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Mathematical foundations

See below for a selection of the latest books from Mathematical foundations category. Presented with a red border are the Mathematical foundations books that have been lovingly read and reviewed by the experts at Lovereading. With expert reading recommendations made by people with a passion for books and some unique features Lovereading will help you find great Mathematical foundations books and those from many more genres to read that will keep you inspired and entertained. And it's all free!

Foundation Maths

Foundation Maths

Author: Anthony Croft, Robert Davison Format: Paperback / softback Release Date: 28/01/2020

Were you looking for the book with access to MyMathLab Global? This product is the book alone, and does NOT come with access to MyMathLab Global. Buy Foundation Maths, 7th edition with MyMathLab Global access card (ISBN 9781292289762) if you need access to MyMathLab Global as well, and save money on this resource. You will also need a course ID from your lecturer to access MyLab. Foundation Maths has been written for students taking higher and further education courses who may not have specialised in mathematics on post-16 qualifications and need to use mathematical and statistical tools in their courses. It is ideally suited to those studying marketing, business studies, management, science, engineering, social science, geography, combined studies and design. It will be particularly useful for those who lack confidence and who need careful, steady guidance in mathematical methods. For those whose mathematical expertise is already established, the book will be a helpful revision and reference guide. The style of the book also makes it suitable for self-study and distance learning. Features of the book * 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. * Exercises that provide a key opportunity to develop competence through practice * Demanding, Challenge Exercises included at the end of chapters to stretch the keenest students. * Test and assignment exercises with answers provided in a lecturer's Solutions Manual on the website) allow lecturers to set regular work to complete throughout the course. * A companion website containing a student support pack and video tutorials, plus PowerPoint slides and a Solutions Manual for lecturers, can be found at www.pearsoned.co.uk/croft New to this seventh 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 MyMathLab, a powerful online homework, tutorial and self-study system. Author biography 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.

Immortality in Singularity

Immortality in Singularity

Author: Alexander N. Kharlamov Format: Hardback Release Date: 30/12/2019

This book explores and reconsiders the current vision of the achievements in mind transfer technology and digital immortality from a biomedical point of view. It provides a systematic review of the technological accomplishments in the field of mind transfer. It introduces a novel analytical philosophical piece of this research in scientific realism with a focus on the probable scenario for the further development of humankind. It analyses that the dramatic progress of biomedical engineering and nanotechnology promises to revolutionize medicine in the upcoming decade. It discusses about some inventions, including the magic-bullet multifunctional devices, that will allow us to develop whole brain emulation technology by 2045, and simultaneously draws attention to the fact that mind transfer will be infeasible until there is a breakthrough in neurophysiology and quantum physics. It highlights that the mind transfer technology has a potential to immortalize a human being in a space-time multidimensional and technological singularity with the assistance of artificial superintelligence. It also pays special attention to sexuality as a cornerstone of the future civilization.

Reflections on the Foundations of Mathematics Univalent Foundations, Set Theory and General Thoughts

Reflections on the Foundations of Mathematics Univalent Foundations, Set Theory and General Thoughts

Author: Stefania Centrone Format: Hardback Release Date: 20/12/2019

This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The volume is divided into three sections, the first two of which focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, which has widely been assumed to serve as a framework for foundational issues, as well as new material elaborating on the univalent foundations, considering an approach based on homotopy type theory (HoTT). The third section then builds on this and is centred on philosophical questions connected to the foundations of mathematics. Here, the authors contribute to discussions on foundational criteria with more general thoughts on the foundations of mathematics which are not connected to particular theories. This book shares the work of some of the most important scholars in the fields of set theory (S. Friedman), non-classical logic (G. Priest) and the philosophy of mathematics (P. Maddy). The reader will become aware of the advantages of each theory and objections to it as a foundation, following the latest and best work across the disciplines and it is therefore a valuable read for anyone working on the foundations of mathematics or in the philosophy of mathematics.

