The University of Newcastle, Australia
Not currently offered
Course code

MATH3510

Units

10 units

Level

3000 level

Course handbook

Description

Combinatorics and Graph Theory is a blend of the mathematical techniques applicable to Computer Science, Information Technology and Statistics. This is 'discrete' mathematics as distinct from the continuous mathematics of calculus. It is a major growth area in modern mathematics, largely because of emerging applications in areas such as biotechnology and communication security.

Much of the subject matter is a continuation of topics studied in MATH1510 such as graphs, trees, and enumeration, and additional topics such as experimental design and finite geometry are introduced. Some use is made of basic techniques from calculus and abstract algebra.


Availability

Not currently offered.

This Course was last offered in Semester 1 - 2018.


Learning outcomes

On successful completion of the course students will be able to:

1. An in-depth knowledge of one specific area of mathematics.

2. An improved ability to communicate mathematical ideas.

3. Some experience with applications of mathematics to the Information Sciences.


Content

  • Enumeration: generating functions, recurrence relations, Polya's Theorem, inclusion-exclusion.
  • Graph theory: paths and cycles, connectivity, factorisations, colouring, planarity applications.
  • Combinatorial Designs: finite fields, Latin squares, Steiner triple systems, finite geometries.

Assumed knowledge

MATH3510Combinatorics and Graph TheoryCombinatorics and Graph Theory is a blend of the mathematical techniques applicable to Computer Science, Information Technology and Statistics. This is 'discrete' mathematics as distinct from the continuous mathematics of calculus. It is a major growth area in modern mathematics, largely because of emerging applications in areas such as biotechnology and communication security.

Much of the subject matter is a continuation of topics studied in MATH1510 such as graphs, trees, and enumeration, and additional topics such as experimental design and finite geometry are introduced. Some use is made of basic techniques from calculus and abstract algebra.FSCITFaculty of Science724School of Mathematical and Physical Sciences103000This Course was last offered in Semester 1 - 2018.MATH1510 Enumeration: generating functions, recurrence relations, Polya's Theorem, inclusion-exclusion. Graph theory: paths and cycles, connectivity, factorisations, colouring, planarity applications. Combinatorial Designs: finite fields, Latin squares, Steiner triple systems, finite geometries. YOn successful completion of this course, students will be able to:1An in-depth knowledge of one specific area of mathematics.2An improved ability to communicate mathematical ideas.3Some experience with applications of mathematics to the Information Sciences. In Term Test: Examination - ClassWritten Assignment: AssignmentsTutorial / Laboratory Exercises: Group/tutorial participation and contribution: Lab exercises and group case studyFormal Examination: Final examination


Assessment items

In Term Test: Examination - Class

Written Assignment: Assignments

Tutorial / Laboratory Exercises: Group/tutorial participation and contribution: Lab exercises and group case study

Formal Examination: Final examination