Stanford.- The Pocha river and the dog Shnura.-
Hong Kong.- The Pongoma river and the Solovetskie islands.-
Brazilian tours.- Leibnitz as Bourbaki’s predecessor.- The
"Mistral" in the "Crown".- How academicians
were elected and eliminated.- From the history of French economy.-
The origins of mathematics: from Greece to Egypt.- Motivation for
mathematical education in Israel.- Struggles against foreigners
and their languages.- "Our Manchuria".- Religion and
science, Martin Luther and anti-semitism.- Ramanujan and Hardy.-
Catching a pike in Cambridge.- Locust swarming and relocation of
deer.- Tamil Tigers at the Swiss consulate in Paris.- Picking
cranberries.- The Yamal peninsula and digging caves in the snow.-
Brain tomography, geometry, and algebra.- Inedible hares.- A
question about the bitch of Rabinovitch.- The cemetery at Aksin’ino
Bemelmans, J.; Binder, C.; Chatterji, S.D.; Hildebrandt, S.;
Purkert, W.; Schmeidler, F.; Scholz, E. (Hrsg.)
Felix Hausdorff - Gesammelte Werke Band 5
Astronomie, Optik und Wahrscheinlichkeitstheorie
Bandwerk Felix Hausdorff - Gesammelte Werke
2006, XVI, 938 S., Geb.
ISBN-10: 3-540-30624-2
ISBN-13: 978-3-540-30624-5
Uber dieses Buch
Band 5 umfast die Themenbereiche Astronomie, Optik und
Wahrscheinlichkeitstheorie. Er enthalt Hausdorffs Dissertation
uber die Refraktion des Lichtes in der Atmosphare, zwei
Folgearbeiten zum gleichen Thema sowie die Habilitationsschrift
uber die Extinktion des Lichtes in der Atmosphare. Es folgt eine
Arbeit uber geometrische Optik, die unmittelbar an die beruhmte
Publikation von H. Bruns uber das Eikonal anschliest und in der
Hausdorff die damals ganz neuen Lieschen Theorien fur die Optik
nutzbar zu machen suchte.
Auf dem Gebiet der Stochastik veroffentlichte Hausdorff zwei
langere Arbeiten, die in verschiedenen Bereichen der
Versicherungsmathematik und der Wahrscheinlichkeitsrechnung ihre
Spuren hinterlassen haben. Von besonderem historischen Interesse
sind die im Band publizierten Stucke aus Hausdorffs Nachlas, etwa
seine Vorlesung "Wahrscheinlichkeitsrechnung" vom
Sommersemester 1923 oder seine Briefe an Richard von Mises aus
dem Jahre 1919.
Inhaltsverzeichnis
Teil I. Astronomie und Optik. - A. Veroffentlichte Arbeiten.- Zur
Theorie der astronomischen Strahlenbrechung (Dissertation).- Zur
Theorie der astronomischen Strahlenbrechung II, III.- Uber die
Absorption des Lichtes in der Atmosphare (Habilitationsschrift).-
Infinitesimale Abbildungen der Optik.- B. Arbeiten aus dem
Nachlas.- Die Vorlesung "Figur und Rotation der
Himmelskorper (1895/96).- Hausdorffs Notizen uber mittlere
Bewegung.- Teil II. Wahrscheinlichkeitstheorie.- A.
Veroffentlichte Arbeiten.- Das Risiko bei Zufallsspielen.-
Beitrage zur Wahrscheinlichkeitsrechnung.- W. Grossmann:
Versicherungsmathematik (Besprechung).- W. Kitt: Grundlinien der
politischen Arithmetik (Besprechung).- B. Arbeiten aus dem
Nachlas.- Vorlesung "Wahrscheinlichkeitsrechnung" (1923).-
[Rademacher-Funktionen].- [Asymptotische Verteilung der Ziffern
in einem g-adischen Bruch].- [Starkes Gesetz der grosen Zahl;
Cantor-Darstellung reeller Zahlen].- [Grose Abweichungen].-
Kettenbruche.- Iterationen.- Verscharfung der Tschebyscheffschen
Ungleichung.- [Gleichheit f.u. von Zufallsvariablen;
Unabhangigkeit].- Kai-Lai Chung, Sur un theoreme de M. Gumbel.-
Zwei Briefe Felix Hausdorffs an Richard von Mises.- Anhang.-
Christian Huygens' nachgelassene Abhandlungen: Uber die Bewegung
der Korper durch den Stos. Uber die Centrifugalkraft.
Herausgegeben und mit Anmerkungen versehen von Felix Hausdorff.-
Personenregister.- Sachregister.
Kabe, D.G., Gupta, A.K.
Experimental Designs: Exercises and Solutions
2006, VIII, 300 p., 3 illus., Softcover
ISBN-10: 0-387-33892-6
ISBN-13: 978-0-387-33892-7
About this book
This volume provides a collection of exercises together with
their solutions in design and analysis of experiments. The
theoretical results, essential for understanding, are given first.
