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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Cutoff phenomenon: Surprising behaviour in card shuffling and other Markov chains
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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
Kathrin Hellmuth, Christian Klingenberg
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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Biological Shape Analysis with Geometric Statistics and Learning
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Representations and degenerations
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Solving inverse problems with Bayes’ theorem
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Jewellery from tessellations of hyperbolic space
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Seeing through rock with help from optimal transport
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Searching for the Monster in the Trees
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The Robinson–Schensted algorithm
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Emergence in biology and social sciences
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Lagrangian mean curvature flow
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Finite geometries: pure mathematics close to applications
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Describing distance: from the plane to spectral triples
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Quantum symmetry
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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
Baptiste Rognerud
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
Sara Lamboglia, Martin Ulirsch
From the dollar game to the Riemann-Roch Theorem
Steven Rayan, Laura P. Schaposnik
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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Vertex-to-Self Trajectories on the Platonic Solids
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Random matrix theory: Dyson Brownian motion
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The Interaction of Curvature and Topology
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Mixed volumes and mixed integrals
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Geometry behind one of the Painlevé III differential equations
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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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The Algebraic Statistics of an Oberwolfach Workshop
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Solving quadratic equations in many variables
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Spaces of Riemannian metrics
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Computing the long term evolution of the solar system with geometric numerical integrators
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Computational Optimal Transport
Justyna Szpond
A few shades of interpolation
George Hagedorn, Caroline Lasser
Molecular quantum dynamics
Marco Radeschi
Closed geodesics on surfaces and Riemannian manifolds
Christian Engwer, Markus Knappitsch
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
Dietmar Gallistl
The adaptive finite element method
Steven Klee
Footballs and donuts in four dimensions
Nikolai Nowaczyk
The Willmore Conjecture
Lior Bary-Soroker
Prime Tuples in Function Fields
Rafael Guglielmetti, Matthieu Jacquemet
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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On the containment problem
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Swarming robots
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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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Ideas of Newton-Okounkov bodies
Ben Schweizer
Darcy’s law and groundwater flow modelling
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Tom Solomon
Chaos and chaotic fluid mixing
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Friezes and tilings
George Willis
Zero-dimensional symmetry
Christine Breiner
Minimizing energy
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Billiards and flat surfaces
Peter Benner, Hermann Mena, René Schneider
Drugs, herbicides, and numerical simulation
Gregory Knese
Operator theory and the singular value decomposition
Alain Valette
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
Wolfgang Lerche
Matrixfaktorisierungen
John E. McCarthy
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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