### Modelling Surface Water Flow in The Lower Campaspe Catchment

By Yinli Wang, The Australian National University Water resource is essential to human’s survival and is also affecting many aspects of our life, including economics, health, and environment. [...]

### Untangling Knot Theory

By Abdul Zreika, The University of Sydney So, say you’re at home on a typical Friday night, having the time of your life untying and retying your shoelace knots over and over again, wishing that [...]

### On the State of Mathematics Education in Australia

By Sheng Xu, The University of Sydney A major problem in the Australian education system, and one which has received significant media coverage lately, is the decline in mathematical ability of [...]

### Genetics of Drought Resistant Chickpeas

By Peter Wreford, RMIT University My AMSI vacation research project involved applying graph theory to the genetics of drought resistant chickpeas. Chickpeas are a highly nutritious food, [...]

### Dualities in String Theory

By Anna Vaughan, Australian National University It has long been realised that mathematics provides a beautiful and powerful framework to describe the universe in which we live. From [...]

### My Choice: Mathematics

By Lachlan Tyrrell, Queensland University of Technology I love mathematics. Maths is somehow miraculous and beautiful despite being perfectly logical. I understand that not everyone feels this [...]

### Unicellularity of Shift Operators

By Timothy Tillman, The University of Newcastle If you buy the exponential growth of tech metrics (such as cost per memory, energy per floating point operations, etc.) staying that way for the [...]

### They call me a ‘Maths Mum’

By Elisa Tancredi, La Trobe University For as long as I can remember, I’ve been ‘teaching’ maths. I have always loved maths and express it in a fun and positive way. My earliest memory is being [...]

### What are numbers?

By Aiden Suter, The University of Queensland As we grow, we become familiar with many types of numbers ranging from fractions to irrational numbers such as π. The first type of numbers we [...]

### Can We Hear Equations?

By Alexander Stokes, The University of Sydney One of the most thrilling things about doing mathematics at any level is seeing how a problem transforms when you think about it in different ways. [...]

### Maths Modelling: Mimic Life

By Amy Stringfellow, Queensland University of Technology When I left school, I rather liked maths. It had beautiful logic, symmetry and best of all, there was one logical solution for any problem [...]

### Just Cause

By Dimitrio Sidi, University of Western Australia There is a popular video game series called Just Cause where players control a character whose objective is to liberate towns from the rule of an [...]

### The World we Live in

By Haris Sahovic, Monash University In human history, mathematics has never been as important as it is today. It has a direct impact on the majority of our everyday lives, as citizens and [...]

### Molecular Dynamics

By Timothy O’Sullivan, The University of Melbourne Most of us are familiar with the concept of Atoms, the idea that everything around us and inside us is made up of these very tiny building [...]

### Maths and Me

By Angus Lewis, The University of Adelaide It’s summer in Australia and Christmas is coming. Friends and family travel from across the country to be together. It’s very exciting for [...]

### Partition Function Zeros and the Ising Model in a Field

By Todd Neve, The University of Melbourne The Ising Model is a mathematical model of ferromagnetism in statistical mechanics. It was first studied by Ernst Ising in the 1920s to analyse critical [...]

### Mass Spectrometry and Missing Data

By Daniel Kon, The University of Adelaide My AMSI VRS project fell somewhere in the intersection of mathematics and genetics. The study of genetics in the age of computers involves dealing with [...]

### A Mathematical Voyage

By Rhiannon Kirby, Monash Univeristy ”The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is [...]

### Statistics and Kittens

By Alex Ligthart-Smith, La Trobe University When I found out I had been accepted into the AMSI Vacation Research Scholarship program I was so excited and grateful. At nearly 26, it has taken me [...]

### Riemannian Geometry and the Prescribed Ricci Curvature Problem

By Anna Kervison, The University of Queensland Riemannian geometry is a branch of non-Euclidean geometry developed by Bernhard Riemann, used to describe curved space. In Riemannian geometry, a [...]

### The Problem with Writing about Mathematics

By Jamieson Kaiser, Monash University I remember when I finally had the idea. I was very excited. After two weeks of working full time on my AMSI project (a life time for a university student), I [...]

### The Unreasonable Effectiveness

By Maxim Jeffs, The Australian National University In 1960, the physicist Eugene Wigner published his essay ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’, partly as a [...]

### Fractional Reaction-Diffusion Models For Anisotropic, Heterogeneous Media

By Emma Johnston, Queensland University of Technology The motion of a particle suspended in a fluid, a malaria infected mosquito zipping around a village or the price of fluctuating stock are [...]

