Proof and Proving in Mathematics Education

Proof and Proving in Mathematics Education PDF Book Detail Author: Gila Hanna
Publisher: Springer Science & Business Media
ISBN: 9400721293
Category : Education
Languages : en
Pages : 475

Book Description
*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.

Advances in Proof Theory

Advances in Proof Theory PDF Book Detail Author: Reinhard Kahle
Publisher: Birkhäuser
ISBN: 331929198X
Category : Mathematics
Languages : en
Pages : 425

Book Description
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.

Space in Weak Propositional Proof Systems

Space in Weak Propositional Proof Systems PDF Book Detail Author: Ilario Bonacina
Publisher: Springer
ISBN: 3319734539
Category : Computers
Languages : en
Pages : 130

Book Description
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.

Proof Logic and Formalization

Proof  Logic and Formalization PDF Book Detail Author: Michael Detlefsen
Publisher: Routledge
ISBN: 1134975287
Category : Philosophy
Languages : en
Pages : 256

Book Description
The mathematical proof is the most important form of justification in mathematics. It is not, however, the only kind of justification for mathematical propositions. The existence of other forms, some of very significant strength, places a question mark over the prominence given to proof within mathematics. This collection of essays, by leading figures working within the philosophy of mathematics, is a response to the challenge of understanding the nature and role of the proof.

Discrete Mathematics Proof Techniques And Mathematical Structures

Discrete Mathematics   Proof Techniques And Mathematical Structures PDF Book Detail Author: Robert Clark Penner
Publisher: World Scientific Publishing Company
ISBN: 9813105615
Category : Mathematics
Languages : en
Pages : 488

Book Description
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.

Rewriting Computation and Proof

Rewriting  Computation and Proof PDF Book Detail Author: Hubert Comon-Lundh
Publisher: Springer Science & Business Media
ISBN: 3540731466
Category : Computers
Languages : en
Pages : 272

Book Description
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.

Conjecture and Proof

Conjecture and Proof PDF Book Detail Author: Miklos Laczkovich
Publisher: American Mathematical Soc.
ISBN: 1470458322
Category : Mathematics
Languages : en
Pages : 118

Book Description
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.

99 Variations on a Proof

99 Variations on a Proof PDF Book Detail Author: Philip Ording
Publisher: Princeton University Press
ISBN: 0691185425
Category : Mathematics
Languages : en
Pages :

Book Description
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.

A Cosmological Reformulation of Anselm s Proof That God Exists

A Cosmological Reformulation of Anselm   s Proof That God Exists PDF Book Detail Author: Richard Campbell
Publisher: BRILL
ISBN: 9004184619
Category : Philosophy
Languages : en
Pages : 504

Book Description
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.

Hybrid Logic and its Proof Theory

Hybrid Logic and its Proof Theory PDF Book Detail Author: Torben Braüner
Publisher: Springer Science & Business Media
ISBN: 9400700024
Category : Philosophy
Languages : en
Pages : 231

Book Description
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).

American Jurisprudence Proof of Facts Second Series

American Jurisprudence Proof of Facts  Second Series PDF Book Detail Author:
Publisher:
ISBN:
Category : Evidence (Law)
Languages : en
Pages :

Book Description
Text and sample testimony to assist in preparing for, and proving facts that may be in issue in, judicial and administrative proceedings.

CliffsNotes TExES Math 4 8 115 and Math 7 12 235

CliffsNotes TExES Math 4 8  115  and Math 7 12  235  PDF Book Detail Author: Sandra Luna McCune
Publisher: Houghton Mifflin Harcourt
ISBN: 0358129966
Category : Study Aids
Languages : en
Pages : 432

Book Description
CliffsNotes TExES Math 4-8 (115) and Math 7-12 (235) is the perfect way to study for Texas’ middle school and high school math teacher certification tests. Becoming a certified middle school math teacher and high school math teacher in Texas means first passing the TExES Math 4-8 (115) teacher certification test for middle school teachers or the TExES Math 7-12 (235) teacher certification test for high school teachers. This professional teacher certification test is required for all teachers who want to teach math in a Texas middle or high school. Covering each test’s six domains and individual competencies with in-depth subject reviews, this test-prep book also includes two model practice tests with answers and explanations for the Math 4-8 and two model practice tests with answers and explanations for the Math 7-12. Answer explanations detail why correct answers are correct, as well as what makes incorrect answer choices incorrect.

Kiplinger s Personal Finance

Kiplinger s Personal Finance PDF Book Detail Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 188

Book Description
The most trustworthy source of information available today on savings and investments, taxes, money management, home ownership and many other personal finance topics.