These exercises have been collected during the authors teaching
courses over a long period of time. These are particularly
helpful to the students studying the design of experiments and
instructors and researchers engaged in the teaching and research
of design by experiment.
Table of contents
Theoretical results.- Exercises.- Solutions.
Bix, Robert
Conics and Cubics, 2nd ed.
A Concrete Introduction to Algebraic Curves
Series: Undergraduate Texts in Mathematics
2006, VIII, 352 p., 151 illus., Hardcover
ISBN-10: 0-387-31802-X
ISBN-13: 978-0-387-31802-8
About this textbook
Conics and Cubics is an accessible introduction to algebraic
curves. Its focus on curves of degree at most three keeps results
tangible and proofs transparent. Theorems follow naturally from
high school algebra and two key ideas, homogeneous coordinates
and intersection multiplicities.
By classifying irreducible cubics over the real numbers and
proving that their points form Abelian groups, the book gives
readers easy access to the study of elliptic curves. It includes
a simple proof of Bezout’s Theorem on the number of
intersections of two curves.
The book is a text for a one-semester course. The course can
serve either as the one undergraduate geometry course taken by
mathematics majors in general or as a sequel to college geometry
for prospective or current teachers of secondary school
mathematics. The only prerequisite is first-year calculus.
The new edition additionally discusses the use of power series to
parametrize curves and analyze intersection multiplicities and
envelopes.
Table of contents
Intersection of Curves.- Conics.- Cubics.- Intersection
Properties.- References.- Index.
Arnold, Vladimir I.
Ordinary Differential Equations, 2nd printing,
Series: Universitext
Original Russion edition published by Nauka, Moscow, 1984
1st ed 1992. 2006, IV, 334 p., 272 illus., Softcover
ISBN-10: 3-540-34563-9
ISBN-13: 978-3-540-34563-3
About this textbook
There are dozens of books on ODEs, but none with the elegant
geometric insight of Arnol'd's book. Arnol'd puts a clear
emphasis on the qualitative and geometric properties of ODEs and
their solutions, rather than on theroutine presentation of
algorithms for solving special classes of equations.Of course,
the reader learns how to solve equations, but with much more
understanding of the systems, the solutions and the techniques.
Vector fields and one-parameter groups of transformations come
right from the startand Arnol'd uses this "language"
throughout the book. This fundamental difference from the
standard presentation allows him to explain some of the real
mathematics of ODEs in a very understandable way and without
hidingthe substance. The text is also rich with examples and
connections with mechanics. Where possible, Arnol'd proceeds by
physical reasoning, using it as a convenient shorthand for much
longer formal mathematical reasoning. This technique helps the
student get a feel for the subject. Following Arnol'd's guiding
geometric and qualitative principles, there are 272 figures in
the book, but not a single complicated formula. Also, the text is
peppered with historicalremarks, which put the material in
context, showing how the ideas have developped since Newton and
Leibniz. This book is an excellent text for a course whose goal
is a mathematical treatment of differential equations and the
related physical systems.
Peter Topping / University of Warwick
Lectures on the Ricci Flow
Series: London Mathematical Society Lecture Note Series (No.
325)
Paperback (ISBN-13: 9780521689472 | ISBN-10: 0521689473)
Hamilton's Ricci flow has attracted considerable attention since
its introduction in 1982, owing partly to its promise in
addressing the Poincar・conjecture and Thurston's geometrization
conjecture. This book gives a concise introduction to the subject
with the hindsight of Perelman's breakthroughs from 2002/2003.
After describing the basic properties of, and intuition behind
the Ricci flow, core elements of the theory are discussed such as
consequences of various forms of maximum principle, issues
related to existence theory, and basic properties of
singularities in the flow. A detailed exposition of Perelman's
entropy functionals is combined with a description of Cheeger-Gromov-Hamilton
compactness of manifolds and flows to show how a 'tangent' flow
can be extracted from a singular Ricci flow. Finally, all these
threads are pulled together to give a modern proof of Hamilton's
theorem that a closed three-dimensional manifold whichcarries a
metric of positive Ricci curvature is a spherical space form.
* Presents the state of the art view of the subject
* Includes results not available in book form anywhere else
* Written in a style which makes it ideal for use in a graduate
level course
Contents
1. Introduction; 2. Riemannian geometry background; 3. The
maximum principle; 4. Comments on existence theory for parabolic
PDE; 5. Existence theory for the Ricci flow; 6. Ricci flow as a
gradient flow; 7. Compactness of Riemannian manifolds and flows;
8. Perelman's W entropy functional; 9. Curvature pinching and
preserved curvature properties under Ricci flow; 10. Three-manifolds
with positive Ricci curvature and beyond.