Bücher der Reihe Mathematics in Mind

This volume examines mathematics as a product of the human mind and analyzes the language of "pure mathematics" from various advanced-level sources.

This is an anthology of contemporary studies from various disciplinary perspectives written by some of the world's most renowned experts in each of the areas of mathematics, neuroscience, psychology, linguistics, semiotics, education, and more. Its purpose is not to add merely to the accumulation of studies, but to show that math cognition is best approached from various disciplinary angles, with the goal of broadening the general understanding of mathematical cognition through the different theoretical threads that can be woven into an overall understanding.This volume will be of interest to mathematicians, cognitive scientists, educators of mathematics, philosophers of mathematics, semioticians, psychologists, linguists, anthropologists, and all other kinds of scholars who are interested in the nature, origin, and development of mathematical cognition.

This volume examines mathematics as a product of the human mind and analyzes the language of "pure mathematics" from various advanced-level sources.

This book examines the critical roles and effects of mathematics education. The exposition draws from the author's forty-year mathematics career, integrating his research in the psychology of mathematical thinking into an overview of the true definition of math.

This book uncovers mathematical structures underlying natural intelligence and applies category theory as a modeling language for understanding human cognition, giving readers new insights into the nature of human thought.

This book brings together ideas from experts in cognitive science, mathematics, and mathematics education to discuss these issues and to present research on how mathematics and its learning and teaching are evolving in the Information Age.

This book is about the relationship between necessary reasoning and visual experience in Charles S. Peirce¿s mathematical philosophy. It presents mathematics as a science that presupposes a special imaginative connection between our responsiveness to reasons and our most fundamental perceptual intuitions about space and time. Central to this view on the nature of mathematics is Peirce¿s idea of diagrammatic reasoning. In practicing this kind of reasoning, one treats diagrams not simply as external auxiliary tools, but rather as immediate visualizations of the very process of the reasoning itself. Thus conceived, one's capacity to diagram their thought reveals a set of characteristics common to ordinary language, visual perception, and necessary mathematical reasoning. The book offers an original synthetic approach that allows tracing the roots of Peirce¿s conception of a diagram in certain patterns of interrelation between his semiotics, his pragmaticist philosophy, his logical andmathematical ideas, bits and pieces of his biography, his personal intellectual predispositions, and his scientific practice as an applied mathematician.

This book examines the correspondence between international relations (IR) theories of structural realism and constructivism and paintings, notably the artwork of Mark Rothko and Jackson Pollock, in a game theory setting. This interdisciplinary approach, through the lens of game theory and semiotics, permits different, enriched interpretations of structural realism and constructivism. These theories constitute an axis of debate between social and systemic approaches to international politics, as well as an axis of differentiation between scientific realism and positivism as philosophies of science. As such, the interpretations explored in this book contribute to what we know about international relations, how semiotics intersect with strategic uncertainty, and explains these interactions in the proposed games model.The book¿s use of game theory and semiotics generate ¿visual semiotic games¿ (VSGs) that shed light on the debate axes through strategic uncertainty, interactions,and players¿ interactive belief systems. VSGs will contribute to literature on experimental semiotics in the sense of players¿ coordination behavior, beliefs, and artistic evaluations. The equilibria, interpreted through branches of philosophy of mind and theories of explanation, will reveal possibilities of agreement among players about which artwork representing the theory at hand is the best, opening innovative research perspectives for the discipline of IR theory.