Authors turn to Wolfram technologies to elucidate complex concepts, from physics to finance. Here is a roundup of the latest publications that feature the Wolfram Language and Mathematica.

Particle and Particle Systems Characterization: Small-Angle Scattering (SAS) Applications
by Wilfried Gille

Small-angle scattering (SAS) is the premier technique for the characterization of disordered nanoscale particle ensembles. SAS is produced by the particle as a whole and does not depend in any way on the internal crystal structure of the particle. Since the first applications of x-ray scattering in the 1930s, SAS has developed into a standard method in the field of materials science. SAS is a non-destructive method and can be directly applied for solid and liquid samples.

This book is geared to any scientist who might want to apply SAS to study tightly packed particle ensembles using elements of stochastic geometry. After completing the book, the reader should be able to demonstrate detailed knowledge of the application of SAS for the characterization of physical and chemical materials.

Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions
by Carsten Schneider and Johannes Blumlein

The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums; multiple integrals, in particular Feynman integrals; and difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science, and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including most recent developments. Besides that, the collection of articles also serves as an up-to-date handbook of available algorithms/software that are commonly used or might be useful in the fields of mathematics, physics, or other sciences.

Mathematics for Physical Science and Engineering
by Frank E. Harris

Mathematics for Physical Science and Engineering is a complete text in mathematics for physical science that includes the use of symbolic computation to illustrate the mathematical concepts and enable the solution of a broader range of practical problems. Due to the increasing importance of symbolic computation and platforms such as Mathematica, the book begins by introducing that topic before delving into its core mathematical topics. Each of those subjects is described in principle and then applied through symbolic computing. The aim of the text is designed to clarify and optimize the efficiency of the student’s acquisition of mathematical understanding and skill and to provide students with a mathematical toolbox that will rapidly become of routine use in a scientific or engineering career.

Multimedia Maths
by Bieke Masselis and Ivo De Pauw

Multimedia Maths provides an accessible guide to understanding and using basic software applications including the golden section, co-ordinate systems, collision detection, vectors, and parameters.

Screen effects and image handling are explained at a complex level using a more detailed outline to build and develop on the basic transformations.

More advanced multimedia themes of quaternion rotation, fractal texture, Bézier curves, and B-splines are deconstructed and usefully linked to an interactive website that includes Mathematica files.

A Math Primer for Engineers
by Colin Walker Cryer

Mathematics and engineering are inevitably interrelated, and this interaction will steadily increase as the use of mathematical modeling grows. Although mathematicians and engineers often misunderstand one another, their basic approach is quite similar, as is the historical development of their respective disciplines. The purpose of this Math Primer is to provide a brief introduction to those parts of mathematics that are, or could be, useful in engineering, especially bioengineering. The aim is to summarize the ideas covered in each subject area without going into exhaustive detail. Formulas and equations have not been avoided, but every effort has been made to keep them simple in the hope of persuading readers that they are not only useful, but also accessible.

The wide range of topics covered includes introductory material such as numbers and sequences, geometry in two and three dimensions, linear algebra, and calculus. Building on these foundations, linear spaces, tensor analysis, and Fourier analysis are introduced. All these concepts are used to solve problems for ordinary and partial differential equations. Illustrative applications are taken from a variety of engineering disciplines, and the choice of a suitable model is considered from the point of view of both the mathematician and the engineer.

This book will be of interest to engineers and bioengineers looking for the mathematical means to help further their work, and it will offer readers a glimpse of many ideas that may spark their interest.

Financial Hacking: Evaluate Risks, Price Derivatives, Structure Trades, and Build Your Intuition Quickly and Easily
by Philip Maymin

This book teaches financial engineering in an innovative way by providing tools and a point of view to quickly and easily solve real, front-office problems. Projects and simulations are not just exercises in this book, but its true backbone. You will not only learn how to do state-of-the-art simulations and build exotic derivatives valuation models, you will also learn how to quickly make reasonable inferences based on incomplete information. This book will give you the expertise to make significant progress in understanding brand new derivatives given only a preliminary term sheet, thus making you valuable to banks, brokerage houses, trading floors, and hedge funds.

Financial Hacking is not about long, detailed mathematical proofs or brief summaries of conventional financial theories; it is about engineering-specific, useable answers to imprecise, but important questions. It is an essential book both for students and for practitioners of financial engineering.

MBAs in finance learn case-method and standard finance mainly by talking. Mathematical finance students learn the elegance and beauty of formulas mainly by manipulating symbols. But financial engineers need to learn how to build useful tools, and the best way to do that is to actually build them in a test environment, with only hypothetical profits or losses at stake; this book gives graduate students and others who are looking to move closer to trading operations the opportunity to do just that.

Introduction to Quantitative Methods for Financial Markets
by Hansjorg Albrecher, Andreas Binder, Volkmar Lautscham, and Philipp Mayer

Swaps, futures, options, structured instruments—a wide range of derivative products is traded in today’s financial markets. Analyzing, pricing, and managing such products often requires fairly sophisticated quantitative tools and methods. This book serves as an introduction to financial mathematics with special emphasis on aspects relevant in practice. In addition to numerous illustrative examples, algorithmic implementations are demonstrated using Mathematica and the software package UnRisk (available for both students and teachers). The content is organized in 15 chapters that can be treated as independent modules.

In particular, the exposition is tailored for classroom use in a bachelor’s or master’s program course, as well as for practitioners who wish to further strengthen their quantitative background.