Knowledge Management Research Group
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Research Areas
The Mathematical Explainatorium
Learning Object Repository
Algebra
Business Algebra
The Universal Production Process
Injecting Learning Loops
User Modeling
Customer Modeling
Experience Transfer
Replication
Product Readiness
The EE(S+O+C)(M+O+P) Model
The Ericsson AXE10 Delay
Corporate Training
Bob’s Mail Order
Innovation Hubs
The Opportunistic Collaboration Agency
Ethical E-Commerce
Clifford Algebra
Combinatorial Clifford Algebra
Blades in Clifford Algebra
Geometric Algebra
Geometric Numbers in the Line and the Plane
Complex Numbers
Trigonometry
Geometric Numbers in Euclidean 3D-space
Quaternions
Geometriska Tal i den Euklidiska 3D-rymden
Blades in Geometric Algebra
The Evolution of Geometric Arithmetic
The Vector Algebra War
Historical Remarks
History and Properties of Geometric Algebra
Linear Algebra
Vector spaces
Linear dependence and linear independence
Basis for a vector space
Representation and Reconstruction
Change of basis for a vector space
Normed vector spaces
Topological vector spaces
Linear Transformations
Representation and Reconstruction
A Linear Space Probe
The Rank-Nullity theorem
Shift of Basis
Determinants
Eigenvalues and Eigenvectors
Diagonalization of Quadrics
Singular Values Decomposition
Vector spaces of finite and infinite dimensions
The Least Squares Method
The Pseudoinverse
Matrix Algebra
Matrices and Gaussian Elimination
Solution of m equations in n unknowns
Knowledge Algebra
The Universal Knowledge Evolution Process
ForeSight and HindSight Process Manager
Knowlecules
Knowledge Tentacles
The Relational Chain Rule
Activities and Participators
Discourse Algebra
Stories
Traps
The Universal Discourse
Cohomology
Abductive Pseudoinverse
Social Algebra
Socially Responsible Algebra
Some basic algebraic concepts
Relations
Group, Ring, Field, Module, Vector Space
Rings of Polynomials
Shift of Basis
Calculus
Calculus of One Complex Variable
Complex Derivative
Complex trigonometry
Conformal Mapping
Inversion
Möbius Transformations
Steiner Circles
Stereographic Projection
The Mercator projection
The Riemann Zeta Function
Laplace transformation
Calculus of One Real Variable
Basic properties of functions
Continuity
Convergence
Differentiation and Affine Approximation
Differentiable versus Fractal Curves
Limits
Big-Ordo and Little-ordo notation
The Chain Rule (in One Real Variable)
The natural exponential function
Taylor Expansion in One Real Variable
Riemann Integration in One Real Variable
Substitution in integrals
The Fundamental Theorem of Calculus
Sequences and series
Fourier Series
Fourier transform
Exact differential forms
Ordinary Differential Equations
Calculus of Several Real Variables
Functions of Several Real Variables
Functions with special properties
Continuous Functions
Partial and Directional Derivatives
Differentiation and Affine Approximation
Gradients
The Chain Rule (in Several Real Variables)
Taylor Expansion in Several Real Variables
Riemann Integration in Several Real Variables
Substitution in integrals
Separating the variables
Integration examples
Different Coordinate Systems
Partial Differential Equations
Differentials
Vector Analysis
Vektoranalys
Social Calculus
The Relational Chain Rule
Category Theory
A Categorical Manifesto
Categorical Informatics
Functors
Limits and Colimits
Functor Categories
Category of Bundles (over a Base Space)
Naturally Related Functors and Processes
