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Science, Seti, and Mathematics by Carl L. DeVito Pdf
Mathematics is as much a part of our humanity as music and art. And it is our mathematics that might be understandable, even familiar, to a distant race and might provide the basis for mutual communication. This book discusses, in a conversational way, the role of mathematics in the search for extraterrestrial intelligence. The author explores the science behind that search, its history, and the many questions associated with it, including those regarding the nature of language and the philosophical/psychological motivation behind this search.
Mathematics and the Natural Sciences by Francis Bailly,Giuseppe Longo Pdf
This book identifies the organizing concepts of physical and biological phenomena by an analysis of the foundations of mathematics and physics. Our aim is to propose a dialog between different conceptual universes and thus to provide a unification of phenomena. The role of “order” and symmetries in the foundations of mathematics is linked to the main invariants and principles, among them the geodesic principle (a consequence of symmetries), which govern and confer unity to various physical theories. Moreover, an attempt is made to understand causal structures, a central element of physical intelligibility, in terms of both symmetries and symmetry breakings. A distinction between the principles of (conceptual) construction and of proofs, both in physics and in mathematics, guides most of the work. The importance of mathematical tools is also highlighted to clarify differences in the models for physics and biology that are proposed by continuous and discrete mathematics, such as computational simulations. Since biology is particularly complex and not as well understood at a theoretical level, we propose a “unification by concepts” which in any case should precede mathematization. This constitutes an outline for unification also based on highlighting conceptual differences, complex points of passage and technical irreducibilities of one field to another. Indeed, we suppose here a very common monist point of view, namely the view that living objects are “big bags of molecules”. The main question though is to understand which “theory” can help better understand these bags of molecules. They are, indeed, rather “singular”, from the physical point of view. Technically, we express this singularity through the concept of “extended criticality”, which provides a logical extension of the critical transitions that are known in physics. The presentation is mostly kept at an informal and conceptual level. Contents:Mathematical Concepts and Physical ObjectsIncompleteness and Indetermination in Mathematics and PhysicsSpace and Time from Physics to BiologyInvariances, Symmetries, and Symmetry BreakingsCauses and Symmetries: The Continuum and the Discrete in Mathematical ModelingExtended Criticality: The Physical Singularity of Life PhenomenaRandomness and Determination in the Interplay between the Continuum and the DiscreteConclusion: Unification and Separation of Theories, or the Importance of Negative Results Readership: Graduate students and professionals in the fields of natural sciences, biology, computer science, mathematics, and physics. Keywords:Foundations of Mathematics and of Physics;Epistemology;Theoretical BiologyKey Features:This book is an epistemological reflection carried out by two working scientists, a physicist and a mathematician, who focus on biology. They first address a comparative analysis of the founding principles of their own disciplines. On the grounds of a three-fold blend, they then introduce a unique proposal, which does not passively transfer the paradigms of the first two theoretically well-established disciplines, to suggest a novel theoretical framework for the third discipline
The Palgrave Handbook of Literature and Mathematics by Robert Tubbs,Alice Jenkins,Nina Engelhardt Pdf
This handbook features essays written by both literary scholars and mathematicians that examine multiple facets of the connections between literature and mathematics. These connections range from mathematics and poetic meter to mathematics and modernism to mathematics as literature. Some chapters focus on a single author, such as mathematics and Ezra Pound, Gertrude Stein, or Charles Dickens, while others consider a mathematical topic common to two or more authors, such as squaring the circle, chaos theory, Newton’s calculus, or stochastic processes. With appeal for scholars and students in literature, mathematics, cultural history, and history of mathematics, this important volume aims to introduce the range, fertility, and complexity of the connections between mathematics, literature, and literary theory. Chapter 1 is available open access under a Creative Commons Attribution 4.0 International License via [link.springer.com|http://link.springer.com/].
