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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!

A Lifetime of Puzzles

A Lifetime of Puzzles

Author: Erik D. Demaine Format: Paperback / softback Release Date: 30/09/2020

Martin Gardner has entertained the world with his puzzles for decades and inspired countless mathematicians and scientists. As he rounds out another decade, his colleagues are paying him tribute with this special collection that contains contributions from some of the most respected puzzlemasters, magicians and mathematicians, including: - John H. Conway - William R. Gosper - Ed Pegg, Jr. - Roger Penrose - Raymond Smullyan - Peter Winkler And of course there is something from the orignal puzzlemaster himself, Martin Gardner.

Primary Maths for Scotland Early Level Assessment Pack

Primary Maths for Scotland Early Level Assessment Pack

Author: Craig Lowther, Carol Lyon, Sheena Dunlop, Lesley Ferguson Format: Paperback / softback Release Date: 17/09/2020

The Assessment Pack supports Early Level teachers in tracking and recording children's progress through the early level numeracy and mathematics Curriculum for Excellence. It is a flexible resource which can also be used as a diagnostic tool, to identify children requiring more support or challenge, and to record and report children's attainment. Each photocopiable Assessment Pack contains: * Comprehensive introduction * Yearly Progress Checks * Bank of Holistic end of level assessments * Answers and Marking guidance * Recording sheets * Resource sheets (online) Yearly progress checks assess knowledge retention and the numeracy and mathematical skills listed in the benchmarks document. Holistic assessments check the ability to apply learning in new and unfamiliar situations. This pack contains everything you need to assess all children working within and at early level.

Primary Maths for Scotland First Level Assessment Pack

Primary Maths for Scotland First Level Assessment Pack

Author: Craig Lowther, Carol Lyon, Liz Langlands, Michelle Mackay Format: Paperback / softback Release Date: 17/09/2020

The Assessment Pack supports First Level teachers in tracking and recording children's progress through the first level numeracy and mathematics Curriculum for Excellence. It is a flexible resource which can also be used as a diagnostic tool, to identify children requiring more support or challenge, and to record and report children's attainment. Each photocopiable Assessment Pack contains: * Comprehensive introduction * Yearly Progress Checks (1A, 1B, 1C) * Bank of Holistic end of level assessments * Answers and Marking guidance * Recording sheets * Resource sheets (online) Yearly progress checks assess knowledge retention and the numeracy and mathematical skills listed in the benchmarks document. Holistic assessments check the ability to apply learning in new and unfamiliar situations. This pack contains everything you need to assess all children working within and at 1st level.

Primary Maths for Scotland Second Level Assessment Pack

Primary Maths for Scotland Second Level Assessment Pack

Author: Craig Lowther, Carol Lyon, Linda Lapere, Scott Morrow Format: Paperback / softback Release Date: 17/09/2020

The Assessment Pack supports Second Level teachers in tracking and recording children's progress through the 2nd level numeracy and mathematics Curriculum for Excellence. It is a flexible resource which can also be used as a diagnostic tool, to identify children requiring more support or challenge, and to record and report children's attainment. Each photocopiable Assessment Pack contains: * Comprehensive introduction * Yearly Progress Checks (2A, 2B, 2C) * Bank of Holistic end of level assessments * Answers and Marking guidance * Recording sheets * Resource sheets (online) Yearly progress checks assess knowledge retention and the numeracy and mathematical skills listed in the benchmarks document. Holistic assessments check the ability to apply learning in new and unfamiliar situations. This pack contains everything you need to assess all children working within and at 2nd level.

Immortality in Singularity

Immortality in Singularity

Author: Alexander N. Kharlamov Format: Hardback Release Date: 31/08/2020

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.

Geometric Set Theory

Geometric Set Theory

Author: Paul B. Larson, Jindrich Zapletal Format: Paperback / softback Release Date: 30/08/2020

This book introduces a new research direction in set theory: the study of models of set theory with respect to their extensional overlap or disagreement. In Part I, the method is applied to isolate new distinctions between Borel equivalence relations. Part II contains applications to independence results in Zermelo-Fraenkel set theory without Axiom of Choice. The method makes it possible to classify in great detail various paradoxical objects obtained using the Axiom of Choice; the classifying criterion is a ZF-provable implication between the existence of such objects. The book considers a broad spectrum of objects from analysis, algebra, and combinatorics: ultrafilters, Hamel bases, transcendence bases, colorings of Borel graphs, discontinuous homomorphisms between Polish groups, and many more. The topic is nearly inexhaustible in its variety, and many directions invite further investigation.

