# Unit Information Sheet for MATH1907: Mathematics Special Studies Programme B

## 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: Tuesday 4pm, New Law 346
• Tutorial: Thursday 10am, Carslaw Room 359 (replaces your 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 be on the material in MATH1903 (see the MATH1903 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:

Weeks 2–5: Sharon Stephen Conformal transformations in fluid dynamics
Transformations are a powerful tool used in many areas of pure and applied mathematics to simplify the solution of a problem. We will consider conformal transformations to solve problems in fluid dynamics by working in the complex plane. Specifically, in solving Laplace's equation for velocity potential, complicated boundary conditions may be converted to simple boundary conditions. Another fascinating example is finding the flow past an aerofoil using the Joukowski transformation, enabling the lift force to be calculated.
Weeks 6–9: Oded Yacobi Three applications of Euler's formula
Euler's formula is a beautifully simple statement about connected planar graphs: (number of vertices)-(number of edges)+(number of faces)=2. We will discuss this formula and present some surprising applications, including the Sylvester-Gallai Theorem regarding lines and points in the plane, and Pick's Theorem about the area of triangles with integral vertex points (spoiler alert: it's always equal to 1/2!).
Weeks 10–13: Rachel Wang A brief introduction to probabilistic graphical models
Probabilistic graphical models provide a succinct framework for representing complex dependencies among random variables. We take a first dip into this field by studying how joint probabilities can be represented using directed and undirected graphs and discussing algorithms for performing simple inferential tasks. Graphical models include many popular statistical models such as hidden Markov models, Gaussian graphical models, as special cases and have been the focus of research in numerous statistical and computational fields ranging from machine learning, artificial intelligence, signal processing, bioinformatics, to statistical physics.

## 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. This counts 80% of the total mark.
• Three assignments for the special topics in the seminar. The total counts 10% towards the total mark. (with bettermark if all assignments are handed in, otherwise no bettermark)

Assignment submission dates: Thu 31 Aug (first topic), Thu 5 Oct (second topic), Thu 2 Nov (third topic)

All assignments have to be submitted through the LMS and passed through the text matching software Turnitin (scanned handwritten assignments are fine, there is absolutely no need to spend time on typesetting!) Late assignments are not allowed and will attract zero marks.

• 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 MATH1903 tutorial. Contact the coordinator Daniel Daners for permission to do so.

## Outcomes

The outcomes for MATH1907 include the outcomes for MATH1903 as well as the following: The student completing MATH1907 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 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 Tuesday 4pm or the tutorial at Thursday 10am. Any solutions will also be handed out in these classes.