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DFG Research Center MATHEON Mathematics for key technologies
Modeling, Simulation and Optimization
of Real-World Processes: New Mathematics
for Key Technologies
Volker Mehrmann
Serbian Academy of Science and Art Belgrade, June 2012
DFG Research Center MATHEON
Mathematics for Key Technologies
DFG Research Center MATHEON
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MATHEON Drives Innovation
DFG Research Center MATHEON
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MATHEON and its Institutions
Freie Universität Berlin (FU)
Humboldt-Universität zu Berlin (HU)
Technische Universität Berlin (TU)
Weierstrass Institute for Applied Analysis and Stochastics (WIAS)
Zuse Institute Berlin (ZIB)
DFG Research Center MATHEON
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The MATHEON vision
• Mathematics is one of the keys to key technologies. Its potential
has not yet been brought to bear. The aim of MATHEON is to
profoundly change this situation.
• The development of key technologies is characterized by two
tendencies: while innovation cycles get shorter and shorter their
complexity is getting higher and higher.
• High complexity is best treated by a high degree of abstraction.
The language of abstraction is mathematics.
• But Mathematics is not only a language, it adds value:
Theoretical insight, efficient algorithms, optimal solutions.
DFG Research Center MATHEON
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A: Life Sciences
C: Production
D: Electronic and Photonic Devices
E: Finance
F: Visualization
ZE: Education
B: Networks
Application Areas & Mathematical Fields
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Scientific Structure
DFG Research Center MATHEON
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Our Competence
Scientists of MATHEON
members 230
Project heads 64
DFG-financed researchers 66
PhD students 71
professors 48
current number of projects 55
Most members from applied mathematics!
Date: May 2012
DFG Research Center MATHEON
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Financial Resources
Spent MATHEON funds (in million €) in 2011
(total of 20,3 million €)
Industrial third party
Other third party public
DFG / personnel
DFG / consumables
DFG / central management
Inst. Core Support personnel
Inst. Core Support consum.
DFG Research Center MATHEON
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Quality of a running project
Publications, plenary talks,
etc.
Additional funding
Networking (cooperations, ext./internal)
Visibility / outreach
Relation to applications a/o industry S
cientific
Exce
llence
Key T
ech
nolo
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(Internal) Quality Management: Criteria
DFG Research Center MATHEON
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9 collaborative research centers (DFG)
10 priority program (DFG)
2 research units (DFG)
2 research training groups (DFG)
2 grad. schools: "Berlin Mathematical School“ and "Berlin School of
Regenerative Therapies“
1 int. Max-Planck research college "Comp. Biology and Scientific Comp.”
1 Marie Curie Initial Training Network (EU)
3 ERC Advanced Grants, 2 ERC Starting Grants, 1 Russian Megagrant
PVcomB - Competence Centre Thin-Film- and Nanotechnology for
Photovoltaics Berlin (BMBF)
Numerous other collaboration projects
Cooperation with science and engineering
DFG Research Center MATHEON
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Industry cooperation – examples
BASF, Bayer-Schering, Merck, Sanofi-Aventis, ...
Siemens, IBM, Infineon, Microsoft, NEC, Philips, ...
Deutsche Telekom (T-Systems), E-Plus, ...
DaimlerChrysler, BMW, Volkswagen, Tebis, Bosch, Nippon Steel, ...
Deutsche Bahn, BVG, IVU, Lufthansa, ABB, ADAC, Herlitz, ...
EdF, Open Grid Europe, DREWAG, Vattenfall (VEAG), Ruhrgas, BHP Billiton, ...
AMRO Bank, Bankgesellschaft Berlin, Commerzbank, Deutsche Bank London, IKB, Reuters Financial Software, ...
