Deepen and broaden subject knowledge to set yourself up for future success Foundation Maths 7th Edition by Croft and Davison has been written for students taking higher and further education courses who may not have specialised in mathematics on post-16 qualifications, and who require a working knowledge of mathematical and statistical tools. By providing careful and steady guidance in mathematical methods along with a wealth of practice exercises to improve your maths skills, Foundation Maths imparts confidence in its readers. For students with established mathematical expertise, this book will be an ideal revision and reference guide. The style of the book also makes it suitable for self-study and distance learning with self-assessment questions and worked examples throughout. Foundation Maths is ideally suited for students studying marketing, business studies, management, science, engineering, social science, geography, combined studies and design. Features: Mathematical processes described in everyday language. Key points highlighting important results for easy reference Worked examples included throughout the book to reinforce learning. Self-assessment questions to test understanding of important concepts, with answers provided at the back of the book. Demanding Challenge Exercises included at the end of chapters stretch the keenest of students Test and assignment exercises with answers provided in a lecturer's Solutions Manual available for download at go.pearson.com/uk/he/resources, allow lecturers to set regular work throughout the course A companion website containing a student support pack and video tutorials, as well as PowerPoint slides for lecturers, can be found at go.pearson.com/uk/he/resources New to this edition: A new section explains the importance of developing a thorough mathematical foundation in order to take advantage of and exploit the full capability of mathematical and statistical technology used in higher education and in the workplace Extensive sections throughout the book illustrate how readily-available computer software and apps can be used to perform mathematical and statistical calculations, particularly those involving algebra, calculus, graph plotting and data analysis There are revised, enhanced sections on histograms and factorisation of quadratic expressions The new edition is fully integrated with MyLab Math, a powerful online homework, tutorial and self-study system that contains over 1400 exercises that can be assigned or used for student practice, tests and homework Anthony Croft has taught mathematics in further and higher education institutions for over thirty years. During this time he has championed the development of mathematics support for the many students who find the transition from school to university mathematics particularly difficult. In 2008 he was awarded a National Teaching Fellowship in recognition of his work in this field. He has authored many successful mathematics textbooks, including several for engineering students. He was jointly awarded the IMA Gold Medal 2016 for his outstanding contribution to mathematics education. Robert Davison has thirty years' experience teaching mathematics in both further and higher education. He has authored many successful mathematics textbooks, including several for engineering students.

Primary Maths for Scotland Textbook 2A is the first of 3 second level textbooks. These engaging and pedagogically rigorous books are the first maths textbooks for Scotland completely aligned to the benchmarks and written specifically to support Scottish children in mastering mathematics at their own pace. Primary Maths for Scotland Textbook 2A is the first of 3 second level textbooks. The books are clear and simple with a focus on developing conceptual understanding alongside procedural fluency. They cover the entire second level mathematics Curriculum for Excellence in an easy-to-use set of textbooks which can fit in with teacher's existing planning, resources and scheme of work. - Packed with problem-solving, investigations and challenging problems - Diagnostic check lists at the start of each unit ensure that pupils possess the required pre-requisite knowledge to engage on the unit of work - Worked examples and non-examples help pupils fully understand mathematical concepts - Includes intelligent practice that reinforces pupils' procedural fluency

For thousands of years, mathematicians have used the timeless art of logic to see the world more clearly. In The Art of Logic, Royal Society Science Book Prize nominee Eugenia Cheng shows how anyone can think like a mathematician - and see, argue and think better.

Learn how to simplify complex decisions without over-simplifying them. Discover the power of analogies and the dangers of false equivalences. Find out how people construct misleading arguments, and how we can argue back.

Eugenia Cheng teaches us how to find clarity without losing nuance, taking a careful scalpel to the complexities of politics, privilege, sexism and dozens of other real-world situations. Her Art of Logic is a practical and inspiring guide to decoding the modern world.

What link might connect two far worlds like quantum theory and music? There is something universal in the mathematical formalism of quantum theory that goes beyond the limits of its traditional physical applications. We are now beginning to understand how some mysterious quantum concepts, like superposition and entanglement, can be used as a semantic resource.

Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory. It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses.

Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities as well as their interactions with different ideational spectra. In all classical algebraic structures, the law of compositions on a given set are well-defined, but this is a restrictive case because there are situations in science where a law of composition defined on a set may be only partially defined and partially undefined, which we call NeutroDefined, or totally undefined, which we call AntiDefined. Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebra introduces NeutroAlgebra, an emerging field of research. This book provides a comprehensive collection of original work related to NeutroAlgebra and covers topics such as image retrieval, mathematical morphology, and NeutroAlgebraic structure. It is an essential resource for philosophers, mathematicians, researchers, educators and students of higher education, and academicians.

This accessible guide is intended for those persons who need to polish up their rusty maths, or who need to get a grip on the basics of the subject for the first time. Each concept is explained, with appropriate examples, and is applied in an exercise. The solutions to all exercises are set out in detail. The book uses informal conversational language and will change the perception that mathematics is only for special people. The author has taught the subject at different levels for many years.

Fuzzy logic, which is based on the concept of fuzzy set, has enabled scientists to create models under conditions of imprecision, vagueness, or both at once. As a result, it has now found many important applications in almost all sectors of human activity, becoming a complementary feature and supporter of probability theory, which is suitable for modelling situations of uncertainty derived from randomness. Fuzzy mathematics has also significantly developed at the theoretical level, providing important insights into branches of traditional mathematics like algebra, analysis, geometry, topology, and more. With such widespread applications, fuzzy sets and logic are an important area of focus in mathematics. Advances and Applications of Fuzzy Sets and Logic studies recent theoretical advances of fuzzy sets and numbers, fuzzy systems, fuzzy logic and their generalizations, extensions, and more. This book also explores the applications of fuzzy sets and logic applied to science, technology, and everyday life to further provide research on the subject. This book is ideal for mathematicians, physicists, computer specialists, engineers, practitioners, researchers, academicians, and students who are looking to learn more about fuzzy sets, fuzzy logic, and their applications.

The overall topic of the volume, Mathematics for Computation (M4C), is mathematics taking crucially into account the aspect of computation, investigating the interaction of mathematics with computation, bridging the gap between mathematics and computation wherever desirable and possible, and otherwise explaining why not.Recently, abstract mathematics has proved to have more computational content than ever expected. Indeed, the axiomatic method, originally intended to do away with concrete computations, seems to suit surprisingly well the programs-from-proofs paradigm, with abstraction helping not only clarity but also efficiency.Unlike computational mathematics, which rather focusses on objects of computational nature such as algorithms, the scope of M4C generally encompasses all the mathematics, including abstract concepts such as functions. The purpose of M4C actually is a strongly theory-based and therefore, is a more reliable and sustainable approach to actual computation, up to the systematic development of verified software.While M4C is situated within mathematical logic and the related area of theoretical computer science, in principle it involves all branches of mathematics, especially those which prompt computational considerations. In traditional terms, the topics of M4C include proof theory, constructive mathematics, complexity theory, reverse mathematics, type theory, category theory and domain theory.The aim of this volume is to provide a point of reference by presenting up-to-date contributions by some of the most active scholars in each field. A variety of approaches and techniques are represented to give as wide a view as possible and promote cross-fertilization between different styles and traditions.

Calculi of temporal logic are widely used in modern computer science. The temporal organization of information flows in the different architectures of laptops, the Internet, or supercomputers would not be possible without appropriate temporal calculi. In the age of digitalization and High-Tech applications, people are often not aware that temporal logic is deeply rooted in the philosophy of modalities. A deep understanding of these roots opens avenues to the modern calculi of temporal logic which have emerged by extension of modal logic with temporal operators. Computationally, temporal operators can be introduced in different formalisms with increasing complexity such as Basic Modal Logic (BML), Linear-Time Temporal Logic (LTL), Computation Tree Logic (CTL), and Full Computation Tree Logic (CTL*). Proof-theoretically, these formalisms of temporal logic can be interpreted by the sequent calculus of Gentzen, the tableau-based calculus, automata-based calculus, game-based calculus, and dialogue-based calculus with different advantages for different purposes, especially in computer science.The book culminates in an outlook on trendsetting applications of temporal logics in future technologies such as artificial intelligence and quantum technology. However, it will not be sufficient, as in traditional temporal logic, to start from the everyday understanding of time. Since the 20th century, physics has fundamentally changed the modern understanding of time, which now also determines technology. In temporal logic, we are only just beginning to grasp these differences in proof theory which needs interdisciplinary cooperation of proof theory, computer science, physics, technology, and philosophy.