Methods Of Solving Sequence And Series Problems
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Methods Of Solving Sequence And Series Problems
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Author : Ellina Grigorieva
language : en
Publisher: Birkhäuser
Release Date : 2016-12-09
Methods Of Solving Sequence And Series Problems written by Ellina Grigorieva and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-09 with Mathematics categories.
This book aims to dispel the mystery and fear experienced by students surrounding sequences, series, convergence, and their applications. The author, an accomplished female mathematician, achieves this by taking a problem solving approach, starting with fascinating problems and solving them step by step with clear explanations and illuminating diagrams. The reader will find the problems interesting, unusual, and fun, yet solved with the rigor expected in a competition. Some problems are taken directly from mathematics competitions, with the name and year of the exam provided for reference. Proof techniques are emphasized, with a variety of methods presented. The text aims to expand the mind of the reader by often presenting multiple ways to attack the same problem, as well as drawing connections with different fields of mathematics. Intuitive and visual arguments are presented alongside technical proofs to provide a well-rounded methodology. With nearly 300 problems including hints, answers, and solutions, Methods of Solving Sequences and Series Problems is an ideal resource for those learning calculus, preparing for mathematics competitions, or just looking for a worthwhile challenge. It can also be used by faculty who are looking for interesting and insightful problems that are not commonly found in other textbooks.
Methods Of Solving Number Theory Problems
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Author : Ellina Grigorieva
language : en
Publisher: Birkhäuser
Release Date : 2018-07-06
Methods Of Solving Number Theory Problems written by Ellina Grigorieva and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-06 with Mathematics categories.
Through its engaging and unusual problems, this book demonstrates methods of reasoning necessary for learning number theory. Every technique is followed by problems (as well as detailed hints and solutions) that apply theorems immediately, so readers can solve a variety of abstract problems in a systematic, creative manner. New solutions often require the ingenious use of earlier mathematical concepts - not the memorization of formulas and facts. Questions also often permit experimental numeric validation or visual interpretation to encourage the combined use of deductive and intuitive thinking. The first chapter starts with simple topics like even and odd numbers, divisibility, and prime numbers and helps the reader to solve quite complex, Olympiad-type problems right away. It also covers properties of the perfect, amicable, and figurate numbers and introduces congruence. The next chapter begins with the Euclidean algorithm, explores therepresentations of integer numbers in different bases, and examines continued fractions, quadratic irrationalities, and the Lagrange Theorem. The last section of Chapter Two is an exploration of different methods of proofs. The third chapter is dedicated to solving Diophantine linear and nonlinear equations and includes different methods of solving Fermat’s (Pell’s) equations. It also covers Fermat’s factorization techniques and methods of solving challenging problems involving exponent and factorials. Chapter Four reviews the Pythagorean triple and quadruple and emphasizes their connection with geometry, trigonometry, algebraic geometry, and stereographic projection. A special case of Waring’s problem as a representation of a number by the sum of the squares or cubes of other numbers is covered, as well as quadratic residuals, Legendre and Jacobi symbols, and interesting word problems related to the properties of numbers. Appendices provide a historic overview of number theory and its main developments from the ancient cultures in Greece, Babylon, and Egypt to the modern day. Drawing from cases collected by an accomplished female mathematician, Methods in Solving Number Theory Problems is designed as a self-study guide or supplementary textbook for a one-semester course in introductory number theory. It can also be used to prepare for mathematical Olympiads. Elementary algebra, arithmetic and some calculus knowledge are the only prerequisites. Number theory gives precise proofs and theorems of an irreproachable rigor and sharpens analytical thinking, which makes this book perfect for anyone looking to build their mathematical confidence.
Theory Of Infinite Sequences And Series
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Author : Ludmila Bourchtein
language : en
Publisher: Springer Nature
Release Date : 2021-11-13
Theory Of Infinite Sequences And Series written by Ludmila Bourchtein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-13 with Mathematics categories.
This textbook covers the majority of traditional topics of infinite sequences and series, starting from the very beginning – the definition and elementary properties of sequences of numbers, and ending with advanced results of uniform convergence and power series. The text is aimed at university students specializing in mathematics and natural sciences, and at all the readers interested in infinite sequences and series. It is designed for the reader who has a good working knowledge of calculus. No additional prior knowledge is required. The text is divided into five chapters, which can be grouped into two parts: the first two chapters are concerned with the sequences and series of numbers, while the remaining three chapters are devoted to the sequences and series of functions, including the power series. Within each major topic, the exposition is inductive and starts with rather simple definitions and/or examples, becoming more compressed and sophisticated as the course progresses. Each key notion and result is illustrated with examples explained in detail. Some more complicated topics and results are marked as complements and can be omitted on a first reading. The text includes a large number of problems and exercises, making it suitable for both classroom use and self-study. Many standard exercises are included in each section to develop basic techniques and test the understanding of key concepts. Other problems are more theoretically oriented and illustrate more intricate points of the theory, or provide counterexamples to false propositions which seem to be natural at first glance. Solutions to additional problems proposed at the end of each chapter are provided as an electronic supplement to this book.
Problem Solving Strategies
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Author : Arthur Engel
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-19
Problem Solving Strategies written by Arthur Engel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-19 with Mathematics categories.