Numerous small and medium enterprises (SME)
Industrial Cooperation
DFG Research Center MATHEON
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1000shapes GmbH (www.1000shapes.com): statistical shape models
Indeed Visual Concepts (www.amiravis.com): 3D data visualization (Amira), today: Mercury
JCMwave (www.jcmwave.com): Simulation software for nano-optical components
atesio (www.atesio.de): Plan, configure, and optimize telecommunication networks
Löbel, Borndörfer & Weider GbR (www.lbw-berlin.de): Optimization and consulting for public transport
Synoptio (www.synoptio.net): Mathematical consulting and software
Lenné 3D (www.lenne3d.de): Digital botany and real-time landscapes
inbion GmbH (inbion.math.fu-berlin.de): Bioinformatics solutions for life sciences
getLig&tar (www.getlig.com): drug design
molConcept GmbH (www.molconcept.com): molecular design & drug design
Spin-Off Companies
DFG Research Center MATHEON
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A – Life Sciences
DFG Research Center MATHEON
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InnoLab „math for diagnostics“: Proteomics
Aim: Development of novel diagnostic tools for early lung cancer detection based on proteomics fingerprinting Methods: Enhanced noise reduction, peak detection and identification of sensitivity-optimal fingerprints via novel robust filtering and dimension-reduced Bayesian classification techniques
C. Schütte (A19)
DFG Research Center MATHEON
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InnoLab „math for diagnostics“: Angiology
Aim: Development of a non-invasive diagnostic tool for detection of cardiovascular pathologies (e.g. stenoses und aneurisms). Methods: Data acquisition via novel devices for multi-channel measurement; novel Bayesian classification techniques based on cardiovascular system model
C. Schütte (A19)
DFG Research Center MATHEON
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InnoLab „math for diagnostics“: Pharmacokinetics
Aim: Development of new HIV long-term therapies that prevent drug resistance Methods: Compute optimal switching times between different drug combinations to avoid that resistant virus is archived; based on detailed model of virus kinetics and mutation
C. Schütte (A19)
DFG Research Center MATHEON
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IT Companies Device manufacturers
Hospitals Research Groups
InnoLab „math for diagnostics“: Partners
C. Schütte (A19)
DFG Research Center MATHEON
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Toxicological Appraisal of Micropollutants
Example: Prediction of estrogenic affinities & activities in drinking
water
Cooperations with industry:
BMBF: TransRisk
Simulation of binding processes Mathematics: Entropy estimation, to the estrogen receptor affinity, interaction models
M. Weber, V. Durmaz, R. Becker, S. Esslinger, 2009 M. Weber, K. Andrae, 2010 V. Durmaz, M. Weber, R. Becker, 2011
measured affinities
pre
dic
ted a
ffin
itie
s
M. Weber (A19)
DFG Research Center MATHEON
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Mathematical Systems Biology
Development of a mathematical model for the human menstrual cycle
Cooperation Partner: Pfizer R&D, Sandwich, UK Duration: 04/2009 – 09/2011
Publications: S. Röblitz, C. Stötzel, P. Deuflhard, H.M. Jones, D.-O. Azulay, P.H. van der Graaf, S. W. Martin, ZR 11-16, Submitted. T. Dierkes, M. Wade, U. Nowak, S. Röblitz, ZR 11-15
• Modelling • Simulation (integration of stiff ODE/DAE and discrete stochastic systems) • Parameter identification (Gauss-Newton methods for nonlinear problems)
Problem: How does administration of gonadotropin-releasing hormone analoga influence the cycle?
Results: • 33 ODEs, 114 parameters • Prediction of hormone profiles and delay of ovulation • Software BioPARKIN
S. Röblitz (A18)
DFG Research Center MATHEON
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Paradigm of virtual medicine
Real patient
Virtual patient
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DFG Research Center MATHEON
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2D segmentation via 3D
classification of known patient data adaptation of new CT stack
Statistical shape analysis
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DFG Research Center MATHEON
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Orthopedic surgery
Modeling, Simulation and
Planning of Orthopedic Surgery
Optimal design of facial implants Bilevel optimal control problem
Numerical implementation on patient-specific geometry
Efficient Algorithms Adaptive time integration
Domain decomposition + multigrid
Dynamical heterogeneous modeling 3d nonlinear contact mechanics
1d Cosserat rods
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DFG Research Center MATHEON
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Cranio-maxillo facial surgery planning
before operation / after operation / overlay
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DFG Research Center MATHEON
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B - Networks
DFG Research Center MATHEON
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Gas Transport
Challenges in the Optimization of Gas Transport
• Gas transport itself
• Gas network capacity planning
• Gas storage
• Legal deregulation rules of the gas transport market
• Price fluctuations
• Seasonal fluctuations
• Development of required mathematical solution technologies
• .....
M. Grötschel, R. Henrion, T. Koch, W. Römisch (B20)
DFG Research Center MATHEON
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• Modeling: network, flow, prices, weather, ....
