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Important dates

Last day to enrol online: Thursday 20th of December. No enrolments will be possible after this date.
Census Date: Monday 31st of December.

Teaching weeks are as follows:

Week 1: Monday 10th – Friday 14th of December,
Week 2: Monday 17th – Friday 21st of December,
Christmas/New Year break: 24th of December to 4th of January,
Week 3: Monday 7th – Friday 11th of January,
Week 4: Monday 14th – Friday 18th of January,
Week 5: Monday 21st – Friday 25th of January,
Public Holiday Monday 28th of January,
Week 6: Tuesday 29th – Friday 1st of February,
Week 7: Monday 4th of February (replacement for public holiday).

Mid Semester Test: Wednesday 16th of January.

Summer Maths IB Exam: Monday 18th of February.

How to enrol

Enrol via Access Adelaide.

Summer Mathematics IB enrolment is split into two parts, one for December and one for January. You must enrol in both parts.

Part 1 in December 2018 is currently open for enrolments and is listed on Access Adelaide under Term 4, MATHS 1012.
For further information, see Course Planner Part 1.

Part 2 in January 2019 will open for enrolments on Monday 3rd of December. Note: It has a different code: MATHS 1021.
For further information, see Course Planner Part 2.

No student will be permitted to enrol into Part 2 if they have not enrolled in Part 1.

Structure

Summer Maths IB is taught double time in 6 weeks instead of the usual 12 weeks. This means that there are 8 lectures per week, 2 tutorials per week and 2 assignments per week. Teaching days are Mondays, Tuesdays, Thursdays and Fridays (as can be seen on Course Planner or Access Adelaide). The only exception is Wednesday the 16th of January which is Mid Semester Test day.

Absences in December

Due to the unusual December start for Summer Maths IB, we have made the following two special arrangements to try and accommodate students who might have made travel plans in advance and can not be present during December.

1) Tutorials

The usual tutorial participation mark will be waived for all students in December. All students are still encouraged to attend and participate in tutorials in December if possible since this would be beneficial for learning.
All students will be expected to attend and participate during tutorials in January, and participation in January will contribute 5% of your final mark.

2) Assignments

Assignment marks will be calculated as the best of either (a) all assignments, or (b) only those due in January.
There will be assignments due in December. These are:

  • Calculus Written Assignment 1 and Maple TA Assignment 1, due Monday 17th of December,
  • Algebra Written Assignment 1 and Maple TA Assignment 1, due Thursday 20th of December.

These assignments will only count towards assignment totals if they improve your final mark.

The next assignments will be due in January. These are:

  • Calculus Written Assignment 2 and Maple TA Assignment 2, due Monday 7th of January.
  • Algebra Written Assignment 2 and Maple TA Assignment 2, due Thursday 10th of January.

All students will be expected to submit these assignments on time.The Monday/Thursday assignment pattern then continues for the rest of the teaching weeks.

Workload

Note that the two weeks of classes in December amounts to a total of 48 hours of study. This includes attending the lectures (or at least watching the recordings), revising lecture notes, doing the tutorial and practice questions, and all of the assignments.

48 hours is of course more than one week of full time work. If you have travel plans that would prevent you from completing all of this study before January 7th then you should not take Summer Maths IB, and instead wait for Semester 1 2019 Maths IB. There will be no time to catch up once classes resume on the 7th of January.

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Upcoming Colloquiums

Title: Random Walks
15:10 Fri 12 October, 2018 :: Napier 208 :: A/Prof Kais Hamza :: Monash University
Abstract:
A random walk is arguably the most basic stochastic process one can define. It is also among the most intuitive objects in the theory of probability and stochastic processes. For these and other reasons, it is one of the most studied processes or rather family of processes, finding applications in all areas of science, technology and engineering. In this talk, I will start by recalling some of the classical results for random walks and then discuss some of my own recent explorations in this area of research that has maintained relevance for decades.

Title: Bayesian Synthetic Likelihood
15:10 Fri 26 October, 2018 :: Napier 208 :: A/Prof Chris Drovandi :: Queensland University of Technology
Abstract:
Complex stochastic processes are of interest in many applied disciplines.  However, the likelihood function associated with such models is often computationally intractable, prohibiting standard statistical inference frameworks for estimating model parameters based on data.  Currently, the most popular simulation-based parameter estimation method is approximate Bayesian computation (ABC).  Despite the widespread applicability and success of ABC, it has some limitations.  This talk will describe an alternative approach, called Bayesian synthetic likelihood (BSL), which overcomes some limitations of ABC and can be much more effective in certain classes of applications.  The talk will also describe various extensions to the standard BSL approach.  This project has been a joint effort with several academic collaborators, post-docs and PhD students.

