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New Foundations in Mathematics

New Foundations in Mathematics
Author: Garret Sobczyk
Publisher: Springer Science & Business Media
Total Pages: 373
Release: 2012-10-26
Genre: Mathematics
ISBN: 0817683852

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The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.


Number Systems and the Foundations of Analysis

Number Systems and the Foundations of Analysis
Author: Elliott Mendelson
Publisher: Dover Books on Mathematics
Total Pages: 0
Release: 2008
Genre: Mathematics
ISBN: 9780486457925

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Geared toward undergraduate and beginning graduate students, this study explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Numerous exercises and appendixes supplement the text. 1973 edition.


Building the Foundation: Whole Numbers in the Primary Grades

Building the Foundation: Whole Numbers in the Primary Grades
Author: Maria G. Bartolini Bussi
Publisher: Springer
Total Pages: 548
Release: 2018-03-29
Genre: Education
ISBN: 3319635557

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This twenty-third ICMI Study addresses for the first time mathematics teaching and learning in the primary school (and pre-school) setting, while also taking international perspectives, socio-cultural diversity and institutional constraints into account. One of the main challenges of designing the first ICMI primary school study of this kind is the complex nature of mathematics at the early level. Accordingly, a focus area that is central to the discussion was chosen, together with a number of related questions. The broad area of Whole Number Arithmetic (WNA), including operations and relations and arithmetic word problems, forms the core content of all primary mathematics curricula. The study of this core content area is often regarded as foundational for later mathematics learning. However, the principles and main goals of instruction on the foundational concepts and skills in WNA are far from universally agreed upon, and practice varies substantially from country to country. As such, this study presents a meta-level analysis and synthesis of what is currently known about WNA, providing a useful base from which to gauge gaps and shortcomings, as well as an opportunity to learn from the practices of different countries and contexts.


The Number Systems: Foundations of Algebra and Analysis

The Number Systems: Foundations of Algebra and Analysis
Author: Solomon Feferman
Publisher: American Mathematical Soc.
Total Pages: 434
Release: 2003
Genre: Number theory
ISBN: 0821829157

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The subject of this book is the successive construction and development of the basic number systems of mathematics: positive integers, integers, rational numbers, real numbers, and complex numbers. This second edition expands upon the list of suggestions for further reading in Appendix III. From the Preface: ``The present book basically takes for granted the non-constructive set-theoretical foundation of mathematics, which is tacitly if not explicitly accepted by most working mathematicians but which I have since come to reject. Still, whatever one's foundational views, students must be trained in this approach in order to understand modern mathematics. Moreover, most of the material of the present book can be modified so as to be acceptable under alternative constructive and semi-constructive viewpoints, as has been demonstrated in more advanced texts and research articles.''


Practical Foundations of Mathematics

Practical Foundations of Mathematics
Author: Paul Taylor
Publisher: Cambridge University Press
Total Pages: 590
Release: 1999-05-13
Genre: Mathematics
ISBN: 9780521631075

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This book is about the basis of mathematical reasoning both in pure mathematics itself (particularly algebra and topology) and in computer science (how and what it means to prove correctness of programs). It contains original material and original developments of standard material, so it is also for professional researchers, but as it deliberately transcends disciplinary boundaries and challenges many established attitudes to the foundations of mathematics, the reader is expected to be open minded about these things.


Foundations Phonics

Foundations Phonics
Author: Carrie Lindquist
Publisher: New Leaf Publishing Group
Total Pages: 31
Release: 2016-08-29
Genre: Education
ISBN: 0890519439

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An easy and fun approach to teaching your child to read A stand-alone phonics & reading program, flexible for use in either kindergarten or first gradeA workbook filled with lessons, instructions, and suggested hands-on activities for a full semester of studySuggested hands-on activities will utilize materials typically found in the kitchen or playroom (e.g., crayons, markers, flour, rice, play-dough) This unique curriculum will take your student on a journey from the beginning of creation to the Resurrection of Christ as they learn each letter and corresponding sound. Designed to meet the needs of students who are ready to begin writing, as well as those who may not have mastered the hand-eye coordination skills yet that are needed for writing.


Supporting Early Numeracy

Supporting Early Numeracy
Author: British Columbia. Ministry of Education
Publisher: British Columbia, Ministry of Education
Total Pages: 155
Release: 2004-01-01
Genre: Arithmetic
ISBN: 9780772651341

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Foundations of Combinatorics with Applications

Foundations of Combinatorics with Applications
Author: Edward A. Bender
Publisher: Courier Corporation
Total Pages: 789
Release: 2013-01-18
Genre: Mathematics
ISBN: 0486151506

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This introduction to combinatorics, the foundation of the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines a variety of applications relevant to computer science and mathematics, including induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises appear throughout the text, along with notes and references. The text concludes with solutions to odd-numbered exercises and to all appendix exercises.