"In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes th…
"These original essays summarize a decade of fruitful research and curriculum development using the LISP-derived language Logo. They discuss a range of issues in the areas of curriculum, learning, and mathematics, illustrating the ways in which Logo continues to provide a rich learning environment, one that allows pupil autonomy within challenging mathematical settings.Essays in the first secti…
In questo testo si introducono i concetti di base per la modellistica numerica di problemi differenziali alle derivate parziali. Si considerano le classiche equazioni lineari ellittiche, paraboliche ed iperboliche, ma anche altre equazioni, quali quelle di diffusione e trasporto, di Navier-Stokes e le leggi di conservazione; si forniscono inoltre numerosi esempi fisici che stanno alla base di t…
Originally presented as the author's thesis (doctoral--Harvard University, 1985).What are computers in education being used for? In this book, Cynthia Solomon takes a welcome look at the possibilities and issues of learning with and about computers in schools or in any other learning environment.Solomon focuses on the use of computers within the framework of recent innovative theories of learni…
Translation of: Matematica come narrazione : raccontare la matematica."This book introduces readers to the narrative structure of mathematical proofs and why mathematicians communicate that way, drawing examples from classic literature and employing metaphors and imagery"--OCLC-licensed vendor bibliographic record.
Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of…
A description of perturbation-based methods developed in machine learning to augment novel optimization methods with strong statistical guarantees.In nearly all machine learning, decisions must be made given current knowledge. Surprisingly, making what is believed to be the best decision is not always the best strategy, even when learning in a supervised learning setting. An emerging body of wo…
This book is open access under a CC BY 4.0 license. The book presents the Proceedings of the 13th International Congress on Mathematical Education (ICME-13) and is based on the presentations given at the 13th International Congress on Mathematical Education (ICME-13). ICME-13 took place from 24th- 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the …
This valuable resource provides an overview of recent research and strategies in developing and applying modelling to promote practice-based research in STEM education. In doing so, it bridges barriers across academic disciplines by suggesting activities that promote integration of qualitative science concepts with the tools of mathematics and engineering. The volume’s three parts offer a com…
Exploring several of the evolutionary branches of the mathematical notion of genus, this book traces the idea from its prehistory in problems of integration, through algebraic curves and their associated Riemann surfaces, into algebraic surfaces, and finally into higher dimensions. Its importance in analysis, algebraic geometry, number theory and topology is emphasized through many theorems. Al…