Technical Reports

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2018

Handbook of the Mathematics of the Arts and Sciences

Bharath Sriraman, University of Montana- Missoula

Abstract: This Handbook aims to become a definitive source with chapters that show the origins, unification, and points of similarity between different disciplines and mathematics. The seven sections in this book explore: Mathematics and Architecture; Mathematics, Biology and Dynamical Systems; Mathematics, Humanities and the Language Arts; Mathematics, Art and Aesthetics; Mathematics, History and Philosophy; Mathematics in Society; and New Directions. Science and Art are used as umbrella terms to encompass the physical, natural and geological sciences, as well as the visual and performing arts.

Keywords: Mathematics and Architecture; Mathematics and Dynamical Systems; Mathematics and Humanities; Mathematics, Art and Aesthetics; Mathematics, History and Philosophy

AMS Subject Classification: 00

Pdf of Table of Contents as of 01/01/2018. Springer Major Reference Works

On Measures of Measurement and Mismeasurement: A commentary on Planning and Assessment

Bharath Sriraman, University of Montana - Missoula

Abstract: In this commentary the six Canadian chapters on planning and assessment in mathematics are critiqued. Some common strands are discussed on what entails a measurable item in mathematics assessments at the secondary school level. Implications are made for teachers.

Keywords: Learning; Teaching; Mathematical Memory; Testing; Rubrics; Assessment

AMS Subject Classification: 097D60

Preprint of Commentary for "Teaching and Learning Secondary School Mathematics: Canadian Perspectives in an International Context", Springer Berlin.

Reconciling the Realist/Anti Realist Dichotomy in the Philosophy of Mathematics

Bharath Sriraman
University of Montana
Per Haavold
University of Tromso, Norway

Abstract:

In the philosophy of mathematics, the realist vs. anti-realist debate continues today with differing positions on the status of mathematical objects. For realists, objects sit in “Plato’s heaven”, immovable, objective, eternal, and we contemplate them, whereas anti-realists (or Constructionists) are the opposite, and emphasize epistemology over ontology, saying that we construct mathematical objects. There are numerous results in mathematics which can be arrived at both from a realist and an anti-realist viewpoint. In other words, they can be contemplated (proved) via methods deemed unsuitable by anti-realists- or simply arrived at it through methods (or construction) as the anti-realist would say. In this chapter, we argue that realism and anti-realism can be seen as two sides of the same coin, or different ways of knowing the same thing, and therefore the so called dichotomy between these positions is reconcilable for particular mathematical objects.

Keywords: Intuitionism - Constructionism - Realism - Platonism - Anti-realism - Brouwer - Constructive mathematics - Philosophy of mathematics

AMS Subject Classification: 03A, 03F

Uncorrected proofs of chapter to appear in "The Map and the Territory": The Frontiers Collection, Springer International Publishing