From the Publisher:
A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols; more than 200 tables and figures; more than 1,000 numbered definitions, facts, examples, notes, and remarks; and over 1,250 significant references, including brief comments on each paper.

Handbook of Applied Cryptography

I. Symmetric functions II. Hall polynomials III. HallLittlewood symmetric functions IV. The characters of GLn over a finite field V. The Hecke ring of GLn over a finite field VI. Symmetric functions with two parameters VII. Zonal polynomials

Symmetric functions and Hall polynomials

Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package--PMTK (probabilistic modeling toolkit)--that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.

Machine Learning : A Probabilistic Perspective

* Glossary of notation * Introduction * Preliminaries * Existence and Construction of Generalized Inverses * Linear Systems and Characterization of Generalized Inverses * Minimal Properties of Generalized Inverses * Spectral Generalized Inverses * Generalized Inverses of Partitioned Matrices * A Spectral Theory for Rectangular Matrices * Computational Aspects of Generalized Inverses * Miscellaneous Applications * Generalized Inverses of Linear Operators between Hilbert Spaces * Appendix A: The Moore of the Moore-Penrose Inverse * Bibliography * Subject Index * Author Index

Generalized inverses: theory and applications

Analytic Combinatorics is a self-contained treatment of the mathematics underlying the analysis of discrete structures, which has emerged over the past several decades as an essential tool in the understanding of properties of computer programs and scientific models with applications in physics, biology and chemistry. Thorough treatment of a large number of classical applications is an essential aspect of the presentation. Written by the leaders in the field of analytic combinatorics, this text is certain to become the definitive reference on the topic. The text is complemented with exercises, examples, appendices and notes to aid understanding therefore, it can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study.

Analytic Combinatorics

Now welcome, the most inspiring book today from a very professional writer in the world, mathematical methods for digital computers. This is the book that many people in the world waiting for to publish. After the announced of this book, the book lovers are really curious to see how this book is actually. Are you one of them? That's very proper. You may not be regret now to seek for this book to read.

Mathematical methods for digital computers

An algorithm is a method for solving a class of problems on a computer. The complexity of an algorithm
is the cost, measured in running time, or storage, or whatever units are relevant, of using the algorithm to
solve one of those problems.
This book is about algorithms and complexity, and so it is about methods for solving problems on
computers and the costs (usually the running time) of using those methods.
Computing takes time. Some problems take a very long time, others can be done quickly. Some problems
seem to take a long time, and then someone discovers a faster way to do them (a ‘faster algorithm’). The
study of the amount of computational effort that is needed in order to perform certain kinds of computations
is the study of computational complexity.
Naturally, we would expect that a computing problem for which millions of bits of input data are
required would probably take longer than another problem that needs only a few items of input. So the time
complexity of a calculation is measured by expressing the running time of the calculation as a function of
some measure of the amount of data that is needed to describe the problem to the computer.
For instance, think about this statement: ‘I just bought a matrix inversion program, and it can invert
an n × n matrix in just 1.2n3 minutes.’ We see here a typical description of the complexity of a certain
algorithm. The running time of the program is being given as a function of the size of the input matrix.
A faster program for the same job might run in 0.8n3 minutes for an n × n matrix. If someone were
to make a really important discovery (see section 2.4), then maybe we could actually lower the exponent,
instead of merely shaving the multiplicative constant. Thus, a program that would invert an n × n matrix
in only 7n2.8 minutes would represent a striking improvement of the state of the art.
For the purposes of this book, a computation that is guaranteed to take at most cn3 time for input of
size n will be thought of as an ‘easy’ computation. One that needs at most n10 time is also easy. If a certain
calculation on an n × n matrix were to require 2n minutes, then that would be a ‘hard’ problem. Naturally
some of the computations that we are calling ‘easy’ may take a very long time to run, but still, from our
present point of view the important distinction to maintain will be the polynomial time guarantee or lack of
it.
The general rule is that if the running time is at most a polynomial function of the amount of input
data, then the calculation is an easy one, otherwise it’s hard.
Many problems in computer science are known to be easy. To convince someone that a problem is easy,
it is enough to describe a fast method for solving that problem. To convince someone that a problem is
hard is hard, because you will have to prove to them that it is impossible to find a fast way of doing the
calculation. It will not be enough to point to a particular algorithm and to lament its slowness. After all,
that algorithm may be slow, but maybe there’s a faster way.
Matrix inversion is easy. The familiar Gaussian elimination method can invert an n ×n matrix in time
at most cn3.
To give an example of a hard computational problem we have to go far afield. One interesting one is
called the ‘tiling problem.’ Suppose* we are given infinitely many identical floor tiles, each shaped like a
regular hexagon. Then we can tile the whole plane with them, i.e., we can cover the plane with no empty
spaces left over. This can also be done if the tiles are identical rectangles, but not if they are regular
pentagons.
In Fig. 0.1 we show a tiling of the plane by identical rectangles, and in Fig. 0.2 is a tiling by regular
hexagons.
That raises a number of theoretical and computational questions. One computational question is this.
Suppose we are given a certain polygon, not necessarily regular and not necessarily convex, and suppose we
have infinitely many identical tiles in that shape. Can we or can we not succeed in tiling the whole plane?
That elegant question has been proved* to be computationally unsolvable. In other words, not only do
we not know of any fast way to solve that problem on a computer, it has been proved that there isn’t any

/pdf/algorithms-and-complexity-58gawv3q9c.pdf

Algorithms and complexity

https://www.ams.org/proc/1965-016-01/S0002-9939-1965-0174934-9/S0002-9939-1965-0174934-9.pdf

Uniqueness theorems for periodic functions

It is shown that every ‘proper-hypergeometric’ multisum/integral identity, orq-identity, with a fixed number of summations and/or integration signs, possesses a short, computer-constructible proof We give a fast algorithm for finding such proofs Most of the identities that involve the classical special functions of mathematical physics are readily reducible to the kind of identities treated here We give many examples of the method, including computer-generated proofs of identities of Mehta-Dyson, Selberg, Hille-Hardy,q-Saalschutz, and others The prospect of using the method for proving multivariate identities that involve an arbitrary number of summations/integrations is discussed

Herbert S. Wilf

Papers

Mathematical methods for digital computers

Algorithms and complexity

Uniqueness theorems for periodic functions

An algorithmic proof theory for hypergeometric (ordinary and “q”) multisum/integral identities

Generating functionology