# Unit Information Sheet for MATH1906: Mathematics Special Studies Programme A

## Classes

The Special Studies Program is formally attached to MATH1901 with one additional seminar and a special tutorial. In particular you attend:

• The same lectures as MATH1901;
• Seminar: Monday 4pm, New Law Seminar Room 442
• Tutorial: Thursday 10am, Carslaw Room 359 (replaces your MATH1901 tutorial).

The special topics in the seminar are independent of MATH1901. There will be three different topics presented by different lecturers.

The tutorial will be on the material in MATH1901 (see the MATH1901 Information Sheet to find out how to obtain tutorial sheets).

## Special Topics

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

Week 2-5: D Daners, Maps of the World

The globe cannot be mapped onto a plane without distortion. We look at map projections of the world and study their properties like for instance area and angle distortions. We discuss suitability of some maps for navigation and other purposes.

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: E Altmann Chaos in dynamical systems

ABSTRACT: The goal of these four lectures is to learn how systems governed by known equations of motion, with no randomness, can still display an unpredictable temporal evolution. This seemingly contradictory phenomenon, known as deterministic chaos, was first discovered in Astronomy and Meteorology but is now known to appear in virtually all scientific disciplines. The complicated chaotic dynamics appears already in very simple (yet non-linear) equations, which we will study analytically and through simple computer simulations. Our excursion to understand chaos will lead us to some fundamental concepts in the mathematical theory of dynamical systems, such as attractors, bifurcations, invariant measure, Lyapunov exponents, and self-similarity.

## Assessment

The final mark in MATH1906 is determined as follows:

• All assessments for MATH1901. For more detail look at the MATH1901 unit information sheet. This counts 80% of the total mark.

• Three equally weighted assignments, one on each special topics in the seminar. The three assignments count 10% towards the total mark. (bettermark applies if all assignments are handed in, otherwise no bettermark)

Assignment submission dates: April 13 (first topic), May 19 (second topic), June 9 (third topic)

All assignments have to be submitted through the LMS to be passed through the text matching software Turnitin (scanned handwritten assignments are fine, there is absolutely no need to spend time on typesetting!).

• One mark for every seminar participation, up to a total of 10. The total counts 10% towards the total mark. (no bettermark!)

Under exceptional circumstances you may be allowed to attend a MATH1901 tutorial. Contact the coordinator D Daners for permission to do so.

## Outcomes

The outcomes for MATH1906 include all outcomes for MATH1901 as well as the following: The student completing MATH1906 will

• gain an appreciation of a diverse range of mathematical problems and applications through participating in class discussions and the completion of assignments.
• be able to grasp new mathematical concepts beyond routine methods and calculations.

## Problem sheets and the like

• You will need the sheets for MATH1901. Check the MATH1901 Web page or the MATH1901 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 Tuesday 4pm or the tutorial at Thursday 10am. Any solutions will also be handed out in these classes.