Adjoint Functors
Institution Theory
The Human Category
Algebraic Thought
Semantic Meta-networks
Infinity Categories
Geometry
Differential Geometry
From Macro to Micro via Differentiation
From Micro to Macro via Integration
Gaussian Curvature
Theorema Egregium
Geodesic Curves
The Embedding is given by The Second Fundamental Form
The Weingarten Map
The Metric is given by The First Fundamental Form
Isometric Deformations
Minding Isometries
Lie’s Sphere Geometry
Line Geometry
Metric Geometry
Euclidean Geometry
Geometric Shapes
Plane Curves
Conics
Evolutes and Involutes
Parallel Curves
Caustics
Cycloids and Trochoids
Inverse Curves
Pedal Curves
Radials
Cissoids
Conchoids
Strophoids
Curves of constant width
The Catenary
The Tractrix
The Brachistochrone
The Tautochrone
Logarithmic Spirals
Surfaces
Canal Surfaces
Dupin Cyclides
Generalized Cylinders
Isometric Deformations
Quadric Surfaces
Confocal Quadrics
Diagonalizing Quadrics
Ruled Surfaces
Developable Surfaces
Pseudospherical Surfaces
Minimal Surfaces
Catenoids
Helicoids
The Klein Bottle
The Moebius Strip
Triangles, Quadrilaterals and Circles
Geometrical Optics
Focal Surfaces
Optical Properties of Conics
Optical Properties of Quadrics
Solar Simulator
The Double-Cylindrical Point Focus
The Golden Section
The lines in the plane and the points on the line at infinity
Linjer i planet och plan i rymden
Non-Euclidean Geometry
Hyperbolic Geometry
The Beltrami-Klein model
The Riemann-Poincaré model
Elliptic Geometry
Inversive Geometry
Affine Geometry
Projective Geometry
Projective Metrics
The Euclidean Degeneration
MathTrek Voyager
The Development of Geometric Methods during the 19th century
Topology
Formula Repository
Physics and its Models
Science, Order and Creativity
Physics: The Pioneer Science
Ideas of Space and Place
Mathematical and Physical Geometry
New Foundations For Classical Mechanics
Origins of Geometric Algebra
Developments in Geometric Algebra
Mechanics of a Single Particle
Central Forces and Two-Particle Systems
Molten-Salt Thorium Nuclear Reactors
The Rise and Fall of Structuralism
Mathematical Art Gallery
First Class Mathematics
Expandable Learning Objects
Music
Pythagorean Intervals
The Logarithmic Piano
Solfege: an Abstract Key System
Chord Ladder
Chord-Set Inclusion-Graph
Tunes by Artists
Harmony and Melody
Instantiations of Solfege in Different Keys
Abstract and Concrete Chord Circles
Transposition = Shift of Base in Music
Interactions of Quarts and Quints
Generating the Quint Circle from the Mathematical Cogwheels
Uniformisation of Intervals
Rhythm
Bengt Ulin om Musik
Numbers
Representation and Reconstruction
Shift of Base
Art
Arcimboldo
Oscar Reutersvärd
M. C. Escher
Surrealism
Shift of Basis in Art
Conformal Face Mapping
Expandable Stories
Einstein for Flatlanders
Tesseracts for Flatlanders
Einstein for Linelanders
The Linear War
Shift of Bases for Stories
Homotopy
Interactive Learning Objects
Arithmetical Crossfire
Arrow Board
Mathematical Cogwheels
Numbers and their Digits in different Bases
Primes Factory
Mathematical Hikes
Exploring and Explaining
Math Makers and Math Fakers
Math Book Reviews
Siffrorna i våra liv
Förändringskalkyl
Osäkerhetskalkyl
From Graph Theory to Category Theory
Abstraktioner och Tillämpningar
Kommentarer och Utvikningar
What is Mathematics?
Mathematics is Representation
What is a Mathematician?
What does it feel like to do Mathematics?
What is the difference between Mathematics and Science?
