Mathematics

Base SAS 9.4 Procedures Guide : Statistical Procedures, Fifth Edition

Perturbative Algebraic Quantum Field Theory: An Introduction for Mathematicians by Kasia Rejzner

Eric Charpentier, Etienne Ghys, Annick Lesne, “The Scientific Legacy of Poincare”

Pierre Del Moral, Spiridon Penev, “Stochastic Processes: From Applications to Theory”

Valentin Deaconu, Donald C. Pfaff, “A Bridge to Higher Mathematics”

Base SAS 9.4 Procedures Guide : Statistical Procedures, Fifth Edition

English | 2016 | ISBN: 1635260191 | 570 Pages | PDF | 6.45 MB

Provides complete documentation of the Base SAS statistical procedures (CORR, FREQ, and UNIVARIATE), including introductory examples, syntax, computational details, and advanced examples.

The fourth maintenance release of Base SAS 9.4 includes enhancements to the FREQ and UNIVARIATE statistical procedures.

FREQ Procedure Enhancements:

The new AGREE(PABAK) and AGREE(AC1) options produce the prevalence-adjusted bias-adjusted kappa coefficient and Gwets AC1 agreement coefficient, respectively. The AGREE(KAPPADETAILS) option provides the following statistics: observed agreement and chance-expected agreement components of the simple kappa coefficient, maximum possible kappa, prevalence index, and bias index. The AGREE(WTKAPDETAILS) option provides the observed agreement and chance-expected agreement components of the weighted kappa coefficient.

You can now specify nonzero null values for the simple and weighted kappa tests by using the AGREE(NULLKAPPA=) and AGREE(NULLWTKAP=) options. You can specify the degrees of freedom for Bowkers test of symmetry by using the AGREE(DFSYM=) option.

When you specify any of the AGREE options that are new in SAS 9.4M4, PROC FREQ displays all tables of AGREE statistics in tabular format (instead of factoid format); to display

Perturbative Algebraic Quantum Field Theory: An Introduction for Mathematicians by Kasia Rejzner

English | PDF,EPUB | 2016 | 186 Pages | ISBN : 3319258990 | 5.69 MB

Perturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesnt require the use of divergent quantities and works on a large class of Lorenzian manifolds.

We discuss in detail the examples of scalar fields, gauge theories and the effective quantum gravity.

pQFT models describe a wide range of physical phenomena and have remarkable agreement with experimental results. Despite this success, the theory suffers from many conceptual problems. pAQFT is a good candidate to solve many, if not all, of these conceptual problems.

Chapters 1-3 provide some background in mathematics and physics. Chapter 4 concerns classical theory of the scalar field, which is subsequently quantized in chapters 5 and 6. Chapter 7 covers gauge theory and chapter 8 discusses effective quantum gravity.

The book aims to be accessible to researchers and graduate students, who are interested in the mathematical foundations of pQFT.

Eric Charpentier, Etienne Ghys, Annick Lesne, “The Scientific Legacy of Poincare”

English | 2010 | ISBN: 082184718X | PDF | pages: 408 | 34.5 mb

Henri Poincare (1854-1912) was one of the greatest scientists of his time, perhaps the last one to have mastered and expanded almost all areas in mathematics and theoretical physics. He created new mathematical branches, such as algebraic topology, dynamical systems, and automorphic functions, and he opened the way to complex analysis with several variables and to the modern approach to asymptotic expansions. He revolutionized celestial mechanics, discovering deterministic chaos. In physics, he is one of the fathers of special relativity, and his work in the philosophy of sciences is illuminating. For this book, about twenty world experts were asked to present one part of Poincare’s extraordinary work. Each chapter treats one theme, presenting Poincare’s approach, and achievements, along with examples of recent applications and some current prospects. Their contributions emphasize the power and modernity of the work of Poincare, an inexhaustible source of inspiration for researchers, as illustrated by the Fields Medal awarded in 2006 to Grigori Perelman for his proof of the Poincare conjecture stated a century before. This book can be read by anyone with a master’s (even a bachelor’s) degree in mathematics, or physics, or more generally by anyone who likes mathematical and physical ideas. Rather than presenting detailed proofs, the main ideas are explained, and a bibliography is provided for those who wish to understand the technical details.

Pierre Del Moral, Spiridon Penev, “Stochastic Processes: From Applications to Theory”

English | ISBN: 1498701833 | 2017 | 916 pages | PDF | 22 MB

Unlike traditional books presenting stochastic processes in an academic way, this book includes concrete applications that students will find interesting such as gambling, finance, physics, signal processing, statistics, fractals, and biology. Written with an important illustrated guide in the beginning, it contains many illustrations, photos and pictures, along with several website links. Computational tools such as simulation and Monte Carlo methods are included as well as complete toolboxes for both traditional and new computational techniques.

Valentin Deaconu, Donald C. Pfaff, “A Bridge to Higher Mathematics”

2017 | ISBN-10: 149877525X, 1138441635 | 218 pages | PDF | 3 MB

A Bridge to Higher Mathematics is more than simply another book to aid the transition to advanced mathematics. The authors intend to assist students in developing a deeper understanding of mathematics and mathematical thought.

The only way to understand mathematics is by doing mathematics. The reader will learn the language of axioms and theorems and will write convincing and cogent proofs using quantifiers. Students will solve many puzzles and encounter some mysteries and challenging problems.

The emphasis is on proof. To progress towards mathematical maturity, it is necessary to be trained in two aspects: the ability to read and understand a proof and the ability to write a proof.

The journey begins with elements of logic and techniques of proof, then with elementary set theory, relations and functions. Peano axioms for positive integers and for natural numbers follow, in particular mathematical and other forms of induction. Next is the construction of integers including some elementary number theory. The notions of finite and infinite sets, cardinality of counting techniques and combinatorics illustrate more techniques of proof.

For more advanced readers, the text concludes with sets of rational numbers, the set of reals and the set of complex numbers. Topics, like Zorns lemma and the axiom of choice are included. More challenging problems are marked with a star.

All these materials are optional, depending on the instructor and the goals of the course.