Undervisning
Jeg underviser i matematik på Niels Brock. Efter at
have afsluttet efterårets kurser har jeg fri indtil
jeg starter 2 nye hold op 20. februar. Nærmere
oplysninger om disse hold kan findes på holdenes
På denne side har jeg samlet diverse materiale som
er mere eller mindre relevant i forhold til
undervisningen. På Niels Brock bruger vi Fronter,
hvor der ligger specifik information til de enkelte hold.
Ud over at undervise forsker jeg også i
informationteori, og er redaktør på det
internationale tidsskrift Entropy.
Endvidere er jeg reviewer for en mængde
tidsskrifter.
Kursushjemmesider
Mere information for de enkelte kurser jeg holder kan
findes på kursernes hjemmeside som løbende
opdateres sålænge kurset varer.
Mat A
Mat B
Statistical
Structure of Quantum Mechanics This graduate cource
was held at the Department of Mathematics, University of
Copenhagen 4/2-22/5 2003.
Probability
Theory assisted by Information Theory This graduate
cource was held at the Department of Mathematics,
University of Copenhagen, Autumn 2003.
Konveksitet
This graduate course was held at the Department of
Mathematics, University of Copenhagen.
Funktioner
af 2 variable og matrixregning Kurset blev holdt
på Copenhagen Business School 2005 mens jeg var
ansat på Matematisk Institut.
Suggested
project for students no. 1
Suggested
project for students no.2
Suggested
project for students no. 3.
Undervisningshæfter
Disse kursusnoter opdaterer jeg løbende.
Kursusmateriale for et givet kursus findes via kursets
hjemmeside.
Logik
Undervisningshæfte på A-niveau. Jeg
planlægger en omskrivning af dette materiale, hvor
konnektiver defineres vha. tabeller med 2 indgange i
stedet for den sædvanlige måde at skrive
sandhedstabeller på.
Produkter
af
vektorer Undervisningshæfte på
A-niveau.
Potens-
Eksponential-
og logaritmefunktioner
Undervisningshæfte på A-niveau.
Potens- Eksponential- og
logaritmefunktioner
Undervisningshæfte på B-niveau.
Spil-
og Beslutningsteori
Undervisningshæfte på A-niveau. Jeg
planlægger en omskrivning, hvor optimale blandede
strategier først beregnes i to-personersspil, som
ikke er nulsumsspil, idet kursisterne
erfarinsmæssigt har svært ved at skifte mellem
at se spillet fra Alices og Bobs side, når kun
Alices payoff-tabel er angivet.
Lecture
notes on the Statistical Structure of Quantum Theory
These lecture notes were used at a graduate course in
information theory and probaiblity theory held at Math.
Dept. Univ. of Copenhagen 2003.
Probability
and Information - Occam's Razor in Action These
lecture notes were used at a graduate course in
information theory and probability theory held at Math.
Dept. Univ. of Copenhagen 2003. The name of the course was
"Probability Theory assisted by Information Theory". Since
the course I have extended it notes into a book draft and
I have discussions with Cambridge Univ. Press to publish
it.
Evalueringer, anbefalinger mv.
Karakterstatistik for mine kurser
på Niels Brock
Evalueringsskemaer
Sammentællinger af evalueringsskemaer for
forskellige af mine hold på Niels Brock.
Udtalelse i forbindelse med
praktisk pædagogikum.
Forprojekt, som jeg lavede
som en del af adjunktpædagogikum.
Anbefaling fra Herlev
Gynmasium.
Anbefaling fra
Aurehøj Gymnasium.
Anbefaling fra
Falkonergården Gymnasium.
How to learn mathematics
Learning mathematics is like exploring a new area. There
are three methods of exploring a new area and the best way
to explore the area is to use all three methods.
Look at a map
In a mathematical education this typically means reading
a textbook. Like a map a textbook should be precise and
comprehensive. One should be able to dig into a detail
and see exactly how the recommended techniques regarding
this detail work. In a mathematical textbook it means
for instance that proofs should be given without any
shortcuts.
Take a guided tour
That means attend a class with a teacher. The teacher
should not try to be complete in the exposition of a
topic but should instead prioritize. The teacher should
be demonstrate devotion to the subject and facilitate a
link between feelings and knowledge. Therefore the
teacher should emphasize feedback on the achievements of
the students.
Explore by your self
The student should explore the topic by their own. Some
exercises should be formulated in an open manner where
the is not only one correct answer. The highest marks
should only be given to students that show their ability
to work with the topic without specific guidance from a
teacher.
I think much math teaching suffers from a bad balance
between these aspects of learning. For instance many
textbooks are not sufficiently detailed so that the
teacher has to fill out details that are missing in the
textbook instead of prioritizing between what can be
found in the textbook. At Danish elementary school it
has become very popular that the pupils should explore
by them selves but exploration often takes a lot of time
so if all too much is left for exploration one does not
get very far. In Danish gymnasium the written exams are
so standardized that one can "easily" get the best marks
without demonstrating any ability to do independent
thinking.
Mathematical notation
I think mathematical notation and terminology is very
important and I think most mathematicians have an all
too dogmatic and conservative view on this topic.
Obviously it is extremely convenient that mathematical
notation is more or less the same all over the world,
but sometimes mathematical notation has got stuck in a
way that makes it unnecessarily difficult to teach or
learn the topic. I wonder how easy math would be if our
language and notation was really "optimized". The basic
mechanism is that the trendsetters are the best or most
famous mathematicians or textbooks. Mathematics is
complicated so most people do not challange the
autorities and just copy the notation and terminology
from the masters.
Links
Ellipse
Lille animation af hvordan man tegner en ellipse og af
nogle af ellipsens egenskaber.
Jeg har også lavet den som video.
LyX-skabelon Jeg har lavet
denne LyX-skabelon i et format egnet til at lave
emneopgaver.
Entropy
Det tidsskrift jeg er redaktør på.
Pyramider
H.C.
Andersens bevis for Pythagoras'
læresætning
Rational trigonometry
Enhver, som underviser i trigonometri, vil have
glæde af at kende disse interessante nye
resultater som Norman Wilderberger har
tilføjet teorien inden for de seneste år.
Han viser, at kvadreret euklidisk afstand
(quadrance som han kalder det) bør spille en mere
aktiv rolle i alle former for trigonometri. Dette er
gode nyheder for alle som forsker i rate distortion
theory eller statistik. Jeg overvejer om jeg skal
oversætte hans bog til dansk.
Tau Manifesto Siden
beskriver fordelene ved at bruge tau som symbol
for 2 π.
Vinkelmåler
Jeg har lavet en vinkelmåler, som måler i
centitørn. Den er vældig praktisk til at
tegne lagkagediagrammer.
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