• Simulation: network, flow, prices, weather, …
• Optimization: discrete/continuous, mixed-integer, stochastic, non-linear
Gas Transport: Mathematical Challenges
M. Grötschel, R. Henrion, T. Koch, W. Römisch (B20)
DFG Research Center MATHEON
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Gas Transport: Research
since 08/2010: Open Grid Europe (OGE)
M. Grötschel, R. Henrion, T. Koch, W. Römisch (B20)
DFG Research Center MATHEON
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Airline network revenue management
• A stochastic programming model for airline network revenue management
based on passenger scenario trees was developed.
• Passenger scenario trees are generated by employing historical data.
• The optimization model is solved by Lagrangian relaxation based on
dualizing leg capacity limits, bundle subgradient methods for the dual
and a Lagrange heuristics exploiting the small duality gap.
• The approach is applicable to mid-size Origin&Destination networks.
The test instance contained 54 O&D itineraries, 27 legs (airplanes),
time horizon with 23 data collection points, 1.441 nodes of the scenario
tree and, thus, totally 3.473.377 mixed-integer variables
and 2.774.445 constraints.
DFG Research Center MATHEON
27 W. Römisch (B6)
In cooperation with Lufthansa Systems Berlin
DFG Research Center MATHEON
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Siemens MSO
Cooperation with department
Modelling, Simulation and Optimization
Optimal planning of water networks
Placement of roboter in circuit board production
Study request for mathematical optimization
T. Koch (B20)
DFG Research Center MATHEON
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Elevator group performance is crucial in today‘s high-rise office buildings
Elevator vendors introduced destination hall-call systems where each passenger
registers his target is assigned to an floor separately elevator in turn
more information and control opportunities
asked MATHEON to help develop advanced algorithms
Up to 120% more passengers served in the same time, with the same service quality in high-load traffic
Now implemented by
Advanced Elevator Control
M. Grötschel (B14)
DFG Research Center MATHEON
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Integrated bus rotation and crew duty planning
Bus rotation planning = multicommodity flow problem (MFP)
Crew duty scheduling = set partitioning problem (SPP)
Integrated planning = MFP + SPP + coupling
Lagrangean relaxation, bundle method (LP), rapid branching (IP)
7 depots, 4 000 trips, 200 vehicles, 250 duties
BMBF Mathematics in Industry, integrated in ivu.plan suite
uvtdyxDyCxbByAxydxc t
uvd
TT ,,}1,0{,;;;1;min
IS-OPT: Integrated Bus & Crew Scheduling
58
50
Actual IS-Opt
- 13,79 %*
number of duties
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Actual IS-Opt
- 5,88 %*
number of vehicles
R. Borndörfer (B15)
DFG Research Center MATHEON
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Bus + aircraft rotations = multicommodity flows (solvable)
Train rotations = multicommodity hyperflows
Min. # vehicles, s.t. train composition, regularity, maintenance
Train compositions = hyperarcs (new), column generation
NP-hard (not approximable), but good extended formulation
1 week, 500 trips, 20 train types, 3*104 nodes, 5*107 hyperarcs
MATHEON B22 (1*hyperflows) + DB (2*implementation)
VR-OPT: Vehicle Rotation Planning for Railways
uvdxtsvvxdvvxvxxc d
uv
ddT ,}1,0{;,1))((;))(())((;min
R. Borndörfer (B22)
DFG Research Center MATHEON
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Traffic optimization on the Kiel Canal
Connects North Sea and Baltic Sea
280 nautical miles saved compared to the way around Skaw
Canal with highest traffic in the World
R. Möhring (B13, B25)
DFG Research Center MATHEON
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Opposing traffic creates problems
Ships must be scheduled to wait in sidings
Waiting can‘t be too long
New ships arrive online
Combines routing and scheduling
Very hard for MIP models
R. Möhring (B13, B25)
DFG Research Center MATHEON
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Goals of the project
Improve manual planning
Recommendations for canal enlargement (widening, new sidings …)
Automated guidance during construction phase
R. Möhring (B13, B25)
DFG Research Center MATHEON
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Steel Slab logistics
steel slabs arrive from casting
intermediate storage on stacks
further processing or delivery
different orders
transport by cranes or vehicles
scheduling = sorting with stacks
R. Möhring (B24)
DFG Research Center MATHEON
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C - Production
DFG Research Center MATHEON
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Mean-risk optimization of electricity portfolios
DFG Research Center MATHEON
37 W. Römisch (C7)
Operation of a municipal power utility
Free (=parameter-free) shape optimization of air/exhaust flow channels in engines.
• Optimization Goals:
o Uniform outflow at outflow (turbo engine).
...velocity; ...average velocity at inflow.
o Alternatively: Minimization of the total pressure loss.