A Handbook of Proofs and Theorems

A Handbook of Proofs and Theorems

Author: Maria Catherine C. Borres Format: Hardback Release Date: 11/11/2019

A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments. In general, a theorem is an embodiment of some general principle that makes it part of a larger theory. The process of showing a theorem to be correct is called a proof. Proofs employ logic but usually include some amount of natural language which usually admits some ambiguity. In fact, the vast majority of proofs in written mathematics can be considered as applications of rigorous informal logic. Purely formal proofs, written in symbolic language instead of natural language, are considered in proof theory. The distinction between formal and informal proofs has led to much examination of current and historical mathematical practice, quasi-empiricism in mathematics, and so-called folk mathematics. Many mathematical theorems are conditional statements. In this case, the proof deduces the conclusion from conditions called hypotheses or premises. In light of the interpretation of proof as justification of truth, the conclusion is often viewed as a necessary consequence of the hypotheses, namely, that the conclusion is true in case the hypotheses are true, without any further assumptions. However, the conditional could be interpreted differently in certain deductive systems, depending on the meanings assigned to the derivation rules and the conditional symbol. The philosophy of mathematics is concerned with the role of language and logic in proofs, and mathematics as a language.

Mathematical Circle Diaries, Year 2 Complete Curriculum for Grades 6 to 8

Mathematical Circle Diaries, Year 2 Complete Curriculum for Grades 6 to 8

Author: Anna Burago Format: Paperback / softback Release Date: 11/11/2019

Mathematical circles, with their question-driven approach and emphasis on problem solving, expose students to the type of mathematics that stimulates the development of logical thinking, creativity, analytical abilities, and mathematical reasoning. These skills, while scarcely introduced at school, are in high demand in the modern world. This book, a sequel to Mathematical Circle Diaries, Year 1, teaches how to think and solve problems in mathematics. The material, distributed among twenty-nine weekly lessons, includes detailed lectures and discussions, sets of problems with solutions, and contests and games. In addition, the book shares some of the know-how of running a mathematical circle. The book covers a broad range of problem-solving strategies and proofing techniques, as well as some more advanced topics that go beyond the limits of a school curriculum. The topics include invariants, proofs by contradiction, the Pigeonhole principle, proofs by coloring, double counting, combinatorics, binary numbers, graph theory, divisibility and remainders, logic, and many others. When students take science and computing classes in high school and college, they will be better prepared for both the foundations and advanced material. The book contains everything that is needed to run a successful mathematical circle for a full year. This book, written by an author actively involved in teaching mathematical circles for fifteen years, is intended for teachers, math coaches, parents, and math enthusiasts who are interested in teaching math that promotes critical thinking. Motivated students can work through this book on their own. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Bridge to Abstract Mathematics

Bridge to Abstract Mathematics

Mathematics is a science that concerns theorems that must be proved within a system of axioms and definitions. With this book, the mathematical novice will learn how to prove theorems and explore the universe of abstract mathematics. The introductory chapters familiarise the reader with some fundamental ideas, including the axiomatic method, symbolic logic and mathematical language. This leads to a discussion of the nature of proof, along with various methods for proving statements. The subsequent chapters present some foundational topics in pure mathematics, including detailed introductions to set theory, number systems and calculus. Through these fascinating topics, supplemented by plenty of examples and exercises, the reader will hone their proof skills. This complete guide to proof is ideal preparation for a university course in pure mathematics, and a valuable resource for educators.