### Strange Happenings in Topology

By Michael Hallam, The University of Adelaide Everyone is familiar with the notion of a space – we live in a space after all. We can imagine one dimensional spaces such as the real number [...]

### Numerical Solutions to the Boltzmann Equation for Rarefied Gas Flows

By Joseph Johnson, The University of Melbourne My research this summer was into numerical solutions to the Boltzmann equation for rarefied gas flows. This is relevant because it is necessary in [...]

### To Math or not to Math

By Logan Haami, University of Technology Sydney Throughout the summer of 2015/16 I was lucky enough to become an AMSI vacation research scholar by conducting my very own research project (which [...]

### Fitting a Mixture Model for Informative Non-Response in Innovation Surveys

By Xiangyuanchai Guo, The Australian National University Suppose you are a very smart student like me (just joking), so that you never fail any exam just like me (joking again). Suppose I am [...]

### Ah, ‘the fun of batteries’

By Luke Ginn, Queensland University of Technology Batteries are becoming increasingly important in today’s society, with the latest release of Tesla’s Powerwall (house battery) and Tesla’s ever [...]

### Geodesic Incompleteness of Spacetime

By John McCarthy, The University of Adelaide In late 1915, Albert Einstein published his first paper on the subject of General Relativity. In it, he described a picture of our universe as a [...]

### What’s in a Wave?

By Padraic Gidney, The University of Sydney For my summer project, I investigated the behaviour of a particular kind of solution – what’s called a periodic wave train solution – [...]

### My Maths History

By Sarah Gazelle, RMIT University As a child I never had an interest to learn mathematics and I never particularly enjoyed it. I was shocked on my first day of Year 6 when my teacher told me and [...]

### A Mathematical Model for Cartilage

By Russell Edson, The University of Adelaide When cartilage is damaged – by injury, genetic disorders, or diseases like Osteoarthritis – the results can be physically debilitating. Currently the [...]

### Cellular Mathematics

By Kevin Duxbury, Monash University I was fortunate enough to embark on a fascinating journey into bio-mathematics taking the form of an AMSI research project. It was wonderful to gain insight [...]

### Complex Numbers

By Penelope Drastik, University of Wollongong What is the square root of -1? Most people would say that it doesn’t exist. Since the product of two positive numbers is positive, and the product of [...]

### Recounting the Numbers

By Andy Chu, University of Technology Sydney Mathematics has been a passion of mine ever since I was a kid. It is relevant to every aspect of life. So it was sad to see fellow students who would [...]

### The Graph Colouring Problem

By An Ran Chen, Australian National University In 1852, the South African mathematician and botanist Francis Guthrie asked a seemingly simple question, “Is it possible to colour any map with at [...]

### A Simple Interval Estimator for the Ratios of Two Medians

By Maxwell Cairns, La Trobe University A simple Interval estimator for the ratios of two medians was given by Bonett and Price in a 2002 paper in the Journal of Statistical Computation and [...]

### Puzzles, Games and Mathematics

By James Bubear, Queensland University of Technology A Sudoku is a puzzle that most of us will be familiar with having become a staple of most newspapers over the last decade. What many of you [...]

### My Life and Mathematics

By Debra Briggs, Federation University Australia My interest in numbers began as a pre-schooler. When I was 3 years old I remember my mother pulling a mandarin in half and talking about how two [...]

### Mathematical Modelling: A passion

By Alexander Baker, The University of Queensland It all began early in my life. Mathematics provided fun little logical puzzles to solve and was far more intriguing than other subjects at school. [...]

### Chaos Encrypted Communications

By Morris Vysma, The University of Newcastle Encrypted Communications are one of the most important inventions of the modern ages. You might not know it but encryption goes far beyond letting [...]

### P vs NP – Hamiltonian Cycles

By Bohao Yao, The University of Melbourne A Hamiltonian cycle in a graph is a cycle that passes through every vertex in the graph exactly once. Determining whether a graph has a Hamiltonian cycle [...]

### If you say 294.583920193485175210293405212343 to a computer, what does it hear?

By John Wormell, University of Sydney Many people have come to rely almost exclusively on computers to carry out the maths they have to do. Throughout the scientific and business worlds, people [...]

### Mathematical Logic

By Campbell Wheeler, The University of Melbourne Around the turn of the 19th century David Hilbert wanted to find a list of rules that completely describe the various areas of mathematics. When [...]

