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Book Proof and Proving in Mathematics Education

Download or read book Proof and Proving in Mathematics Education written by Gila Hanna and published by Springer Science & Business Media. This book was released on 2012-06-14 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: *THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.

Book Advances in Proof Theory

Download or read book Advances in Proof Theory written by Reinhard Kahle and published by Birkhäuser. This book was released on 2016-05-04 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this volume is to collect original contributions by the best specialists from the area of proof theory, constructivity, and computation and discuss recent trends and results in these areas. Some emphasis will be put on ordinal analysis, reductive proof theory, explicit mathematics and type-theoretic formalisms, and abstract computations. The volume is dedicated to the 60th birthday of Professor Gerhard Jäger, who has been instrumental in shaping and promoting logic in Switzerland for the last 25 years. It comprises contributions from the symposium “Advances in Proof Theory”, which was held in Bern in December 2013. ​Proof theory came into being in the twenties of the last century, when it was inaugurated by David Hilbert in order to secure the foundations of mathematics. It was substantially influenced by Gödel's famous incompleteness theorems of 1930 and Gentzen's new consistency proof for the axiom system of first order number theory in 1936. Today, proof theory is a well-established branch of mathematical and philosophical logic and one of the pillars of the foundations of mathematics. Proof theory explores constructive and computational aspects of mathematical reasoning; it is particularly suitable for dealing with various questions in computer science.

Book Space in Weak Propositional Proof Systems

Download or read book Space in Weak Propositional Proof Systems written by Ilario Bonacina and published by Springer. This book was released on 2018-01-11 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers logical proof systems from the point of view of their space complexity. After an introduction to propositional proof complexity the author structures the book into three main parts. Part I contains two chapters on resolution, one containing results already known in the literature before this work and one focused on space in resolution, and the author then moves on to polynomial calculus and its space complexity with a focus on the combinatorial technique to prove monomial space lower bounds. The first chapter in Part II addresses the proof complexity and space complexity of the pigeon principles. Then there is an interlude on a new type of game, defined on bipartite graphs, essentially independent from the rest of the book, collecting some results on graph theory. Finally Part III analyzes the size of resolution proofs in connection with the Strong Exponential Time Hypothesis (SETH) in complexity theory. The book is appropriate for researchers in theoretical computer science, in particular computational complexity.

Book Proof  Logic and Formalization

Download or read book Proof Logic and Formalization written by Michael Detlefsen and published by Routledge. This book was released on 2005-07-08 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of essays from distinguished contributors looking at why it is that mathematical proof is given precedence over other forms of mathematical justification.

Book Discrete Mathematics   Proof Techniques And Mathematical Structures

Download or read book Discrete Mathematics Proof Techniques And Mathematical Structures written by Robert Clark Penner and published by World Scientific Publishing Company. This book was released on 1999-10-19 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to mathematical proofs and to the fundamentals of modern mathematics. No real prerequisites are needed other than a suitable level of mathematical maturity. The text is divided into two parts, the first of which constitutes the core of a one-semester course covering proofs, predicate calculus, set theory, elementary number theory, relations, and functions, and the second of which applies this material to a more advanced study of selected topics in pure mathematics, applied mathematics, and computer science, specifically cardinality, combinatorics, finite-state automata, and graphs. In both parts, deeper and more interesting material is treated in optional sections, and the text has been kept flexible by allowing many different possible courses or emphases based upon different paths through the volume.

Book Manual of Style for Use in Composition and Proof Reading

Download or read book Manual of Style for Use in Composition and Proof Reading written by United States. Government Printing Office and published by . This book was released on 1904 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Conjecture and Proof

    Book Details:
  • Author : Miklos Laczkovich
  • Publisher : American Mathematical Soc.
  • Release : 2001-12-31
  • ISBN : 1470458322
  • Pages : 118 pages

Download or read book Conjecture and Proof written by Miklos Laczkovich and published by American Mathematical Soc.. This book was released on 2001-12-31 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Budapest semesters in mathematics were initiated with the aim of offering undergraduate courses that convey the tradition of Hungarian mathematics to English-speaking students. This book is an elaborate version of the course on Conjecture and Proof. It gives miniature introductions to various areas of mathematics by presenting some interesting and important, but easily accessible results and methods. The text contains complete proofs of deep results such as the transcendence of $e$, the Banach-Tarski paradox and the existence of Borel sets of arbitrary (finite) class. One of the purposes is to demonstrate how far one can get from the first principles in just a couple of steps. Prerequisites are kept to a minimum, and any introductory calculus course provides the necessary background for understanding the book. Exercises are included for the benefit of students. However, this book should prove fascinating for any mathematically literate reader.

