Series: London Mathematical Society Student Texts
Hardback (ISBN-10: 0521848164 | ISBN-13: 9780521848169)
Paperback (ISBN-10: 0521612756 | ISBN-13: 9780521612753)
Sieve theory has a rich and romantic history. The ancient
question of whether there exist infinitely many twin primes (primes
p such that p+2 is also prime), and Goldbach's conjecture that
every even number can be written as the sum of two prime numbers,
have been two of the problems that have inspired the development
of the theory. This book provides a motivated introduction to
sieve theory. Rather than focus on technical details which can
obscure the beauty of the theory, the authors focus on examples
and applications, developing the theory in parallel. The text can
be used for a senior level undergraduate course or an
introductory graduate course in analytic number theory, and non-experts
can gain a quick introduction to the techniques of the subject.
* Non-experts can gain a quick introduction to the techniques of
Sieve Theory
* Contains many concrete examples and applications
* The book has over 200 exercises
Contents
1. Some basic notions; 2. Some elementary sieves; 3. The normal
order method; 4. The Turan sieve; 5. The sieve of Eratosthenes; 6.
Brunfs sieve; 7. Selbergfs sieve; 8. The large sieve; 9. The
Bombieri-Vinogradov theorem; 10. The lower bound sieve; 11. New
directions in sieve theory; Bibliography.
Hardback (ISBN-10: 052184889X | ISBN-13: 9780521848893)
Paperback (ISBN-10: 0521613256 | ISBN-13: 9780521613255)
Geometry provides a whole range of views on the universe, serving
as the inspiration, technical toolkit and ultimate goal for many
branches of mathematics and physics. This book introduces the
ideas of geometry, and includes a generous supply of simple
explanations and examples. The treatment emphasises coordinate
systems and the coordinate changes that generate symmetries. The
discussion moves from Euclidean to non-Euclidean geometries,
including spherical and hyperbolic geometry, and then on to
affine and projective linear geometries. Group theory is
introduced to treat geometric symmetries, leading to the
unification of geometry and group theory in the Erlangen program.
An introduction to basic topology follows, with the Mobius strip,
the Klein bottle and the surface with g handles exemplifying
quotient topologies and the homeomorphism problem. Topology
combines with group theory to yield the geometry of
transformation groups,having applications to relativity theory
and quantum mechanics. A final chapter features historical
discussions and indications for further reading. With minimal
prerequisites, the book provides a first glimpse of many research
topics in modern algebra, geometry and theoretical physics. The
book is based on many years' teaching experience, and is
thoroughly class-tested. There are copious illustrations, and
each chapter ends with a wide supply of exercises. Further
teaching material is available for teachers via the web,
including assignable problem sheets with solutions.
* Exercises and practical illustrations introduce topics across
maths and its applications
* Prerequisites are minimal: ideally suited to beginner courses
and newcomers to the subject
* Further teaching material is available for teachers, including
assignable problem sheets with solutions
Contents
0. Introduction; 1. Euclidean geometry; 2. Composing maps; 3. Non-Euclidean;
4. Affine geometry; 5. Projective geometry; 6. Geometry and group
theory; 7. Topology; 8. Geometry of transformation groups; 9.
Concluding remarks; A. Metrics; B. Linear algebra; References;
Index.
Series: Cambridge Series in Statistical and Probabilistic
Mathematics
Hardback (ISBN-10: 052184472X | ISBN-13: 9780521844727)
October 2005 | 528 pages | 253 x 177 mm
This detailed introduction to distribution theory uses no measure
theory, making it suitable for students in statistics and
econometrics as well as for researchers who use statistical
methods. Good backgrounds in calculus and linear algebra are
important and a course in elementary mathematical analysis is
useful, but not required. An appendix gives a detailed summary of
the mathematical definitions and results that are used in the
book. Topics covered range from the basic distribution and
density functions, expectation, conditioning, characteristic
functions, cumulants, convergence in distribution and the central
limit theorem to more advanced concepts such as exchangeability,
models with a group structure, asymptotic approximations to
integrals, orthogonal polynomials, and saddlepoint approximations.
The emphasis is on topics useful in understanding statistical
methodology; thus, parametric statistical models and the
distribution theory associated with the normal distribution are
covered comprehensively.
* Provides a comprehensive discussion of the major results of
distribution theory at a level not requiring advanced probability
theory
* There are over 300 examples and 340 exercises, and it contains
detailed proofs of nearly every result
* The topics are chosen in order to prepare the reader for
advanced study in statistics, rather than distribution or
probability theory easy to understand
Contents
1. Properties of probability distributions; 2. Conditional
distributions and expectation; 3. Characteristic functions; 4.
Moments and cumulants; 5. Parametric families of distributions; 6.
Stochastic processes; 7. Distribution theory for functions of
random variables; 8. Normal distribution theory; 9. Approximation
of integrals; 10. Orthogonal polynomials; 11. Approximation of
probability distributions; 12. Central limit theorems; 13.
Approximation to the distributions of more general statistics; 14.
Higher-order asymptotic approximations.
Text and Readings in Mathematics/ 35
October 2005
184 pages
Hardcover
ISBN 81-85931-59-3
This book is based on a course of lectures given to PhD students at the Delhi Centre of the Indian Statistical Institute during the years 1980-1985. The approach is inspired by the lectures of G.W.Mackey and V.S.Varadarajan and brings out the role of group representations as the main thread passing through some major results like Gleason's theorem on the characterization of quantum states, Wigner's unitarity-antiunitarity theorem on the automorphisms of the lattice of orthogonal projections in a Hilbert space, Mackey's imprimitivity theorem for quantum systems with a configuration observable, and the rise of important and physically meaningful observables through the infinitesimal generators of projective unitary representations of the Galilean and the inhomogeneous Lorentz groups.
Contents
Chapter 1. PROBABILITY THEORY ON THE LATTICE OF PROJECTIONS IN A HILBERT SPACE
Chapter 2. SYSTEMS WITH A CONFIGURATION UNDER A GROUP ACTION
Chapter 3. MULTIPLIERS ON LOCALLY COMPACT GROUPS
Chapter 4. THE BASIC OBSERVABLES OF A QUANTUM MECHANICAL SYSTEM
Bibliography