### Bouncing Droplets and Quantum Mechanics

By Rahil Valani, Monash University You might be wondering how can bouncing droplets – a macroscopic system, be related to the theory of Quantum Mechanics, which governs the microscopic [...]

### Decision Making and Cricket Team Selection

By Hamish Thorburn, The University of Queensland Cricket is one of the most popular sports in Australia, and the men’ s test team has a huge following here. Often debates will occur as to which [...]

### What is a Statistical Model and Why Does it Matter?

By Xun Chun Tee, The Australian National University As a student, we might be interested to ask, are boys or girls achieving better performance in the Australian Tertiary Admission Rank (ATAR)? [...]

### How do Fingerprints get matched?

By John Tait, RMIT University A fingerprint is incredibly detailed, with lots of tiny ridges circling round, sometimes joining up, and sometime ending, that trying to determine if two prints [...]

### Playing with probability

By Angus Southwell, Monash University The spotlight glares at you as Mr Hall explains the game to you and thousands of viewers. “You have three doors to choose from. Behind one is a car, and [...]

### How are decisions made?

By Laura Smith, Deakin University We are all too familiar with situations where we are a part of a group that has to make a decision. Going out to dinner with friends requires a group decision [...]

### Solutions to the Schrodinger equation and l-conformal Galilei algebras

By Trent Skorka, University of Queensland When most people ask what I’m studying and I respond with mathematics, I can see from their expressions that the first question they want to ask me is [...]

### The Mathematics behind a Flapping Flag

By Eric Shen, The University of Melbourne We are also familiar with the phenomenon where a rectangular shaped object can be excited into oscillations in a medium, like a flag flapping in air. [...]

### Periodic presumptive treatment for sexually transmitted infections in the context of a moderate HIV epidemic

By Christopher Rock, University of New South Wales Infectious disease is an area where mathematical modelling is particularly important. Infectious disease has significant real-world costs. [...]

### 1324 avoiding permutations

By Thomas Robinson, University of Newcastle My AMSI VRS project involved the study of permutations that avoid the pattern 1324. A permutation of length n is a rearrangement of the numbers from 1 [...]

### My Passion for Mathematics

By Anas Rahman, The University of Melbourne For as long as I can remember, I’ve enjoyed mathematics. I’ve always looked forward to learning new mathematics, and tackling new problems. I like it [...]

### Mathematics: The Science of Life

By Liam Polkinghorne, Queensland University of Technology Growing up, I never truly loved Mathematics. I’ve always been good at it but never found the spark to keep Mathematics in my life as a [...]

### Factorisation Fun

By Adrian Petersen, University of Western Australia My AMSI vacation research project was based upon factorisation. During school, everyone learnt the basic properties of factorisation. We [...]

### Big Data in Ice Hockey

By Stephen Pang, RMIT University ‘Big data’ refers to extremely large volumes of data that is difficult or impossible to analyse by a conventional means. In sports this refers to the vast amount [...]

### Getting ahead of the traffic

By Gilbert Oppy, Monash University Have you ever noticed how, on your regular commute to work/uni/school, you’ll be stuck in traffic at certain points of your journey but be moving freely at [...]

### The Dirichlet-to-Neumann Map

By Abraham Chi Shun Ng, University of Sydney Mathematics governs much of the observed and unobserved physical reality that surrounds us. However, the relationship between mathematics and the [...]

### Mathematical analysis, where amazing happens

By Tingyu Mao, UNSW Australia Banach space is currently a very basic concept in functional analysis as well as a common object under extensive research. A complete normed vector space is called a [...]

### Beginning from the small to the large and from simplicity to complexity

By Simon Lu, RMIT University Ants in a colony exhibits extraordinary behaviour, to such a degree that intense research has been placed in studying their social paradigms. Ant colonies achieve [...]

### Mathematical biology: biology is mathematics’ next physics

By Jiemi Lin, Monash University Many high school students and even university students choose to do biology because they are scared of the maths in other sciences such as physics. But as we [...]

### Mathematics – My Passion

By Tyson Liddell, Monash University Throughout my secondary education, for the most part, I thoroughly enjoyed mathematics and to this day I still recall vividly the first time I encountered the [...]

### Rohit Kumar’s Experience

By Rohit Kumar, RMIT University Since I entered primary school, I always had a passion for numbers and used to be strong at them. I was very quick with my addition, subtraction, multiplication [...]