Graduate Studies in Mathematics, Volume: 160
2014; 371 pp; hardcover
ISBN-13: 978-1-4704-1706-2
Expected publication date is January 30, 2015.
This book is an introduction to analytic number theory suitable for beginning graduate students. It covers everything one expects in a first course in this field, such as growth of arithmetic functions, existence of primes in arithmetic progressions, and the Prime Number Theorem. But it also covers more challenging topics that might be used in a second course, such as the Siegel-Walfisz theorem, functional equations of L-functions, and the explicit formula of von Mangoldt. For students with an interest in Diophantine analysis, there is a chapter on the Circle Method and Waring's Problem. Those with an interest in algebraic number theory may find the chapter on the analytic theory of number fields of interest, with proofs of the Dirichlet unit theorem, the analytic class number formula, the functional equation of the Dedekind zeta function, and the Prime Ideal Theorem.
The exposition is both clear and precise, reflecting careful attention to the needs of the reader. The text includes extensive historical notes, which occur at the ends of the chapters. The exercises range from introductory problems and standard problems in analytic number theory to interesting original problems that will challenge the reader.
The author has made an effort to provide clear explanations for the techniques of analysis used. No background in analysis beyond rigorous calculus and a first course in complex function theory is assumed.
Graduate students interested in number theory.
Mathematical Surveys and Monographs, Volume: 200
2014; 240 pp; hardcover
ISBN-13: 978-1-4704-1710-9
Expected publication date is January 19, 2015.
This book presents applications of noncommutative and nonassociative algebras to constructing unusual (nonclassical and singular) solutions to fully nonlinear elliptic partial differential equations of second order. The methods described in the book are used to solve a longstanding problem of the existence of truly weak, nonsmooth viscosity solutions. Moreover, the authors provide an almost complete description of homogeneous solutions to fully nonlinear elliptic equations. It is shown that even in the very restricted setting of "Hessian equations", depending only on the eigenvalues of the Hessian, these equations admit homogeneous solutions of all orders compatible with known regularity for viscosity solutions provided the space dimension is five or larger. To the contrary, in dimension four or less the situation is completely different, and our results suggest strongly that there are no nonclassical homogeneous solutions at all in dimensions three and four.
Thus this book gives a complete list of dimensions where nonclassical homogeneous solutions to fully nonlinear uniformly elliptic equations do exist; this should be compared with the situation of, say, ten years ago when the very existence of nonclassical viscosity solutions was not known.
Graduate students and research mathematicians interested in non-linear partial differential equations.
Translations of Mathematical Monographs, Volume: 245
Iwanami Series in Modern Mathematics
2014; approx. 234 pp; softcover
ISBN-13: 978-0-8218-9849-9
Expected publication date is January 26, 2015.
This is the second volume of the book on the proof of Fermat's Last Theorem by Wiles and Taylor (the first volume is published in the same series; see MMONO/243). Here the detail of the proof announced in the first volume is fully exposed. The book also includes basic materials and constructions in number theory and arithmetic geometry that are used in the proof.
In the first volume the modularity lifting theorem on Galois representations has been reduced to properties of the deformation rings and the Hecke modules. The Hecke modules and the Selmer groups used to study deformation rings are constructed, and the required properties are established to complete the proof.
The reader can learn basics on the integral models of modular curves and their reductions modulo p that lay the foundation of the construction of the Galois representations associated with modular forms. More background materials, including Galois cohomology, curves over integer rings, the Neron models of their Jacobians, etc., are also explained in the text and in the appendices.
Graduate students and research mathematicians interested in number theory and arithmetic geometry.
Modular curves over Z
Modular forms and Galois representations
Hecke modules
Selmer groups
Curves over discrete valuation rings
Finite commutative group scheme over Zp
Jacobian of a curve and its Neron model
Bibliography
Symbol index
Subject index
Subject Area: Higher Education - Probability & Statistics
ISBN-13: 9780128001141
Pub Date: 09/25/2014
Weight: 1,250.00 grams
Pages: 624
Illus: Approx. 100 illustrations
Size: 7 1/2 X 9 1/4 in
Product Type: Hardcover
Roussas introduces readers with no prior knowledge in probability or statistics, to a thinking process to guide them toward the best solution to a posed question or situation. An Introduction to Probability and Statistical Inference provides a plethora of examples for each topic discussed, giving the reader more experience in applying statistical methods to different situations.
"The text is wonderfully written and has the most
comprehensive range of exercise problems that I have ever seen." - Tapas K. Das, University of South Florida
"The exposition is great; a mixture between conversational tones and formal mathematics; the appropriate combination for a math text at [this] level. In my examination I could find no instance where I could improve the book." - H. Pat Goeters, Auburn, University, Alabama
Content, examples, an enhanced number of exercises, and graphical illustrations where appropriate to motivate the reader and demonstrate the applicability of probability and statistical inference in a great variety of human activities
Reorganized material in the statistical portion of the book to ensure continuity and enhance understanding
A relatively rigorous, yet accessible and always within the prescribed prerequisites, mathematical discussion of probability theory and statistical inference important to students in a broad variety of disciplines
Relevant proofs where appropriate in each section, followed by exercises with useful clues to their solutions
Brief answers to even-numbered exercises at the back of the book and detailed solutions to all exercises available to instructors in an Answers Manual
Expected Release Date: 01 Dec 2014
Print Book ISBN : 9780444634313
Pages: 414
Dimensions: 229 X 152
Providing core training in R for a successful career in statistics practice
Hardcover
Not Yet Available
Addresses data examples that can be downloaded directly from the R website
No other source is needed to gain practical experience
Focus on the essentials in graphical outlays
R is open source statistical computing software. Since the R core group was formed in 1997, R has been extended by a very large number of packages with extensive documentation along with examples freely available on the internet. It offers a large number of statistical and numerical methods and graphical tools and visualization of extraordinarily high quality. R was recently ranked in 14th place by the Transparent Language Popularity Index and 6th as a scripting language, after PHP, Python, and Perl.
The book is designed so that it can be used right away by novices while appealing to experienced users as well. Each article begins with a data example that can be downloaded directly from the R website. Data analysis questions are articulated following the presentation of the data. The necessary R commands are spelled out and executed and the output is presented and discussed. Other examples of data sets with a different flavor and different set of commands but following the theme of the article are presented as well. Each chapter predents a hands-on-experience. R has superb graphical outlays and the book brings out the essentials in this arena. The end user can benefit immensely by applying the graphics to enhance research findings. The core statistical methodologies such as regression, survival analysis, and discrete data are all covered.
Teachers of statistics, students, statistical consultants, statisticians and biostatisticians in industry