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Associate ProfessorGuillermo Pineda Villavicencio

Associate Professor

Faculty of Science Engineering and Built Environment/School of Information Technology

Orcid identifier0000-0002-2904-6657 (opens in a new tab)⁠
  • Associate Professor
    Faculty of Science Engineering and Built Environment/School of Information Technology
  • +61 3 522 73711 (Work)
  • Geelong Waurn Ponds Campus, 75 Pigdons Road, Waurn Ponds, Victoria 3216

TEACHING EXPERTISE

My teaching experience and expertise are broad, encompassing courses from
discrete mathematics and statistics to analysis and optimisation.

- Mathematics

TEACHING ACTIVITIES

  • UNIT TAUGHT
    SIT106 Fundamental concepts of mathematics
    Deakin University, Australia
  • UNIT TAUGHT
    SIT190 Introduction to functions, relations and graphs
    Deakin University, Australia
  • UNIT TAUGHT
    SIT192 Discrete mathematics
    Deakin University, Australia
  • UNIT TAUGHT
    SIT199 Applied algebra and statistics
    Deakin University, Australia
  • UNIT TAUGHT
    SIT281 Cryptography
    Deakin University, Australia
  • UNIT TAUGHT
    SIT292 Linear algebra for data analysis
    Deakin University, Australia
  • UNIT TAUGHT
    MATH3001 Modelling and change (Advanced level), a calculus III unit
    Federation University, Australia
  • UNIT TAUGHT
    MATHS2012 Graphs, digraphs and networks
    Federation University, Australia
  • UNIT TAUGHT
    MATHS1001 Modelling and change (Introductory level), a calculus I unit
    Federation University, Australia
  • UNIT TAUGHT
    ENCOR1140 Calculus and physics
    Federation University, Australia
  • UNIT TAUGHT
    MATHS2003 Profit, loss and gambling, an introductory unit on probability
  • UNIT TAUGHT
    MATHS1000 Upon the shoulders of giants, a precalculus unit
    Federation University, Australia
  • UNIT TAUGHT
    MATHS1005 Secrets of the matrix
    Federation University, Australia
  • UNIT TAUGHT
    STATS1000 Statistical methods
    Federation University, Australia
  • EXTERNAL SUPERVISION
    Large networks bounded in degree and diameter
  • EXTERNAL SUPERVISION
    Large interconnection networks with given degree and diameter
  • EXTERNAL SUPERVISION
    Assessing healthcare providers’ performance with and without risk
  • SUPERVISION PROJECT VACANCY
    Graphs of convex polytopes (opens in a new tab)⁠
    A polytope is the convex hulls of finitely many points in R^d for some d. Polytopes arise in various contexts, including as sets of feasible solutions in linear programming. The platonic solids are prominent examples of convex polytopes. This project focusses on the combinatorial structure of polytopes, represented by the partial ordering faces by the inclusion. A face of a polytope P is P itself (the trivial face) or the intersection of P with a hyperplane which contains P in one of its closed half-spaces (proper faces). The dimension of a polytope is the dimension of its affine hull. The 0-dimensional faces are vertices, and 1-dimensional faces are edges. The graph of a polytope is the abstract graph defined on the vertices of the polytope with two vertices being adjacent if they share an edge. This proposal investigates the combinatorial structure of polytopes by studying their graphs. Key questions include the existence of Hamiltonian cycles, minors, and colourings in graphs of polytopes. While these topics are well studied in graph theory, they remain underexplored for graphs of polytopes.
    MORELEARN MORE (opens in a new tab)
  • SUPERVISION PROJECT VACANCY
    Unlocking the multifaceted structure of convex polytopes (opens in a new tab)⁠
    A polytope is the convex hulls of finitely many points in R^d for some d. Polytopes arise in various contexts, including as sets of feasible solutions in linear programming. The platonic solids are prominent examples of convex polytopes. A face of a polytope P is P itself (the trivial face) or the intersection of P with a hyperplane that contains P in one of its closed half-spaces (proper faces). This project examines the facial structure of polytopes at two levels: 1. Establishing relations satisfied by the face numbers of a polytope. 2. Identifying properties and constructions that elucidate these relations. To realise these aims, we focus on questions that capture modern trends in this field, with special attention to prominent class of polytopes, such as simplicial polytopes, polytopes whose faces are all simplices, and cubical polytopes, polytopes whose faces are all cubes.
    MORELEARN MORE (opens in a new tab)
  • COMPLETED DOCTORAL SUPERVISION
    Combinatorial Properties of Polytopes: Face Bounds, Cliques, Independent Sets, and Colourings
    Aholiab Tegar Tritama - School of Information Technology - 2025