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Modelling and Mathematics

TEDxINSA talk, Thursday May 7th 2015, Porto DrIVE-MATH Nov 27th, 2017
by

Christian Mercat

on 21 April 2018

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Transcript of Modelling and Mathematics



1. Posing the right questions
2. Real world → math formulation
3. Computation
4. Back to reality, verification
Christian Mercat
IREM de Lyon

nstitut
de
echerche
sur l'
nseignement
des
athématiques
Université Claude Bernard
1
Association des Professeurs de Mathématiques de l'Ens. Public
Institut Camille Jordan
ESPÉ
cole
up
érieure
rofessorat
ducation
du
et de l'
Modelling and Mathematics
Lady of Shalott
Cédric Villani
© Yann Pineill & Nicolas Lefaucheux
© Cédric Villani
≈≈
≈≈
≈≈
≈≈
≈≈
≈≈
≈≈
≈≈
Temple Grandin
mc
Squared
Idea
Business
Business
model
What are you dealing with?

What is the universe?

What are the relationships?
Identify
Define
Connect
novel character by Alfred Lord Tennyson
William Maw Egley
Vito Volterra
Validate
X
X
Albert Einstein
Werner Heisenberg
Uncertainty of the individual replaced by certainty of probabilities
Albert
Bernard
Cheryl
knows the month
knows the day
I don't know when
Cheryl's birthday is,
but I know that Bernard
does not know too.
At first I don't know
when Cheryl's birthday
is, but I know now!
Then I
also
know!
Occam's razor
Horst.Burkhardt - Waldir - wikimedia CC BY SA
mc
Squared
What is math?
http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers
math >> computation
> ≠ =
>
Lateral Thinking
*
parasitic vs symbiotic relationships
birth rate
environment
ecology
Iterate
Tip!
If you don't use it, please don't mention it...
make genuine choices that matter
Nobody likes to be wrong. There is not a unique model for a situation.
Abstraction is not the problem, reality is messy, simplifying it means making choices.
Create a world for your situation, give names to your creation.
What are the rules in your game? How do we get around your world?
Maths of XXI: graph, algorithmic, fuzzy logic, information
complexity, control
mining, game theory
probability, decisions
logistic, optimisation
preparation
incubation
translation
verification
Ilummination
Preparation
Incubation
Ilummination
Translation
Verification
Preparation
Incubation
Ilummination
translation
verificatión
Divergent
Convergent
Henri de Toulouse-Lautrec, Au lit (huile sur carton, 1892, Musée d'Orsay, Paris)
publication
reflexion
Action, formulation, validation
Changes in the
milieu
http://bit.ly/GeogebraBookOpArt
http://bit.ly/StrasbourgIREM2016
Heads or Tails
Odd
Equal!
Side
Diagonal
Diagonal
Side
Unique
Perseverance
Tolerance
Csíkszentmihályi, Liljedahl
Motivation
https://www.researchgate.net/publication/317784785_Creativity_and_Technology_in_Mathematics_From_Story_Telling_to_Algorithmic_with_Op%27Art
Art
http://bit.ly/dernierclic
http://bit.ly/magie1-31
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