Book 99 Variations on a Proof

Download or read book 99 Variations on a Proof written by Philip Ording and published by Princeton University Press. This book was released on 2019-01-22 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: An exploration of mathematical style through 99 different proofs of the same theorem This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics. Inspired by the experiments of the Paris-based writing group known as the Oulipo—whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp—Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau’s Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor. Readers will gain not only a bird’s-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape.

Book Rewriting  Computation and Proof

Download or read book Rewriting Computation and Proof written by Hubert Comon-Lundh and published by Springer Science & Business Media. This book was released on 2007-06-22 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Jean-Pierre Jouannaud has played a leading role in the field of rewriting and its technology. This Festschrift volume, published to honor him on his 60th Birthday, includes 13 refereed papers by leading researchers, current and former colleagues. The papers are grouped in thematic sections on Rewriting Foundations, Proof and Computation, and a final section entitled Towards Safety and Security.

Book A Cosmological Reformulation of Anselm   s Proof That God Exists

Download or read book A Cosmological Reformulation of Anselm s Proof That God Exists written by Richard Campbell and published by BRILL. This book was released on 2021-11-15 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Richard Campbell reformulates Anselm’s proof to show that factual evidence confirmed by modern cosmology validly implies that God exists. Anselm’s proof, which was never the “ontological argument” attributed to him, emerges as engaging with current philosophical issues concerning existence and scientific explanation.

Book Hybrid Logic and its Proof Theory

Download or read book Hybrid Logic and its Proof Theory written by Torben Braüner and published by Springer Science & Business Media. This book was released on 2010-11-17 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model (where the points represent times, possible worlds, states in a computer, or something else). This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relationships between proof systems for different modal logics are often unclear. In the present book we demonstrate that hybrid-logical proof-theory remedies these deficiencies by giving a spectrum of well-behaved proof systems (natural deduction, Gentzen, tableau, and axiom systems) for a spectrum of different hybrid logics (propositional, first-order, intensional first-order, and intuitionistic).

Book Kiplinger s Personal Finance

Download or read book Kiplinger s Personal Finance written by and published by . This book was released on 1999-08 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most trustworthy source of information available today on savings and investments, taxes, money management, home ownership and many other personal finance topics.

Book The Hamilton Palace Libraries

Download or read book The Hamilton Palace Libraries written by William Beckford and published by . This book was released on 1882 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book The Codes and General Laws of Oregon

Download or read book The Codes and General Laws of Oregon written by Oregon and published by . This book was released on 1887 with total page 1090 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book The Law and Practice in Bankruptcy

Download or read book The Law and Practice in Bankruptcy written by Roland Lomax Vaughan Williams and published by . This book was released on 1898 with total page 1036 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book A Treatise on Marine  Fire  Life  Accident and All Other Insurances

Download or read book A Treatise on Marine Fire Life Accident and All Other Insurances written by Joseph Asbury Joyce and published by . This book was released on 1897 with total page 1080 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Wittgenstein s Philosophy of Mathematics

Download or read book Wittgenstein s Philosophy of Mathematics written by Pasquale Frascolla and published by Routledge. This book was released on 2006-12-05 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wittgenstein's role was vital in establishing mathematics as one of this century's principal areas of philosophic inquiry. In this book, the three phases of Wittgenstein's reflections on mathematics are viewed as a progressive whole, rather than as separate entities. Frascolla builds up a systematic construction of Wittgenstein's representation of the role of arithmetic in the theory of logical operations. He also presents a new interpretation of Wittgenstein's rule-following considerations - the `community view of internal relations'.