Curriculum development in university mathematics: where mathematicians and education collide

Schnappschüsse moderner Mathematik aus 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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Mathematisches Fachgebiet

Analysis

Verbindung zu anderen Gebieten

Überlegungen zur Mathematik

Autor(en)

Christopher Sangwin

Lizenz

DOI (Digital Object Identifier)

10.14760/SNAP-2015-011-EN

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2015-011-sangwin.pdf

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snapshots: overview

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The geometry of fair division
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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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What is Pattern?
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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
Chr istina Frederick, Yunan Yang
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
Francesca Arici, Bram Mesland
Describing distance: from the plane to spectral triples
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Quantum symmetry
Fadoua Balabdaoui, Yulia Kulagina
The Enigma behind the Good–Turing formula
Anna Haensch
Reflections on hyperbolic space
Isaac Goldbring
Ultrafilter methods in combinatorics
Gandalf Lechner
Zopfgruppen, die Yang–Baxter-Gleichung und Unterfaktoren
Baptiste Rognerud
Invitation to quiver representation and Catalan combinatorics
Po-Ling Loh
Searching for structure in complex data: A modern statistical quest
David Kerr
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
Behrend Heeren, Martin Rumpf
Shape space - a paradigm for character animation in computer graphics
Joshua Zahl
Rotating needles, vibrating strings, and Fourier summation
Moritz Weber
Quantum symmetry
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Determinacy versus indeterminacy
Jayadev S. Athreya, David Aulicino
Vertex-to-Self Trajectories on the Platonic Solids
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Random matrix theory: Dyson Brownian motion
Holger Kammeyer, Roman Sauer
From Betti numbers to l2-Betti numbers
Martin J. Gander
Is it possible to predict the far future before the near future is known accurately?
Jan-Bernhard Kordaß
The Interaction of Curvature and Topology
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The Mathematics of Fluids and Solids
Jake Fillman, Tom van den Boom
A surprising connection between quantum mechanics and shallow water waves
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Formation Control and Rigidity Theory
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Expander graphs and where to find them
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Deep Learning and Inverse Problems
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Mixed-dimensional models for real-world applications
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Configuration spaces and braid groups
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Limits of graph sequences
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On Logic, Choices and Games
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Nonlinear Acoustics
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Random permutations
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Counting self-avoiding walks on the hexagonal lattice
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Algebra, matrices, and computers
Jonathan Rosenberg, David Wraith
Positive Scalar Curvature and Applications
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Diophantine equations and why they are hard
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On radial basis functions
Ralf Schiffler
Snake graphs, perfect matchings and continued fractions
Nicolai Baldin
Estimating the volume of a convex body
Liran Rotem
Mixed volumes and mixed integrals
Filippo Santambrogio
A short story on optimal transport and its many applications
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Number theory in quantum computing
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Data assimilation: mathematics for merging models and data
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Geometry behind one of the Painlevé III differential equations
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The codimension
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The mathematics of aquatic locomotion
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Tropical geometry
Alex Barnett
Fast Solvers for Highly Oscillatory Problems
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Topological Complexity, Robotics and Social Choice
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Prony’s method: an old trick for new problems
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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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Mathematics plays a key role in scientific computing
Mauricio Bustamante, Jan-Bernhard Kordaß
Spaces of Riemannian metrics
Shaula Fiorelli Vilmart, Gilles Vilmart
Computing the long term evolution of the solar system with geometric numerical integrators
Justin Solomon
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
Manfred Deistler, Andreas Graef
Fokus-Erkennung bei Epilepsiepatienten mithilfe moderner Verfahren der Zeitreihenanalyse
Robert Altmann, Jan Heiland
Wie steuert man einen Kran?
Anthony T Patera, Karsten Urban
High performance computing on smartphones
Eugenio Giannelli, Jay Taylor
Symmetry and characters of finite groups
Maria Dostert, Stefan Krupp, Jan Hendrick Rolfes
Das Problem der Kugelpackung
Tomasz Szemberg
On the containment problem
Éric Fusy
Random sampling of domino and lozenge tilings
Magnus Egerstedt
Swarming robots
Ulrich Krähmer
From computer algorithms to quantum field theory: an introduction to operads
Juanjo Rué
Domino tilings of the Aztec Diamond
Sebastian Funk
The mystery of sleeping sickness – why does it keep waking up?
Antti Knowles
Quantum diffusion
Amanda Swan, Albert Murtha
Modelling the spread of brain tumours
J. Marron
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Curriculum development in university mathematics: where mathematicians and education collide
Jürg Kramer, Anna-Maria Pippich
Special values of zeta functions and areas of triangles
Victoria Powers
How to choose a winner : the mathematics of social choice
Valentina Kiritchenko, Evgeny Smirnov, Vladlen Timorin
Ideas of Newton-Okounkov bodies
Ben Schweizer
Darcy’s law and groundwater flow modelling
Raluca Eftimie
Modelling communication and movement: from cells to animals and humans
Tom Solomon
Chaos and chaotic fluid mixing
Thorsten Holm
Friezes and tilings
George Willis
Zero-dimensional symmetry
Christine Breiner
Minimizing energy
Diana Davis
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
Howell Tong
Statistics and dynamical phenomena
Brian Harbourne, Thomas Szemberg
Arrangements of lines
Bruce Reznick
What does ">" really mean?
Harald Helfgott
The ternary Goldbach Problem
Wolfgang Lerche
Matrixfaktorisierungen
John E. McCarthy
Dirichlet Series

Mathematisches Fachgebiet

Algebra und Zahlentheorie
Analysis
Didaktik und Bildung
Diskrete Mathematik und Grundlagen
Geometrie und Topologie
Numerik und Wissenschaftliches Rechnen
Wahrscheinlichkeitstheorie und Statistik

Verbindung zu anderen Gebieten

Chemie und Geowissenschaft
Informatik
Ingenieurwissenschaft und Technik
Finanzwesen
Geistes- und Sozialwissenschaft
Biowissenschaft
Physik
Überlegungen zur Mathematik

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