• Constraints to be considered:
o construction space; inflow (given position + flow profile), position of outflow boundary.
• State system:
o Stationary 3D Navier-Stokes-system with specific lateral boundary conditions.
Shape Optimization in the Automotive Industries
Sketch.
38 DFG Research Center MATHEON
38 M. Hintermüller (C11, 28, 31) in coop. w/ BMW Motoren GmbH and MathTech
Shape Optimization in the Automotive Industries
Reduction of objectives: 5-15% relative to initial configuration (shape from engineering-CAD-CFD-development)
Implemented modules (OpenFoam, STAR-CD CCM+)
Navier-Stokes-System
Adjoint-System
Shape Gradient
Remeshing
Graphic. after 60 iterations.
DFG Research Center MATHEON
39 M. Hintermüller (C11, 28, 31) in coop. w/ BMW Motoren GmbH and MathTech
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Adaptive solution of parametric eigenvalue problems for PDEs
Industrial application Optimization of interior acoustics Fluid-structure interaction Large scale eigenvalue problems (N> ) Problem Most of the CPU-time is spent to solve eigenvalue problems Solutions Application of iterative eigenvalue solvers Use mesh adaptivity to reduce the size while maintain accuracy Balance the modeling, the FE and the iteration error Make use of modern computer architectures
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DFG Research Center MATHEON
40 C. Carstensen (C22)
Typical instance:
• production line
• 4 robots in a work cell
• 50 weld points on a car door
Questions:
• Which points does each robot weld? (task assignment)
• In which order? (sequencing)
• What is the fastest and collision-free trajectory between two points? (path-planning)
At the moment:
Task assignment, sequencing and path-planning for all robots are done by hand.
Automatic reconfiguration of welding cells
DFG Research Center MATHEON
41 D. Hömberg, M. Skutella (C30)
Automatic reconfiguration of welding cells
MATHEON Approach:
Combine discrete and continuous optimization
• Trajectory planning for robots avoiding collisions • Represent robots and obstacles as finite unions of polyhedra • Allows collision detection using linear programming arguments
• Graph representation for each robot: • Nodes: weld points that can be visited • Arcs: paths between two weld points • Each arc has a fixed and predefined travel time
In cooperation with Rücker EKS GmbH, Weingarten
DFG Research Center MATHEON
42 D. Hömberg, M. Skutella (C30)
DFG Research Center MATHEON
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D – Electronic & Photonic Devices
Computational Nano-Lithography
Source mask optimization in computational lithography
Real-time inverse scatterometry
Photomask Aerial image
Optimized process window
Phase grating
Electric field
Correlation of reconstructed parameters
[J. Pomplun et al. SPIE (2010)] [B. Kleemann et al. SPIE (2011)]
DFG Research Center MATHEON
44 F. Schmidt (D23)
Computational Photovoltaics
Challenge: Increase efficiency of industrially produced thin film solar cells from currently < 9% to 13%.
Efficiency enhancement by rough surfaces
DFG Research Center MATHEON
45 F. Schmidt (D23)
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Global photonic programs
US: Harnessing Light II – Photonics for 21st Century Competitiveness
EU: “Strategic Research Agenda – Lighting the way ahead“ (2010)
Germany: Photonik 2020 (2010)
Nano-optical components
Model optical structures with size comparable to wavelength
Exploit nano-scale effects like plasmonic waveguiding and plasmonic resonances
Combine effects to form functional units
Optimize the structures
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Circular grating resonator, cf. biomedical sensing
Optical fields in a thin film solar cell layer
Material-light interaction
Linear and nonlinear interaction
Interaction of electronic and optical properties
Using model hierarchies: classical models, semi classical models, quantum models
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Example Left: Classical model of plasmonic field (wrong) Right: Semi classical hydro- dynamical model (coincides with experiments)
Material-light interaction
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Semiconductor laser devices for optical communication
•Modeling and analysis of nonlinear material–light interaction •Multiscale structure of devices •Complex dynamical behavior
Different dynamical regimes in a mode-locked quantum-dot laser
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Nonlinear Optics: Pulse propagation
Maxwell equations for fields Nonlinear material response for fibers
Controlling Light by Light with an Optical Event Horizon
Physical Review Letters 106, 163901 (2011)
Challenge Controlling light by light in time and frequency
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Nonlinear optics: All-optical transistors
Switching
Weak control pulse
Strong signal pulse
Propagation model
provided by
MATHEON
Fundamental research leads to a novel technological concept!
