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

Research Areas

Subpages of this page are:

• The Mathematical Explainatorium
• Knowledge Management
• Technology Enhanced Learning
• Asynchronous Public Service
• Presence Production

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