This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the...
Calculus: Early Transcendentals, originally by D. Guichard, has been redesigned by the Lyryx editorial team. Substantial portions of the content, examples, and diagrams have been redeveloped, with additional contributions provided by experienced and practicing instructors. This approachable textbook provides a comprehensive understanding of the nec...
This book integrates the vital areas of object-orientation, functional programming, design patterns, and language design. The most important concepts from functional programming are captured with six design patterns: FUNCTION OBJECTS (Black-box behaviour parameterisation) LAZY OBJECTS (Evaluation-by-need semantics) VALUE OBJECTS (Immutable values) ...
These Proceedings offer a selection of peer-reviewed research and survey papers by some of the foremost international researchers in the fields of finance, energy, stochastics and risk, who present their latest findings on topical problems. The papers cover the areas of stochastic modeling in energy and financial markets; risk management with envir...
This book shows how to use sensitivity analysis in demography. It presents new methods for individuals, cohorts, and populations, with applications to humans, other animals, and plants. The analyses are based on matrix formulations of age-classified, stage-classified, and multistate population models. Methods are presented for linear and nonlinear,...
This free book, or really a "coursebook" for a college freshman-level class, has been updated for Spring 2014 and provides an introduction to programming and problem solving using both Matlab and Mathcad. We provide a balanced selection of introductory exercises and real-world problems (i.e. no "contrived" problems). We include ...
Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research.
The book explains how conceptual hurdles in the development of numbers and number systems were overcome i...
This book covers the standard material for a one-semester course in multivariable calculus. The topics include curves, differentiability and partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of Green, Stokes, and Gauss. Roughly speaking, the book is organized into three main parts corresponding to ...
This book constitutes the proceedings of the 15th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2012, held as part of the joint European Conference on Theory and Practice of Software, ETAPS 2012, which took place in Tallinn, Estonia, in March/April 2012.
The 29 papers presented in this book toget...
This book constitutes the proceedings of the 27th European Symposium on Programming, ESOP 2018, which took place in Thessaloniki, Greece in April 2018, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2018.
The 36 papers presented in this volume were carefully reviewed and selected from 114 submissions. The ...
This book provides an overview of Felix Klein's ideas, highlighting developments in university teaching and school mathematics related to Klein's thoughts, stemming from the last century. It discusses the meaning, importance and the legacy of Klein's ideas today and in the future, within an international, global context. Presenting e...
This book constitutes the proceedings of the 21st International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2018, which took place in Thessaloniki, Greece, in April 2018, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2018.The 31 papers presented in this volume were ca...
This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups...
This engaging volume celebrates the life and work of Theodor Holm "Ted" Nelson, a pioneer and legendary figure from the history of early computing. Presenting contributions from world-renowned computer scientists and figures from the media industry, the book delves into hypertext, the docuverse, Xanadu, and other products of Ted Nelson�...
This book, inspired by the ICME 13 topic study group "Affect, beliefs and identity in mathematics education", presents the latest trends in research in the area. Following an introduction and a survey chapter providing a concise overview of the state-of-art in the field of mathematics-related affect, the book is divided into three main se...
This book bridges the gap between playing with robots in school and studying robotics at the upper undergraduate and graduate levels to prepare for careers in industry and research. Robotic algorithms are presented formally, but using only mathematics known by high-school and first-year college students, such as calculus, matrices and probability. ...
This text provides a very simple, initial introduction to the complete scientific computing pipeline: models, discretization, algorithms, programming, verification, and visualization. The pedagogical strategy is to use one case study – an ordinary differential equation describing exponential decay processes – to illustrate fundamental concepts ...
This book provides a comprehensive overview of the core subjects comprising mathematical curricula for engineering studies in five European countries and identifies differences between two strong traditions of teaching mathematics to engineers. The collective work of experts from a dozen universities critically examines various aspects of higher ma...
This topical survey focuses on research in tertiary mathematics education, a field that has experienced considerable growth over the last 10 years. Drawing on the most recent journal publications as well as the latest advances from recent high-quality conference proceedings, our review culls out the following five emergent areas of interest: mathem...
This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability...
This open access book, inspired by the ICME 13 Thematic Afternoon on "European Didactic Traditions", consists of 17 chapters, in which educators from the Netherlands reflect on the teaching and learning of mathematics in their country and the role of the Dutch domain-specific instruction theory of Realistic Mathematics Education.Written b...
Modeling and simulation are powerful tools for explaining the world, making predictions, designing things that work, and making them work better. Learning to use these tools can be difficult; this book is my attempt to make the experience as enjoyable and productive as possible.
By reading this book - and working on the exercises - you will lear...
Principles of Microeconomics is an adaptation of the textbook, Microeconomics: Markets, Methods, and Models by D. Curtis and I. Irvine, which provides concise yet complete coverage of introductory microeconomic theory, application and policy in a Canadian and global environment.
This adaptation employs methods that use equations sparingly and do...
The revised 2nd edition of this book provides the reader with a solid foundation in probability theory and statistics as applied to the physical sciences, engineering and related fields. It covers a broad range of numerical and analytical methods that are essential for the correct analysis of scientific data, including probability theory, distribut...
This book develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation ...
This book helps students to master the material of a standard US undergraduate first course in Linear Algebra.
The material is standard in that the subjects covered are Gaussian reduction, vector spaces, linear maps, determinants, and eigenvalues and eigenvectors. Another standard is book's audience: sophomores or juniors, usually with a ba...
Designed for those wishing to study mathematics beyond linear algebra but unready for abstract material, this "invitation" to the excitement of dynamical systems appeals to readers from a wide range of backgrounds. Rather than taking a theorem-proof-corollary-remark approach, it stresses geometry and intuition. Topics include both the cla...
Two dramatically different philosophical approaches to classical mechanics were proposed during the 17th - 18th centuries. Newton developed his vectorial formulation that uses time-dependent differential equations of motion to relate vector observables like force and rate of change of momentum. Euler, Lagrange, Hamilton, and Jacobi, developed power...
This open book have three themes have been central to Leydesdorff's research: (1) the dynamics of science, technology, and innovation; (2) the scientometric operationalization of these concept; and (3) the elaboration in terms of a Triple Helix of university-industry-government relations. In this study, I discuss the relations among these them...
This open access State-of-the-Art Survey presents the main recent scientific outcomes in the area of reversible computation, focusing on those that have emerged during COST Action IC1405 "Reversible Computation - Extending Horizons of Computing", a European research network that operated from May 2015 to April 2019.Reversible computation ...
Types are the central organizing principle of the theory of programming languages. Language features are manifestations of type structure. The syntax of a language is governed by the constructs that define its types, and its semantics is determined by the interactions among those constructs. The soundness of a language design - the absence of ill-d...
The purpose of the 3rd edition of this book is to give a sound and self-contained (in the sense that the necessary probability theory is included) introduction to classical or mainstream statistical theory. It is not a statistical-methods-cookbook, nor a compendium of statistical theories, nor is it a mathematics book. The book is intended to be a ...