MATH2300 - Linear Algebra & Graph Theory
COURSE CONTENT:
Linear Algebra:
· Basics
· Vector Spaces and Subspaces
· Basis and Dimension
· Orthonormal Bases
· Null, Column and Row Space
· Linear Transformations
· Eigenvalues and Eigenvectors
Graph Theory:
· Basics
· Algorithms and Tree Searches
· Planar Graphs
· Matchings and Scheduling
· Vertex and Edge Colourings
WHERE IS IT USED:
Linear Algebra:
Linear Algebra has applications in almost every other areas of mathematics.
Graph Theory:
Graphs arise naturally as models in a remarkably wide variety of situations from engineering applications (such as design of computer hardware) to leisure activities (such as puzzle solving and game playing). Graph theory is used in complex timetabling problems, scheduling of sporting tournaments, optimization problems, genetics, chemistry, studies of evolution and many other areas.
Due partly to the demands of these applications and partly to the numerous intriguing theoretical problems in the field, graph theory is a vibrant area of theoretical research in mathematics. For example, the deceptively simple sounding "four colour problem", which asks whether it is possible to colour any map with four or fewer colours such that adjacent countries are coloured differently, remained unsolved (despite the attention of numerous mathematicians around the world) for 150 years until a proof involving hundreds of hours of computer calculations was provided in 1976. Many problems in graph theory remain unsolved and are the focus of ongoing international research.
WHO IS INTERESTED:
Linear Algebra:
The first part of the course is designed to introduce students to linear algebra. Historically the subject arose from the study of linear equations, but now has applications to many branches of mathematics, as well as to engineering and economics.Graph Theory:
Graph theory is a branch of mathematics for which minimal background knowledge is required. This aspect makes it a very accessible, attractive and enjoyable topic for many students.
The graph theory component of MATH2300 provides an excellent introduction for students who may wish to study graph theory further in third and/or fourth year. More advanced graph theory is available in MATH3301 - Graph Theory and Geometry and in MATH4303 - Advanced Combinatorics. Further study in graph theory may also be undertaken via the Special Topics in Mathematics courses MATH4001 and MATH4002, and in the Honours Project course MATH4000. Graph theory is a very active research area at The University of Queensland and PhD and Masters degrees in the field are also available.
WHAT DO I NEED:
For the linear algebra component, students should have background equivalent to completion of the course MATH1051.For the graph theory component, a reasonable mathematical maturity, and knowledge of techniques such as mathematical induction, proof by contradiction etc., would be an advantage. These are covered in the course MATH1061. The first few lectures will deal quickly with a lot of basic graph theoretic definitions that we shall need subsequently.
WHEN IS IT AVAILABLE:
Semester 2.