Section outline

►Week 1

  • Nonlinear algebra

    The toolbox of linear algebra is often not sufficient to meet the nonlinear world. Polynomials offer a natural generalization. The course offers participants hands-on investigations (via both proofs and coding) of wide classes of algebraic optimization problems and algebraic inverse problems, coming from various fields of engineering (robotics, computer vision, deep learning, etc).

    The course covers: Overview of the necessary background in algebra/algebraic geometry. Solving polynomial systems with symbolic and numeric methods, optimization over semi-algebraic sets, tensor geometry, metric algebraic geometry. Applications of the theory to solve problems within engineering, machine learning, data science, AI.

    Teaching

    Teachers: Kathlén Kohn, kathlen[at]kth[dot]se
    TA:  Kim Kiehn, kiehn[at]kth[dot]se

    Course literature

    • Mateusz Michałek & Bernd Sturmfels, Invitation to Nonlinear Algebra, American Mathematical Society [2021]
    • Paul Breiding, Kathlén Kohn & Bernd Sturmfels, Metric Algebraic Geometry, Springer Nature [2023]

    • Igor. R. Shafarevich, Basic Algebraic Geometry Vol 1: Varieties in Projective Space. 3rd ed. Springer [2013]

    Schedule:  starting on September 2: 9:00-12:00 on Wednesdays

    see details here
    The class always starts at 9:00 sharp!

    For detailed planning (lecture/exercise) see sections below

    Examination

    Examiner:  Sofia Tirabassi

    Examination Form:
    Written exam (in-person, on campus): 70%,
    Labs (in-person, on campus): 30%. 
    Participants can obtain up to 10% bonus points for active participation in class.

    Preliminary grading scale:

    A B C D E
    94% 83% 72% 61% 50%

    To obtain passing grade E, participants have to take part in at least 1 Lab.

    Labs:
    There will be 2 labs, each giving 15 points. Each lab will consist of an individual part (like a kontrollskrivning) and a team project.
    The labs are taking place during 9:00-12:00 at the following days:
    Lab 1: We, September 30, 2026
    Lab 2: TBD
    In case a participant cannot take part in one of the 2 labs or is not satisfied with the amount of points during one of the 2 labs, there will be a bonus lab. The final amount of points obtained from the labs will be calculated as follows:
    Points(Lab1)+Points(Lab2)+Points(BonusLab)-min{Points(Lab1),Points(Lab2),Points(BonusLab)}.
    Time and date of the bonus lab will be determined at a later point.

    Resources
►Week 1