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This book features the complete set of answers to the exercises in Mathematics Year 6, to save you time marking work and enable you to identify areas requiring further attention. The book includes diagrams and working where necessary, to ensure pupils understand how to present their answers. Also available from Galore Park www.galorepark.co.uk :. - Mathematics Year 5. - 11+ Maths Practice Exercises. - 11+ Maths Revision Guide. - 10-Minute Maths Tests Workbook Age 8-10. - 10-Minute Maths Tests Workbook Age 9-11. - Mental Arithmetic Workbook Age 8-10. - Mental Arithmetic Workbook Age 9-11
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O primeiro capítulo, assim, introduz osconceitos de módulo, inteiro algébrico, norma e traço de um elemento,discriminante, base integral, anel de Dedekind e outros conceitosindispensáveis ao desenvolvimento dos demais capítulos. Estuda ainda as formas quadráticas, as quais se aplicam para determinar o raio de empacotamento da realização geométricade um ideal em questão. O capítulo 2 apresenta um estudo sobre corpos de números, com ênfase nos anéis dos inteiros e discriminantes de corpos quadráticos e ciclotômicos, além de abordar a decomposição de um ideal primo em uma extensão fazendo uso do Teorema de Kummer. As definições de reticulado, empacotamento esférico, volume e densidade de centro são abordadas no terceiro capítulo, que ainda trata do método de Minkowski para obtenção de reticulados via representação geométrica de ideais dos anéis de inteiros algébricos.
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Innovative thinking backed by logical reasoning is the key to the puzzles in Popular Problems and Puzzles in Mathematics. Collected over several years by the author, more than 150 elegant, intriguing numerical challenges are presented here. The answers are easy to explain, but one would devilishly find it hard without this book. One's ability to construct a mathematical proof will be rigorously tested in these problems - even in the case of a mathematics teacher. For true maths lovers, there is even a section on historically prominent problems. Designed for high-school students and teachers with an interest in mathematical problem solving, this stimulating collection provides a new twist to familiar topics that introduce unfamiliar topics.
Key features
1. Suitable for high-school students and maths buffs
2. More than 150 problems covering different areas of elementary mathematics
3. Brainstorming problems graded as easy, moderate and difficult
4. Complete solutions included
5. Appendices showing various applications in the end
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Mathematical Neuroscience is a book for mathematical biologists seeking to discover the complexities of brain dynamics in an integrative way. It is the first research monograph devoted exclusively to the theory and methods of nonlinear analysis of infinite systems based on functional analysis techniques arising in modern mathematics. Neural models that describe the spatio-temporal evolution of coarse-grained variables-such as synaptic or firing rate activity in populations of neurons -and often take the form of integro-differential equations would not normally reflect an integrative approach. This book examines the solvability of infinite systems of reaction diffusion type equations in partially ordered abstract spaces. It considers various methods and techniques of nonlinear analysis, including comparison theorems, monotone iterative techniques, a truncation method, and topological fixed point methods. Infinite systems of such equations play a crucial role in the integrative aspects of neuroscience modeling. The first focused introduction to the use of nonlinear analysis with an infinite dimensional approach to theoretical neuroscience. Combines functional analysis techniques with nonlinear dynamical systems applied to the study of the brain. Introduces powerful mathematical techniques to manage the dynamics and challenges of infinite systems of equations applied to neuroscience modeling.
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Laboratory Statistics: Handbook of Formulas and Terms presents common strategies for comparing and evaluating numerical laboratory data. In particular, the text deals with the type of data and problems that laboratory scientists and students in analytical chemistry, clinical chemistry, epidemiology, and clinical research face on a daily basis. This book takes the mystery out of statistics and provides simple, hands-on instructions in the format of everyday formulas. As far as possible, spreadsheet shortcuts and functions are included, along with many simple worked examples. This book is a must-have guide to applied statistics in the lab that will result in improved experimental design and analysis. Comprehensive coverage of simple statistical concepts familiarizes the reader with formatted statistical expression; simple, worked examples make formulas easy to use in real life; spreadsheet functions demonstrate how to find immediate solutions to common problems; in-depth indexing and frequent use of synonyms facilitate the quick location of appropriate procedures.
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"Beyond simulation and algorithm development, many developers increasingly use MATLAB even for product deployment in computationally heavy fields. This often demands that MATLAB codes run faster by leveraging the distributed parallelism of Graphics Processing Units (GPUs). While MATLAB successfully provides high-level functions as a simulation tool for rapid prototyping, the underlying details and knowledge needed for utilizing GPUs make MATLAB users hesitate to step into it. Accelerating MATLAB with GPUs offers a primer on bridging this gap. Starting with the basics, setting up MATLAB for CUDA (in Windows, Linux and Mac OS X) and profiling, it then guides users through advanced topics such as CUDA libraries. The authors share their experience developing algorithms using MATLAB, C++ and GPUs for huge datasets, modifying MATLAB codes to better utilize the computational power of GPUs, and integrating them into commercial software products. Throughout the book, they demonstrate many example codes that can be used as templates of C-MEX and CUDA codes for readers' projects. Download example codes from the publisher's website: http://booksite.elsevier.com/9780124080805/ Shows how to accelerate MATLAB codes through the GPU for parallel processing, with minimal hardware knowledge -- Explains the related background on hardware, architecture and programming for ease of use -- Provides simple worked examples of MATLAB and CUDA C codes as well as templates that can be reused in real-world projects."--Provided by publisher.
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Provides an in-depth treatment of hierarchical problem solving, computational complexity, and the principles and applications of multi-granular computing, including inference, information fusing, planning, and heuristic search.
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