Statistical optics
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Example: Yablonovitch limit 4n2 in ray optics limit What is the transition to wave optics?
qualitative influence on the
optical field
Statistical properties of sources in space and time
Statistical properties of media in space
DFG Research Center MATHEON
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E - Finance
Trading in Illiquid Markets
Traditional financial market models assume that all trades can be settled at prevailing prices without market impact
Large investors usually move prices in an unfavorable direction
Alternative trading venues allow for a reduction in market impact
Objectives of various projects with Deutsche Bank AG:
• Mathematical models for liquidating large portfolios under market impact
• Optimal display strategies for iceberg orders
• Optimal order routing between primary and alternative trading venues (crossing networks, dark pools)
• Reduced form models of limit order books
• ...
DFG Research Center MATHEON
54 U. Horst (E2)
General Financial Modeling Framework
Option Pricing
Valuation of Risk
Modeling Calibration
Interest Rate Market Stock Market
DFG Research Center MATHEON
55 J. Schoenmakers (E5)
Topics in Interest Rate Modeling
• Stochastic differential equations → LIBOR Interest rate modeling
• Numerics for stochastic optimal control → Pricing Products
• Inverse problems → Calibration
DFG Research Center MATHEON
56 J. Schoenmakers (E5)
DFG Research Center MATHEON
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F - Visualization
Algorithmic developments
Statistical models of anatomical shape variability
Model-based auto-segmentation of 3D medical images
3D geometry reconstruction from 2D X-ray images
Optimal shape design in implant/transplant surgery
Industry collaborations
Visage Imaging GmbH / Visualization Sciences Group SAS visualization systems (80k-150k EUR p.a. since 2005)
Implant Manufacturer (undisclosed) CT data segmentation (180k EUR)
Spin-Off 1000shapes GmbH statistical shape modeling and applications
Atlas-based 3D Image Segmentation
DFG Research Center MATHEON
58 H.-C. Hege (F2)
www.dzlm.de
German Center for Mathematics Teacher Education
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Integral View
Teac
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uca
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Co
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Doctoral Studies / BMS Phase II
Studies of Mathematics / BMS Phase I
Secondary School / Berlin Network Schools
Primary School / Profiled Classes in Grades 5/6
Te
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Trai
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Integral View
Te
ach
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Trai
nin
g
Teac
he
r Ed
uca
tio
n /
Co
op
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tio
n
Doctoral Studies / BMS Phase II
Studies of Mathematics / BMS Phase I
Secondary School / Berlin Network Schools
Primary School / Profiled Classes in Grades 5/6
Dezember 2010 April 2011
Initiative of founding a German Center for Mathematics Teacher Education (DZLM) by Deutsche Telekom Stiftung All German universities are invited to submit their concepts for the establishing of a DZLM
July 2011 Success for the concept of the Berlin/NRW-consortium headed by HU Berlin jointly with two other Berlin and three NRW universities
September 2011 Start of the work by the DZLM
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Chronology
Goals
Foundation of the DZLM with the following objectives:
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Development of comprehensive training programs for mathematics educators
In particular, training programs to educate mentor teachers as well as out-of-field teachers
Establishment of nationwide mentor teacher master degree programs
Example of a successful acting center for teacher education in Germany
Concept
Ongoing professionalization of teachers with regard to:
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Mathematics at the interface of content and pedagogical content knowledge
Competence-orientation in mathematics education
Mathematical teaching and learning processes
Educational research
Implementation
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1. Master degree programs for mentor teachers
2. Qualification programs for out-of-field teachers and educators
3. In-service teacher training for all teachers
4. Information and communication platform
Attracting the next generation researchers
Digital „Adventskalender“
(> 12700 participants in 2011)
MATHEatlON 2009, 2010, 2011
„Mathe klingt gut“, 2009
MathFilm-Festival 2008 (> 20 000 DVD’s to schools in Germany)
Year of Mathematics 2008
Rent-the-Center platform
MathInside – Math is everywhere
Highlights
Fotos: Kay Herschelmann
DFG Research Center MATHEON
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DFG Research Center MATHEON 67
Participation in (international) High School Competitions
First-Lego-League-Competition 2011
• Since 2011 in cooperation with ESA • Two MATHEON Network Schools: Käthe-Kollwitz-Oberschule & Heinrich-Hertz-Gymnasium • Three MATHEON-Teams in ISS-Finals on 23.01.2012
Thank you for your attention