The historical struggle to get rid of meaning
The Impossibility of Teaching Mathematics
Some patterns underlying traditional math education
Mathematical Courtesy
The Legendary Lusitania
Mathematical Concepts
Binary relations
Equivalence
Disambiguation
Disambiguating equality
Disambiguating minus
Disambiguating plus
Functions
Continuity
Fourier Series
Fourier Transforms
Space
Time
Laurent Expansion of Time
Products
Inner Products
Outer Products
Geometric Product
Quotients
Topos
Entropy
Shannon Entropy
InformationsEntropi
Historic Entropy
BioEntropy
Evolutionary Entropy
Semiotic Entropy
The Decadence of Work
The Entropy Law and the Economic Process
Promethean Technologies
The Economic Partial Process
Homology and Cohomology
Homotopy
Duality
Topology
Uncertainty
Dimension
Vedic Mathematics
MathTrek
MathTrek Enterprise
Math Bandages
The Difficultification Industry
New Paradigms and Tools for Math Education
Reawakening Interest
Knowledge Management
Modeling and Mapping
Social Modeling for Social Mediation
Systems Modeling
Shifting the Burden
Eroding Goals
Creative Tension
Prostitution
Defensive Routines
Workload-Stress-Alcohol
Shifting the Burden to the Intervenor
Personel Performance Problems
Shifting the Burden to Science and Technology
Limits to Growth
Losing the Vision
From Engineers to Managers
Growth and Underinvestment
Tragedy of the Commons
Fixes that Fail
Militarism-Terrorism
Escalation
Success to the Sucsessful
Global Food Production
Political Modeling
Att skapa ansvarsfrihet genom att skylla på andra
Från allmän välfärd till värdebaserad vård
From Emotional Opiniocracy to Reasonable Visionocracy
Sveriges Afrikanska Krig
Swedish Migration Policy
The Middle East
The Small-Mart Revolution
The nEUrotic economy: finance without resistance
The Big Switch
Creating lack of liability by blaming others
Provocative Modeling
Feeding the Greed
Penetrating the Glass Ceiling
Permission to Steal
The Corporation
The Stock Market
Large Bureaucracies
Gender Tranformations
Modeling Learning
The Learn-Err Model
The Learning Organization
The Wheel of Learning
Theory U
Deliberate Practice
Knowledge Mapping
Knowledge Gap Mapping
Pulling back the Known into the Unknown
Represent –> Deduce –> Interpret
Metadata Modeling
The Evolving Metadata Ecology
Modeling Change
Conceptual Modeling
Knowledge Negotiations
Knowledge Manifolds
Conceptual Browsing
Disagreement Management
Collectigence
Common Sense
Climate change
Humanity Inc.: from Corporation to Cooperation
SECI-ASR
The Corruption of Capitalism
The Humanisation of Globalisation
The New Class War
Moral Capitalism
The System: Who Rigged It? How We Fix It
The New Corporation
The Tyranny of Merit
Consequences of Capitalism
Technology Enhanced Learning
E-learning Frameworks and Semantic Web Technologies
Component-Based Learning Technologies
Semantic Interoperability
Asynchronous Public Service
CHARGE
MATCH
Framtidens Bibliotek
Virtual Campuses
Presence Production
Site Overview
Copyable direct links
Projects
International Projects
European Projects
TELL ME
Abstract Service Interfaces
Opening Up the TELL ME System
TELL ME Exploitation Plans for KTH
The TELL ME Knowlecule
Widgets and Spaces
Work Spaces and Work Places
Blended training within a corporate ecosystem
TELL ME Deliverables
The TELL ME Innovation Cycle
TEL-Map
TEL-Map Deliverables
TEL-Mapping
ROLE
ROLE Deliverables
The Learner Cockpit
e-Portfolio City
H-Net
H-Net Deliverables
Organic.Edunet
Organic.Edunet Deliverables
LUISA
LUISA Deliverables
PROLEARN
PROLEARN Deliverables
Wallenberg Global Learning Network
APE
Folio Thinking
PADLR
National Projects
NSDL
NSDL på YouTube
The Semantic Slide Rule
NSDL next phase
UtbildningsRadions Mediebibliotek
ECIMF
Garden of Knowledge
FLIT Matematik
openLMS
Matriks
Potential Projects
Norm-Critical Innovation
Enhancing Social Integration
Norm-Creative Influence Mapping
Norm-Critical Innovation Algebra
Digital Bolshevism
New Dark Age
Rage Inside The Machine
Artificial Ethics
Matteplåster
Digitally Enhanced Learning
Publications
Knowledge Manifolds
Conceptual Browsing
New Paradigms and Tools for Mathematics Education
Experimental Projects in Mathematics Education
Mathematics produced at CVAP
Historical Manuscripts
Technology Enhanced Learning
E-learning Frameworks / Semantic Web Technologies
Component-based Learning Technologies
Semantic Interoperability
Presence Production
Software
Confolio
Conzilla
3D-Conzilla
People
Ambjörn Naeve
Papers by Ambjörn Naeve
The Mathematics Library of Ambjörn Naeve
The YouTube Channel of Ambjörn Naeve
Doctoral students
About
Affiliations
KTH
Math. Dept. at KTH
CVAP/NADA at KTH
CID/NADA at KTH
Interactive Learning Environments at CID
International Evaluation of CID in 2003
MID/CSC at KTH
KTHB/ECE at KTH
Open University
KMi
RWTH Aachen
Uppsala University
Uppsala Learning Lab
Stockholm University
DSV at Stockholm University
David Hestenes
Geometric Algebra
Geometric Calculus
Modeling
Metasolutions
Oxford Brookes University
Performance Augmentation Lab
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