Recent Colloquiums

Title: Interactive theorem proving for mathematicians
15:10 Fri 5 October, 2018 :: Napier 208 :: A/Prof Scott Morrison :: Australian National University
Abstract:
Mathematicians use computers to write their proofs (LaTeX), and to do their calculations (Sage, Mathematica, Maple, Matlab, etc, as well as custom code for simulations or searches). However today we rarely use computers to help us to construct and understand proofs.
There is a long tradition in computer science of interactive and automatic theorem proving; particularly today these are important tools in engineering correct software, as well as in optimisation and compilation. There have been some notable examples of formalisation of modern mathematics (e.g. the odd order theorem, the Kepler conjecture, and the four-colour theorem). Even in these cases, huge engineering efforts were required to translate the mathematics to a form a computer could understand. Moreover, in most areas of research there is a huge gap between the interests of human mathematicians and the abilities of computer provers.
Nevertheless, I think it’s time for mathematicians to start getting interested in interactive theorem provers! It’s now possible to write proofs, and write tools that help write proofs, in languages which are expressive enough to encompass most of modern mathematics, and ergonomic enough to use for general purpose programming.
I’ll give an informal introduction to dependent type theory (the logical foundation of many modern theorem provers), some examples of doing mathematics in such a system, and my experiences working with mathematics students in these systems.

Title: Mathematical modelling of the emergence and spread of antimalarial drug resistance
15:10 Fri 14 Sep, 2018 :: Napier 208 :: Dr Jennifer Flegg :: University of Melbourne
Abstract:
Malaria parasites have repeatedly evolved resistance to antimalarial drugs, thwarting efforts to eliminate the disease and contributing to an increase in mortality. In this talk, I will introduce several statistical and mathematical models for monitoring the emergence and spread of antimalarial drug resistance. For example, results will be presented from Bayesian geostatistical models that have quantified the space-time trends in drug resistance in Africa and Southeast Asia. I will discuss how the results of these models have been used to update public health policy.

Title: Topological Data Analysis
15:10 Fri 31 August, 2018 :: Napier 208 :: Dr Vanessa Robins :: Australian National University
Abstract:
Topological Data Analysis has grown out of work focussed on deriving qualitative and yet quantifiable information about the shape of data. The underlying assumption is that knowledge of shape – the way the data are distributed – permits high-level reasoning and modelling of the processes that created this data. The 0-th order aspect of shape is the number pieces: “connected components” to a topologist; “clustering” to a statistician. Higher-order topological aspects of shape are holes, quantified as “non-bounding cycles” in homology theory.  These signal the existence of some type of constraint on the data-generating process.
Homology lends itself naturally to computer implementation, but its naive application is not robust to noise. This inspired the development of persistent homology: an algebraic topological tool that measures changes in the topology of a growing sequence of spaces (a filtration). Persistent homology provides invariants called the barcodes or persistence diagrams that are sets of intervals recording the birth and death parameter values of each homology class in the filtration.  It captures information about the shape of data over a range of length scales, and enables the identification of “noisy” topological structure.
Statistical analysis of persistent homology has been challenging because the raw information (the persistence diagrams) are provided as sets of intervals rather than functions. Various approaches to converting persistence diagrams to functional forms have been developed recently, and have found application to data ranging from the distribution of galaxies, to porous materials, and cancer detection.