A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.
Pemecahan Masalah Matematis
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Author : Herry Pribawanto Suryawan
language : id
Publisher: Sanata Dharma University Press
Release Date : 2021-02-19
Pemecahan Masalah Matematis written by Herry Pribawanto Suryawan and has been published by Sanata Dharma University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-19 with Education categories.
Buku Pemecahan Masalah Matematis ini disusun untuk memberikan gambaran tentang berbagai strategi dasar pemecahan masalah matematis. Dengan melihat kurangnya buku-buku berbahasa Indonesia yang membahas pemecahan masalah matematis secara sistematis, penulis juga berharap bahwa buku ini dapat memberikan sedikit kontribusi untuk pengembangan matematika di Indonesia khususnya terkait pemecahan masalah matematis. Sebagian besar isi buku ini dapat dibaca oleh siswa sekolah menengah atas. Mahasiswa S1 matematika/pendidikan matematika tentu saja akan menemukan banyak manfaat dengan membaca buku ini. Berbagai teknik dan strategi yang dibahas di buku ini akan sering muncul dalam berbagai perkuliahan matematika dari tingkat dasar sampai tingkat lanjut. Buku ini juga sangat bermanfaat bagi mahasiswa S2 matematika/pendidikan matematika untuk memberikan dasar-dasar teknis melakukan penelitian matematika. Buku ini juga akan menarik bagi para penggemar matematika yang gemar menyelesaikan soal-soal matematika yang bersifat tak rutin, baik sebagai persiapan untuk menghadapi berbagai kompetisi matematika ataupun hanya sekedar untuk mengisi waktu luang. Buku ini disusun dengan prinsip belajar dengan mengerjakan (learning by doing). Pemecahan masalah matematis bukan sekedar teori yang harus dihafalkan namun hanya dapat dikuasai dengan cara membaca (dan mengerjakan ulang) contoh soal dan mengerjakan sebanyak mungkin soal latihan dengan tekun. Hal ini sejalan dengan prinsip heuristik yang memerlukan banyak pengalaman untuk dapat mempelajarinya.
Problem Solving Through Problems
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Author : Loren C. Larson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Problem Solving Through Problems written by Loren C. Larson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam.
Assessment And Intervention
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Author : Thomas E. Scruggs
language : en
Publisher: Emerald Group Publishing
Release Date : 2011-03-31
Assessment And Intervention written by Thomas E. Scruggs and has been published by Emerald Group Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-31 with Education categories.
Includes chapters on curriculum based measurement and response to intervention, dynamic assessment and working memory, diagnostic accuracy and functional diagnosis, assessment of social behavior, assessment and intervention in reading and writing, and assessment and intervention in social and emotional competence and self-determination.
Handbook Of Evidence Based Practices In Intellectual And Developmental Disabilities
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Author : Nirbhay N. Singh
language : en
Publisher: Springer
Release Date : 2016-05-11
Handbook Of Evidence Based Practices In Intellectual And Developmental Disabilities written by Nirbhay N. Singh and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-11 with Psychology categories.
This handbook presents a diverse range of effective treatment approaches for individuals with intellectual and developmental disabilities (IDD). Its triple focus on key concepts, treatment and training modalities, and evidence-based interventions for challenging behaviors of individuals with IDD provides a solid foundation for effective treatment strategies, theory-to-implementation issues, and the philosophical and moral aspects of care. Expert contributions advocate for changes in treating individuals with intellectual and developmental disabilities by emphasizing caregiver support as well as respecting and encouraging client autonomy, self-determination, and choice. With its quality-of-life approach, the handbook details practices that are person-centered and supportive as well as therapeutically sound. Topics featured in the handbook include: Functional and preference assessments for clinical decision making. Treatment modalities from cognitive behavioral therapy and pharmacotherapy to mindfulness, telehealth, and assistive technologies. Self-determination and choice as well as community living skills. Quality-of-life issues for individuals with IDD. Early intensive behavior interventions for autism spectrum disorder. Skills training for parents of children with IDD as well as staff training in positive behavior support. Evidence-based interventions for a wide range of challenging behaviors and issues. The Handbook of Evidence-Based Practices in Intellectual and Developmental Disabilities is a must-have resource for researchers, clinicians, scientist-practitioners, and graduate students in clinical psychology, social work, behavior therapy, and rehabilitation.
Task Analysis Methods For Instructional Design
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Author : David H. Jonassen
language : en
Publisher: Routledge
Release Date : 1998-10-01
Task Analysis Methods For Instructional Design written by David H. Jonassen and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-01 with Education categories.
Task Analysis Methods for Instructional Design is a handbook of task analysis and knowledge elicitation methods that can be used for designing direct instruction, performance support, and learner-centered learning environments. To design any kind of instruction, it is necessary to articulate a model of how learners should think and perform. This book provides descriptions and examples of five different kinds of task analysis methods: *job/behavioral analysis; *learning analysis; *cognitive task analysis; *activity-based analysis methods; and *subject matter analysis. Chapters follow a standard format making them useful for reference, instruction, or performance support.
Encyclopaedia Of Mathematics
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Encyclopaedia Of Mathematics written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.