#### Naturally Reductive Metrics on Homogeneous Spaces

Marcus Flook

The University of Queensland

A smooth manifold is a topological space which locally resembles a Euclidean space, allowing us to perform calculus. Curves in ...

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#### Music > Notes Played

Anthony Warwick

Western Sydney University

Many people associate the word ‘mathematics’ with a palpable sense of dread, but there is a lot that can be ...

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#### Population Heterogeneity and COVID-19

Tianze Wei

University of Wollongong

For well over a year, the current COVID-19 pandemic has transformed the way we live, resulting in over one hundred ...

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#### Cats and the Quantum Measurement Problem

Alex Paviour

University of Wollongong

Is the cat in the box alive or dead? In fact, until we look at it, both. By the mid-1920s, ...

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#### From Games to Mathematics

John Cu

University of Technology Sydney

As a child, I loved video games. I could spend all day just sitting in front of the computer screen ...

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#### Nanoscale Droplets

Benjamin Babu

University of South Australia

My project focused on nanoscale droplets (extremely small droplets), more specifically, nanoscale oil droplets that are on a flat surface ...

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#### Building Good Policy with Data

Luke Thomas

The University of Western Australia

Australia faces unprecedented challenges over the coming decade. We need to fight off COVID-19 and rebuild the economy. We need ...

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#### On the Joys of Mathematics Education

Joshua Crawford

The University of Western Australia

It’s incredible to think how my view on mathematics has changed over the last ten years, and It couldn’t have ...

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#### Modelling Complicated Things Might Not Be So Complicated

Jack Mulqueeney

The University of Western Australia

Over the summer, I investigated how effective stochastic modelling methods can be in modelling overly complicated physical behaviour. Using fairly ...

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#### Characterising Geometric Objects

Youheng Yao

The University of Sydney

The problem of characterising geometric objects is always interesting. In a three dimensional space, we can characterise a compact surface ...

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#### Probability in Mathematics

Andrew Rajchert

The University of Sydney

Probability is almost always treated as an entirely separate field of mathematics, more akin to statistics and not treated in ...

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#### The Forests of Research

Dibyendu Roy

The University of Sydney

Mathematical research is unique in that it is physically accessible to anyone with pen and paper but also so abstract ...

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#### Collaboration in Climate Modelling

Elizabeth Rose

The University of Sydney

Mathematical models are incredibly powerful tools that use the relationships between variables to understand how a system will evolve. One ...

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#### The Box-Ball System

Benjamin Solomon

The University of Queensland

The box-ball system is a discrete dynamical system composed of a finite number of balls in an infinite line of ...

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#### How to Handle Correlated Data

Wilson Lorensyah

The University of Queensland

In simplest term, linear model can describe a continuous response variable as a function of predictor variables. For example, a ...

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#### Mathematical Creativity

Bowen Parnell

The University of Newcastle

When trying to create an artwork, you are often trying to send a message. The purpose of your art might ...

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#### The Puzzle of Mathematics

Cameron Shaw-Carmody

The University of Newcastle

My interest in mathematics is so much a part of my life that it is difficult to know how or ...

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#### Why Maths?

Sona Reddy

UNSW

Beauty, creativity and... maths? Most people do not associate being creative and expression with mathematics, when speaking of creativity, we ...

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#### The Solid of Minimal Resistance

Juan Avila Molina

UNSW

What is the first thing we envision when we think of something aerodynamic? A sports car, maybe? A bullet train, ...

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#### What’s the Most Painless Way to Implement a Large Search on a Computer?

Tiana Tsang Ung

UNSW

In this AMSI project, the solution I found was simply to avoid implementing the search completely. Instead, code was written ...

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#### The Sum of Its Parts

Saleh Naghdi

The University of Melbourne

Say, what’s so natural about the natural numbers, that is, {1, 2, 3, …}? Well, you might agree with me ...

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#### Rules Governing the Motion of Ground-Feeding Galahs

Rebecca Rasmussen

The University of Melbourne

Have you ever wondered how flocks of birds or schools of fish can move so well as a group? Research ...

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#### How I Fell in Love with Machine Learning

Gyu Hwan Park

The University of Melbourne

What is machine learning? Why is it so interesting? Will the advancements in these technologies lead to the development of ...