Title: Tales of Multiple Regression: Informative missingness, Recommender Systems, and R2-D2
15:10 Fri 17 August, 2018: Napier 208: Prof Howard Bondell: University of Melbourne
Abstract:
In this talk, we briefly discuss two projects tangentially related under the umbrella of high-dimensional regression. The first part of the talk investigates informative missingness in the framework of recommender systems. In this setting, we envision a potential rating for every object-user pair. The goal of a recommender system is to predict the unobserved ratings in order to recommend an object that the user is likely to rate highly. A typically overlooked piece is that the combinations are not missing at random. For example, in movie ratings, a relationship between the user ratings and their viewing history is expected, as human nature dictates the user would seek out movies that they anticipate enjoying. We model this informative missingness, and place the recommender system in a shared-variable regression framework which can aid in prediction quality. The second part of the talk deals with a new class of prior distributions for shrinkage regularization in sparse linear regression, particularly the high dimensional case. Instead of placing a prior on the coefficients themselves, we place a prior on the regression R-squared. This is then distributed to the coefficients by decomposing it via a Dirichlet Distribution. We call the new prior R2-D2 in light of its R-Squared Dirichlet Decomposition. Compared to existing shrinkage priors, we show that the R2-D2 prior can simultaneously achieve both high prior concentration at zero, as well as heavier tails. These two properties combine to provide a higher degree of shrinkage on the irrelevant coefficients, along with less bias in estimation of the larger signals.

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Upcoming Seminars

Title: Newton’s method in the case of non-simple and non-unique roots
Date and Time: Wednesday 3 October, 1:10 pm
Location: Ingkarni Wardli 218
Speaker: Dr Brendan Harding
Abstract: Newton’s method is a fundamental numerical method and is ubiquitous throughout scientific computing. However, there are cases where the method can behave unexpectedly. Two such cases are when a function has non-simple and/or several roots. This talk will describe techniques that can be used to compensate for these problems and in some cases improve on the usual method.

Recent Seminars

Title: From cows to inductive types; or What are numbers?
Date and Time:  Wednesday 5 September; 1:10 pm
Location: Room 218, Ingkarni Wardli
Speaker: Dr David Roberts
Abstract:We all use numbers every day, but have you stopped to think how numbers are defined? About what they are? What they should and cannot be? This talk will span several thousand years of the history of numbers, from ancient Mesopotamian accounting to contemporary structuralism.

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Congratulations to Michael Hallam for winning the Elsevier Young Scientist Award in 2018! The award was presented at the workshop entitled, Index theory and applications to positive scalar curvature and related areas, funded by the Institute for Geometry and its Applications (Adelaide) and AMSI (Melbourne), held at University of Adelaide, June 4-8, 2018. Michael Hallam […]

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The MPhil student, Michael Hallam (supervisors Varghese and Baraglia), won the 2018 Elsevier Young Scientist Award for the best student talk at the IGA/AMSI workshop entitled,  Index theory and applications to positive scalar curvature and related areas,  held June 4-8, 2018. He also receives a cash award of USD 750. Congratulations to Michael!

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Congratulations to MPhil student in Pure Mathematics, John McCarthy (Supervisors Varghese, Baraglia) who has been admitted with full scholarship to the PhD program at Imperial College (London) to work with Richard Thomas! Congratulations to PhD student in Pure Mathematics, Hao Guo (Supervisors Varghese, Hang Wang) who has been offered an NSF funded postdoc at Texas […]

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Title: A Hecke module structure on the KK-theory of arithmetic groups When: Friday, 2 March 2018 at 1:10pm in Barr Smith South Polygon Lec theatre  Speaker: Bram Mesland (Unversität Bonn) Abstract: Let $G$ be a locally compact group, $\Gamma$ a discrete subgroup and $C_{G}(\Gamma)$ the commensurator of $\Gamma$ in $G$. The cohomology of $\Gamma$ is a […]

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Congratulations to our AMSI Vacation Research Scholars, Tobin South and Michael Ucci who received both of the prizes for the best presentation at the recent #AMSIConnect2018 conference. It is an outstanding achievement for our students that have won all of the available prizes against a field of students from across the country!

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Congratulations to Mr Michael Hallam (supervisors Varghese and Baraglia) on being awarded the prestigious 2017 B H Neuman prize for the most outstanding student talk presented at the Annual Meeting of the Australian Mathematical Society. He has also been admitted with a full PhD scholarship to the University of Oxford. More information: http://www.austms.org.au/The+Bernhard+Neumann+Prize”

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Title: Calculating optimal limits for transacting credit card customers 15:10 Fri 2 Mar, 2018 :: Horace Lamb 1022 :: Prof Peter Taylor :: University of Melbourne Abstract: Credit card users can roughly be divided into `transactors’, who pay off their balance each month, and `revolvers’, who maintain an outstanding balance, on which they pay substantial interest. In […]

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