Geometry with Applications, 6 credits (TATA49)

Geometri med tillämpningar, 6 hp

Main field of study

Mathematics Applied Mathematics

Level

First cycle

Course type

Programme course

Examiner

Milagros Izquierdo Barrios

Director of studies or equivalent

Jesper Thorén

Available for exchange students

Yes
Course offered for Semester Period Timetable module Language Campus VOF
6KMAT Mathematics 5 (Autumn 2017) 1, 2 4, 4 Swedish/English Linköping o

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

  • Mathematics

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

First courses in Linear algebra and Discrete mathematics (desirable)

Intended learning outcomes

The course presents methods and concepts in modern geometry, i.e. it is based on geometrical transformations. The course treats Euclidean and non-euclidean geometry, and real and finite projective geometry. By generalization of Euclidean transformation one obtains projective geometries. These geometries form the mathematical basis for computer graphics, latin squares and error-correcting codes. Students should be able to:

  • use the concept of group to study different geometries
  • classify and to determine the different (Euclidean) transformations of the plane.
  • study frieze and wallpaper patterns with the help of transformations
  • know of hyperbolic and elliptic geometry.
  • work with the projective plane and its transformations: collineations and projectivities
  • use collineations and projectivities to explain the foundations of computer graphics
  • recognise finite projective geometries and their applications to coding theory and configurations.
  • apply quaternions to computer animations

  • Course content

    Groups: cyclic and dihedral groups. Quaternions. Stereographic projection. Euclidean plane geometry: isometries, reflections, direct and inverse isometries. Frieze and wallpaper patterns. Three-dimensional isometries. Hyperbolic and elliptic geometries. Projective plane: harmonic sets, perspectivity, projectivity, conics, cross ratios, collineations and polarity. Application in computer graphics Finite projective planes. Applications to error-correcting codes, configurations, design and latin squares.

    Teaching and working methods

    Lectures and tutorials.

    Examination

    UPG1Hand-in assignmentsU, 3, 4, 56 credits

    Grades

    Four-grade scale, LiU, U, 3, 4, 5

    Other information

    Supplementary courses: Linear Algebra, honours course. Combinatorics
     

    Department

    Matematiska institutionen

    Director of Studies or equivalent

    Jesper Thorén

    Examiner

    Milagros Izquierdo Barrios

    Education components

    Preliminary scheduled hours: 56 h
    Recommended self-study hours: 104 h

    Course literature

    Additional literature

    Books
    J. N. Cederberg, A course in Modern Geometries (Undergraduate Texts in Mathematics)
    Compendiums

    Additional literature

    Books

    J. N. Cederberg, A course in Modern Geometries (Undergraduate Texts in Mathematics)

    Compendia

    UPG1 Hand-in assignments U, 3, 4, 5 6 credits

    Regulations (apply to LiU in its entirety)

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    LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva. 

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