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#### The Strong Law of Small Numbers

Michael Law

The University of Melbourne

According to the Strong Law of Small Numbers: ‘There aren’t enough small numbers to meet the many demands made of ...

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#### Intensive Care Units Behaving Strategically

Ashley Hanson

The University of Melbourne

Many large hospitals include an intensive care unit (ICU) for the care and treatment of patients who are critically ill ...

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#### Bayesian Statistics and the Intuition Behind Thinking in Context

Meg Tully

The University of Melbourne

My blog post briefly summarises an interesting example used to teach students about application of conditional probabilities—the high rates of ...

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#### Influence Online

Bridget Smart

The University of Adelaide

Fake news, misinformation, echo chambers—recently, these words have been popping up in our news articles. But what do they mean ...

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#### The Joys and Pains of Real Data

Liam Blake

The University of Adelaide

Experimental data allows mathematicians to verify their results and understand and predict the world around us. However, real data brings ...

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#### My Maths Journey

Ngoc Phuong Van Nguyen

Swinburne University of Technology

I have been studying and have interest in mathematics since the age of seven years old. I continuously achieved many ...

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#### How I Became a Mathematician

Joshua Rogers

Swinburne University of Technology

Mathematics isn’t something that many people choose to do, but it is a necessity of life. From counting change at ...

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#### My Journey in Maths

Eamonn Kashyap

RMIT University

Maths has been in my life in many forms over the years, throughout primary school, high school, leisure, and university ...

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#### My Vacation Research Scholarship Summer Project

Cameron Mclaren

RMIT University

I feel that this research project has broadened my horizons. I have wandered through the desert of coursework and have ...

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#### Don’t Be Afraid of Maths!

Angus Walsh

RMIT University

While I was homeschooled I was free to direct my own learning. One of my hobbies was card games, and ...

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#### How Mathematics Became My Personality

Montana Wickens

Queensland University of Technology

A raw recount of my childhood encounters with mathematics and how small, insignificant events made huge impacts. By the age ...

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#### Inference for a Complex World

Abhishek Varghese

Queensland University of Technology

A quick glance at the United Nations list of global issues here shows us the myriad of complex and diverse ...

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#### Making Elective Surgery More Equitable and Transparent

Jack Powers

Queensland University of Technology

Elective surgery is a fundamental part of any modern-day health care system. If a patient requires elective surgery in the ...

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#### A Tale of Two Disciplines

Monica Seeber

Murdoch University

Some people think philosophy and mathematics don’t mix. Those people are wrong. By the time I began my final year ...

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#### People of Mathematics

Aram Perez

Monash University

Mathematics is exciting and all, but I’d like to discuss some of the people in mathematics. Growing up I found ...

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#### My Journey Towards Mathematics

Jiayu Li

Monash University

I grew up with the doubts about my ability to do maths as a girl by hearing the voices from ...

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#### Why I Make My Life More Problematic

Jacob Vandenberg

Monash University

Since restrictions have lifted, I have had the chance to do an escape room with a few of my friends ...

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#### Can Machine Learning Predict Complex Time-Series Models?

Gaurangi Gupta

Macquarie University

We know humans learn from their past experiences and machines follow instructions given by humans, but what if humans can ...

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#### Exploring Exotic Probability Theory

Ashley (Yannan) Lin

Macquarie University

It is universally acknowledged that the Kolmogorov probability axioms are the foundations of classical probability theory. The first axiom states ...

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#### Where Finance and Mathematics Come Together

Peter Nguyen

Macquarie University

Mathematics exists everywhere around us. Almost all greatest achievements of mankind have been built on the foundation of Mathematics, more ...

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#### Fighting Viruses with Numbers?

Kristian Caracciolo

La Trobe University

Whenever science is mentioned in the context of viruses and disease, it’s likely that the first image that comes into ...

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#### My VRS Project

Nauvoo Perez

La Trobe University

I often feel as if mathematics is extremely far removed from real life. However, sometimes there are surprise instances where ...

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#### Where Mathematics Meets Biology

Susanna Grigson

Flinders University

Mathematics is valuable to our understanding of the living world around us. Throughout history mathematics has been used to solve ...

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#### Our World Is a Function

Bob La

Deakin University

No! Really! This world can all be considered as a function if you think deeply enough. After all, in the ...

