Curriculum development in university mathematics: where mathematicians and education collide

Snapshots of modern mathematics from Oberwolfach

Curriculum development in university mathematics: where mathematicians and education collide

This snapshot looks at educational aspects of the design of curricula in mathematics. In particular, we examine choices textbook authors have made when introducing the concept of the completness of the real numbers. Can significant choices really be made? Do these choices have an effect on how people learn, and, if so, can we understand what they are?

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Mathematical subjects

Analysis

Connections to other fields

Reflections on Mathematics

Author(s)

Christopher Sangwin

License

DOI (Digital Object Identifier)

10.14760/SNAP-2015-011-EN

Download PDF

2015-011-sangwin.pdf

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snapshots: overview

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Algebras and quantum games
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Felder und Räume: Symmetrie und Lokalität in Mathematik und theoretischen Wissenschaften
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The periodic tables of algebraic geometry
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Patterns and waves in theory, experiment, and application
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Closed geodesics on surfaces
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Route planning for bacteria
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Characterizations of intrinsic volumes on convex bodies and convex functions
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A tale of three curves
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Representations and degenerations
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Jewellery from tessellations of hyperbolic space
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The Robinson–Schensted algorithm
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Lagrangian mean curvature flow
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Finite geometries: pure mathematics close to applications
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Quantum symmetry
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Describing distance: from the plane to spectral triples
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The Enigma behind the Good–Turing formula
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Reflections on hyperbolic space
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Ultrafilter methods in combinatorics
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Zopfgruppen, die Yang–Baxter-Gleichung und Unterfaktoren
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Invitation to quiver representation and Catalan combinatorics
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Searching for structure in complex data: A modern statistical quest
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C∗-algebras: structure and classification
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From the dollar game to the Riemann-Roch Theorem
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Higgs bundles without geometry
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Shape space - a paradigm for character animation in computer graphics
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Rotating needles, vibrating strings, and Fourier summation
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Quantum symmetry
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Determinacy versus indeterminacy
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Mixed volumes and mixed integrals
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The mathematics of aquatic locomotion
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Tropical geometry
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Computing with symmetries
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Topological recursion
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Solving quadratic equations in many variables
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Computational Optimal Transport
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A few shades of interpolation
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Molecular quantum dynamics
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Closed geodesics on surfaces and Riemannian manifolds
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Mathematische Modellierung von Krebswachstum
Michael Baake, David Damanik, Uwe Grimm
Aperiodic Order and Spectral Properties
Lukas Pottmeyer
News on quadratic polynomials
Felix Günther
Winkeltreue zahlt sich aus
Jacob Bedrossian
Towards a Mathematical Theory of Turbulence in Fluids
Laurent Bartholdi
Profinite groups
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The adaptive finite element method
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Footballs and donuts in four dimensions
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The Willmore Conjecture
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Prime Tuples in Function Fields
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Polyhedra and commensurability
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High performance computing on smartphones
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Symmetry and characters of finite groups
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Das Problem der Kugelpackung
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Domino tilings of the Aztec Diamond
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Quantum diffusion
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Modelling the spread of brain tumours
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Curriculum development in university mathematics: where mathematicians and education collide
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Special values of zeta functions and areas of triangles
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Tom Solomon
Chaos and chaotic fluid mixing
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Friezes and tilings
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Zero-dimensional symmetry
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Minimizing energy
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Billiards and flat surfaces
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Drugs, herbicides, and numerical simulation
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Operator theory and the singular value decomposition
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The Kadison-Singer problem
Ragnar-Olaf Buchweitz, Eleonore Faber
Swallowtail on the shore
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Statistics and dynamical phenomena
Brian Harbourne, Thomas Szemberg
Arrangements of lines
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What does ">" really mean?
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The ternary Goldbach Problem
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Matrixfaktorisierungen
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Dirichlet Series

Mathematical subjects

Algebra and Number Theory
Analysis
Didactics and Education
Discrete Mathematics and Foundations
Geometry and Topology
Numerics and Scientific Computing
Probability Theory and Statistics

Connections to other fields

Chemistry and Earth Science
Computer Science
Engineering and Technology
Finance
Humanities and Social Sciences
Life Science
Physics
Reflections on Mathematics

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