Maths & Stats / Teaching program / Junior / MATH1907 / Info Sheet

MATH1907: Mathematics Special Studies Program A
Unit Information Sheet for Semester 1, 2009

Classes

The Special Studies Program is formally attached to MATH1903 with one additional seminar and a special tutorial. In particular you attend:

  • The same lectures as MATH1903;
  • Seminar: Monday 4pm, Carslaw Room 359;
  • Tutorial: Thursday 10am, Carslaw Room 351 (replaces your other MATH1903 tutorial).

The special topics in the seminar are independent of MATH1903. There will be three different topics presented by different lecturers.

The tutorial will mainly be on the material in MATH1903 (see the MATH1903 Information Sheet to find out how to obtain tutorial sheets) and occasionally about the material from the seminars.

Special Topics

There will be three topics from various fields of mathematics and statistics presented by different lecturers:

Week 2-5: H Dullin, Mathematics and Musical Scales
The Pythagorean scale is based on the frequency ratios 2:1 for the octave and 3:2 for a perfect fifth. Constructing all notes from these ratios leads to inconsistencies, which can be resolved using continued fractions, the theory of which we will develop.
Week 6-9: F Cîrstea Fractals
Many objects in nature can be modelled by fractals. Fractal sets or images have the property that if we look at them under a microscope, using larger and larger magnifications, we continue to see similar features at all scales. Examples of fractals include biology (blood vessel patterns, structure and development of plants), physics (statistical mechanics, dynamical systems), computer science (image compression, compression for multimedia), engineering (image encoding, antennae, signal processing), and chemistry (pattern-forming alloy solidification). We will look at a number of fractals and discuss how to generate them. We will also study some of their surprising properties.
Week 10-13: M Stewart Markov Chains and Google PageRank
Google's PageRank procedure effectively uses Markov Chain theory to determine the long-run probabilistic behaviour of a "random surfer" who browses the Internet according to a relatively simple, random link- following scheme. We develop the necessary theory to explain PageRank and accompany this with some computing using the R statistical environment.

Assessment

The final mark in MATH1907 is determined as follows:

  • All the assessment for MATH1903. For more details look at the MATH1903 unit information sheet.
  • Three assignments for the special topics in the seminar. If you perform well, the marks will be used to “top up” your MATH1903 mark.

To get a mark in MATH1907 you must hand in all assignments. If you attend less than 80% of seminars and tutorials you may be given a mark for MATH1903, not MATH1907! Under exceptional circumstances you may be allowed to attend a MATH1903 tutorial. Contact the coordinator D Daners for permission to do so.

Problem sheets and the like

  • You will need the sheets for MATH1903. Check the MATH1903 Web page or the MATH1903 Unit Information Sheet on how to get these.
  • Additional handouts for the special topics in the seminar may be given out in the seminar at Monday 4pm or the tutorial at Thursday 10am. Any solutions will also be handed out in these classes.