Responsive Teaching in Science and Mathematics by Amy D. Robertson,Rachel Scherr,David Hammer Pdf
Answering calls in recent reform documents to shape instruction in response to students’ ideas while integrating key concepts and scientific and/or mathematical practices, this text presents the concept of responsive teaching, synthesizes existing research, and examines implications for both research and teaching. Case studies across the curriculum from elementary school through adult education illustrate the variety of forms this approach to instruction and learning can take, what is common among them, and how teachers and students experience it. The cases include intellectual products of students’ work in responsive classrooms and address assessment methods and issues. Many of the cases are supplemented with online resources (http://www.studentsthinking.org/rtsm) including classroom video and extensive transcripts, providing readers with additional opportunities to immerse themselves in responsive classrooms and to see for themselves what these environments look and feel like.
Using the Mathematics Literature by Kristine K. Fowler Pdf
This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.
The Sibley Guide to Bird Life & Behavior by David Allen Sibley Pdf
Provides basic information about the biology, life cycles, and behavior of birds, along with brief profiles of each of the eighty bird families in North America.
Use of Mathematical Literature by A.R. Dorling Pdf
Use of Mathematical Literature discusses the bibliographic concerns of mathematical literature. The book is comprised of 14 chapters that cover characteristics of mathematical literature and provide reviews of some of the major literature in various mathematical fields. The text first discusses the role of the literature in mathematics, and then proceeds to tackling major organizations, journals, and reference materials. Next, the book provides critical accounts of the major literature in various mathematical fields, such as combinatorics, topology, and mathematical programming. The book will be of great use to students, practitioners, and researchers of mathematics. Other profession handling math literature, such as teachers, librarians, and translators will also find this book invaluable.
"Sciencia" gathers together six individual volumes spanning the realms of mathematics, physics, chemistry, biology, evolution, and astronomy. Lavishly illustrated with engravings, woodcuts, and original drawings and diagrams, it inspires readers of all ages to take an interest in the interconnected knowledge of the modern sciences.
The Education of T.C. MITS by Lillian R. Lieber Pdf
Whether you are stumped by the "commutative law" in algebra or a whiz at multiplying three-digit numbers in your head, this book opens the door to the wonders of mathematical imagining. By using simple language and intriguing illustrations drawn by her husband, Hugh, Lillian Lieber presents subtle mathematical concepts in an easy-to-understand way. Over sixty years after its release, this whimsical exploration of how to think in a mathematical mood will continue to delight math-lovers of all ages. Barry Mazur's new introduction is a tribute to the Liebers' influence on generations of mathematicians.
Empowering Science and Mathematics Education in Urban Schools by Edna Tan,Angela Calabrese Barton,Maura Varley Gutiérrez,Erin Turner Pdf
Argues that teachers and schools should create hybrid third spaces--neither classroom nor home--in which underserved students can merge their personal worlds with those of math and science.
The P-NP problem is the most important open problem in computer science, if not all of mathematics. Simply stated, it asks whether every problem whose solution can be quickly checked by computer can also be quickly solved by computer. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. Lance Fortnow traces the history and development of P-NP, giving examples from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of this compelling problem.
Exploring Mathematics and Science Teachers' Knowledge by Hamsa Venkat,Marissa Rollnick,John Loughran,Mike Askew Pdf
Globally, mathematics and science education faces three crucial challenges: an increasing need for mathematics and science graduates; a declining enrolment of school graduates into university studies in these disciplines; and the varying quality of school teaching in these areas. Alongside these challenges, internationally more and more non-specialists are teaching mathematics and science at both primary and secondary levels, and research evidence has revealed how gaps and limitations in teachers’ content understandings can lead to classroom practices that present barriers to students’ learning. This book addresses these issues by investigating how teachers’ content knowledge interacts with their pedagogies across diverse contexts and perspectives. This knowledge-practice nexus is examined across mathematics and science teaching, traversing schooling phases and countries, with an emphasis on contexts of disadvantage. These features push the boundaries of research into teachers’ content knowledge. The book’s combination of mathematics and science enriches each discipline for the reader, and contributes to our understandings of student attainment by examining the nature of specialised content knowledge needed for competent teaching within and across the two domains. Exploring Mathematics and Science Teachers’ Knowledge will be key reading for researchers, doctoral students and postgraduates with a focus on Mathematics, Science and teacher knowledge research.