Higher Order Fourier Analysis

Higher Order Fourier Analysis

Author: Terence Tao Format: Hardback Release Date: 08/11/2019

Traditional Fourier analysis, which has been remarkably effective in many contexts, uses linear phase functions to study functions. Some questions, such as problems involving arithmetic progressions, naturally lead to the use of quadratic or higher order phases. Higher order Fourier analysis is a subject that has become very active only recently. Gowers, in groundbreaking work, developed many of the basic concepts of this theory in order to give a new, quantitative proof of Szemeredi's theorem on arithmetic progressions. However, there are also precursors to this theory in Weyl's classical theory of equidistribution, as well as in Furstenberg's structural theory of dynamical systems. This book, which is the first monograph in this area, aims to cover all of these topics in a unified manner, as well as to survey some of the most recent developments, such as the application of the theory to count linear patterns in primes. The book serves as an introduction to the field, giving the beginning graduate student in the subject a high-level overview of the field. The text focuses on the simplest illustrative examples of key results, serving as a companion to the existing literature on the subject. There are numerous exercises with which to test one's knowledge.

Numerical Methods

Numerical Methods

Author: Arvind Pragati Gautam Format: Hardback Release Date: 31/10/2019

Where Do Numbers Come From?

Where Do Numbers Come From?

Author: T. W. (University of Cambridge) Koerner Format: Paperback / softback Release Date: 24/10/2019

Why do we need the real numbers? How should we construct them? These questions arose in the nineteenth century, along with the ideas and techniques needed to address them. Nowadays it is commonplace for apprentice mathematicians to hear 'we shall assume the standard properties of the real numbers' as part of their training. But exactly what are those properties? And why can we assume them? This book is clearly and entertainingly written for those students, with historical asides and exercises to foster understanding. Starting with the natural (counting) numbers and then looking at the rational numbers (fractions) and negative numbers, the author builds to a careful construction of the real numbers followed by the complex numbers, leaving the reader fully equipped with all the number systems required by modern mathematical analysis. Additional chapters on polynomials and quarternions provide further context for any reader wanting to delve deeper.

Where Do Numbers Come From?

Where Do Numbers Come From?

Author: T. W. (University of Cambridge) Koerner Format: Hardback Release Date: 24/10/2019

Why do we need the real numbers? How should we construct them? These questions arose in the nineteenth century, along with the ideas and techniques needed to address them. Nowadays it is commonplace for apprentice mathematicians to hear 'we shall assume the standard properties of the real numbers' as part of their training. But exactly what are those properties? And why can we assume them? This book is clearly and entertainingly written for those students, with historical asides and exercises to foster understanding. Starting with the natural (counting) numbers and then looking at the rational numbers (fractions) and negative numbers, the author builds to a careful construction of the real numbers followed by the complex numbers, leaving the reader fully equipped with all the number systems required by modern mathematical analysis. Additional chapters on polynomials and quarternions provide further context for any reader wanting to delve deeper.

Automata, Graphs and Logic

Automata, Graphs and Logic

Author: D. Gnanaraj Thomas, Robinson Thamburaj Format: Hardback Release Date: 23/10/2019

Wondrous One Sheet Origami

Wondrous One Sheet Origami

Author: Meenakshi Mukerji Format: Hardback Release Date: 18/10/2019

Wondrous One Sheet Origami is a how-to book full of beautiful origami designs covering a wide range of folding levels from simple to high intermediate, with more emphasis on the latter. The book is meant for audiences 12 years of age and above, and children folding at higher than age level. Most of the designs are flat and suitable for mounting on cards or framing as gifts. Features * Richly illustrated full-color book with clear, crisp diagrams following international standard, and an abundance of photographs of finished models * Select designs hand-picked by the author based on social media responses * Most of the designs incorporate color-change, a technique showing both sides of paper for enhanced beauty Meenakshi Mukerji's work is both intricate and lovely. She's greatly respected in the origami world, one of the well-known world leaders in modular origami. Her books offer a nice exposition of the mathematical elements, but you're not being hit over the head with math lessons. You learn things without even realizing that you have. -Dr. Robert J. Lang Meenakshi Mukerji is one of today's masters of modular origami, designs comprised of multiple pieces of paper. She also brings her ingenuity and creativity to designs made from a single piece of paper. Among the most appealing aspects of her single sheet work is the way she subtly manipulates a purely geometric form to fold a flower, a leaf, a butterfly, or card suits. -Peter Engel