Higher Category Theory

Higher Category Theory

Author: Ezra Getzler Format: Paperback / softback Release Date: 08/08/2020

This volume presents the proceedings of the workshop on higher category theory and mathematical physics held at Northwestern University. Exciting new developments were presented with the aim of making them better known outside the community of experts. In particular, presentations in the style, 'Higher Categories for the Working Mathematician', were encouraged. The volume is the first to bring together developments in higher category theory with applications. This collection is a valuable introduction to this topic - one that holds great promise for future developments in mathematics.

Mathematical Circle Diaries, Year 2

Mathematical Circle Diaries, Year 2

Author: Anna Burago Format: Paperback / softback Release Date: 07/08/2020

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.

Ultrafilters across Mathematics

Ultrafilters across Mathematics

Author: Vitaly Bergelson Format: Paperback / softback Release Date: 28/07/2020

This volume originated from the International Congress ULTRAMATH: Applications of Ultrafilters and Ultraproducts in Mathematics , which was held in Pisa, Italy, from June 1-7, 2008. The volume aims to present the state-of-the-art of applications in the whole spectrum of mathematics which are grounded on the use of ultrafilters and ultraproducts. It contains two general surveys on ultrafilters in set theory and on the ultraproduct construction, as well as papers that cover additive and combinatorial number theory, nonstandard methods and stochastic differential equations, measure theory, dynamics, Ramsey theory, algebra in the space of ultrafilters, and large cardinals. The papers are intended to be accessible and interesting for mathematicians who are not experts on ultrafilters and ultraproducts. Greater prominence has been given to results that can be formulated and presented in non-special terms and be, in principle, understandable by any mathematician, and to those results that connect different areas of mathematics, revealing new facets of known important topics.|This volume originated from the International Congress ULTRAMATH: Applications of Ultrafilters and Ultraproducts in Mathematics , which was held in Pisa, Italy, from June 1-7, 2008. The volume aims to present the state-of-the-art of applications in the whole spectrum of mathematics which are grounded on the use of ultrafilters and ultraproducts. It contains two general surveys on ultrafilters in set theory and on the ultraproduct construction, as well as papers that cover additive and combinatorial number theory, nonstandard methods and stochastic differential equations, measure theory, dynamics, Ramsey theory, algebra in the space of ultrafilters, and large cardinals. The papers are intended to be accessible and interesting for mathematicians who are not experts on ultrafilters and ultraproducts. Greater prominence has been given to results that can be formulated and presented in non-special terms and be, in principle, understandable by any mathematician, and to those results that connect different areas of mathematics, revealing new facets of known important topics.

Harmonic Analysis

Harmonic Analysis

Author: Maria Cristina Pereyra, Lesley A. Ward Format: Paperback / softback Release Date: 27/07/2020

In the last 200 years, harmonic analysis has been one of the most influential bodies of mathematical ideas, having been exceptionally significant both in its theoretical implications and in its enormous range of applicability throughout mathematics, science, and engineering. In this book, the authors convey the remarkable beauty and applicability of the ideas that have grown from Fourier theory. They present for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization). While concentrating on the Fourier and Haar cases, the book touches on aspects of the world that lies between these two different ways of decomposing functions: time-frequency analysis (wavelets). Both finite and continuous perspectives are presented, allowing for the introduction of discrete Fourier and Haar transforms and fast algorithms, such as the Fast Fourier Transform (FFT) and its wavelet analogues. The approach combines rigorous proof, inviting motivation, and numerous applications. Over 250 exercises are included in the text. Each chapter ends with ideas for projects in harmonic analysis that students can work on independently. This book is published in cooperation with IAS/Park City Mathematics Institute.

4th Grade Math Workbook

4th Grade Math Workbook

Author: Apex Test Prep Format: Paperback / softback Release Date: 11/05/2020