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MAU34303 Discrete geometry

Module Code MAU34303
Module Title Discrete geometry
Semester taught Semester 1
ECTS Credits 5
Module Lecturer Prof. Marvin Anas Hahn
Module Prerequisites
 
MAU11100 Linear algebra and
MAU11201 Single-variable calculus

Assessment Details

  • This module is examined in a 2-hour examination at the end of Semester 1.
  • Continuous assessment contributes 10% towards the overall mark.
  • The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows: 
    1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session; 
    2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam; 
    3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session.

    Capping of reassessments applies to Theoretical Physics (TR035) students enrolled in this module. See full text at https://www.tcd.ie/teaching-learning/academic-affairs/ug-prog-award-regs/derogations/by-school.php  Select the year and scroll to the School of Physics.

Contact Hours

11 weeks of teaching with 3 lectures per week.

Learning Outcomes

On successful completion of this module, students will be able to

  • Apply basic theorems to structures in polyhedral geometry.
  • Compute examples of polytopes, cones and fans from discrete input data.
  • Describe various types of subdivisions of polytopes.
  • Relate regular subdivisions to the secondary fan and secondary polytope.
  • Apply basic theorems about Ehrhart polynomials and discrete volumes.

Module Content

  • Polytopes
  • Cones
  • Fans
  • Regular subdivisions
  • Mixed subdivisions
  • Secondary fans
  • Secondary polytopes
  • Discrete volumes
  • Ehrhart polynomials

Recommended Reading

  • Ziegler, Günter M. Lectures on polytopes. Springer 2012.
  • Gelfand, Israel M., Kapranov, Mikhail M., and Zelevinsky, Andrei V.. Discriminants, resultants and multidimensional determinants. Springer 2008.