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#### My Mathematical Journey

Ponpot Jartnillaphand

Curtin University

When I was in elementary school, I took extra tutorial classes of mathematics as I found mathematics interesting. Mathematics generally ...

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#### The Complexity of Entanglement

Nick Bermingham

Australian National University

Entanglement as a concept is simultaneously plainly obvious and quite abstract. Anyone can look at an object or a drawing ...

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#### How I Became Interested in Mathematics

Pavel Stoilescu

Australian National University

Although I now spend the majority of my waking hours doing something mathematics-related, this wasn’t always so; mediocre high-school teachers ...

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#### Maths to Physics and Beyond

Lucky Antonopoulos

RMIT University

At the age of 17 years old, I had begun to find interest in mathematics and the sciences, thanks to ...

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#### Bouncing Balls on Oscillating Tables

Julian Ceddia

La Trobe University

I know what you’re thinking… “Bouncing balls? Bouncing balls on oscillating tables? Err.. ok… cool project man. Take the easy ...

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#### Groups and Abstraction

Rohan Hitchcock

University of Western Australia (The University of Melbourne)

Consider a square. How can we transform the square so that its shape doesn't change? One way we can do ...

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#### Researching NLP Techniques

Daniel Stratti

Western Sydney University

I enjoyed the AMSI Vacation Research Scholarship project. It allowed me to explore the mathematical formulation of a wide array ...

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#### Why I Became Interested in Mathematics

Luke Robinson

University of Western Australia

I became interested in mathematics halfway through my first year at University. I had originally planned to do a Bachelor ...

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#### Group Theory

Aaron Jenkins

University of Western Australia

Group theory is an important topic in pure mathematics that has many different applications. Examples of mathematical groups are all ...

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#### Identifying Influential Molecular Factors of Wheat Genomes

Timothy Chapman

University of Western Australia

Wheat is the world's most prevalent food source. An improved understanding of how molecular parameters affect the physical characteristics can ...

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#### Inner Product Spaces on Subsets of the Powerset of Riemannian Manifolds

David Perrella

University of Western Australia

The original title for this project was “Subsets of the powerset of R^n as inner product spaces”. Meaning I wanted ...

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#### Stochastic Differential Equations

Rory Jacques

University of Technology Sydney

When we hear symmetries we think of geometry. A symmetry of a shape is a manipulation or transformation of the ...

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#### What I Wish I’d Known

Alexander Hiller

University of Technology Sydney

There are three realisations I have come to me over my summer of research that I wish I knew at ...

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#### Machine Learning in the Age of Big Data

Alex Oakley

University of Tasmania

The amount of data in the world is growing exponentially. The question is, can we use machine learning to find ...

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#### Why I Study Maths

Nicholas Maurer

University of Queensland.

How did I end up studying mathematics? What are some of the lessons I have learnt along the way? This ...

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#### The Rise of Machine Learning

Jonathan Wilton

University of Queensland

When the topic of Machine Learning arises, it is often accompanied by topics such as artificially intelligent terminator robots taking ...

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#### How Best to Model Diffusion?

Dylan Green

University of Wollongong

What is diffusion and how can it be described using mathematics? While scientists and mathematicians have put a lot of ...

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#### The Galerkin Method

Dean Noble

University of Wollongong

This blog post was written in February of 2020. The post introduces and explains the purpose of the Galerkin method ...

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#### Fredholm Operators

Dion Nikolic

University of Wollongong

Throughout this project I studied Fredholm operators (a certain subset of bounded linear operators) and used them to study the ...

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#### Pure Maths and Computer Science

Amelia Lee

University of Wollongong

Pure mathematics and computer science intersect more than the people in either field would have you believe. As a software ...

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#### Bragg Edge Neutron Strain Tomography

Thomas Vandenberg

The University of Newcastle

Weaknesses in materials can arise from a variety of sources. If too much force or heat is applied to a ...

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#### What We Can Learn From Effect Size

Mikayla Goodwin

The University of Newcastle

In simple terms, effect size is the quantifiable differences between two population parameters. While frequently overlooked in many statistical readings, ...

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#### “So What Have You Actually Been Doing as a Mathematics Researcher?”

Luke Yerbury

The University of Newcastle

I have been in pursuit of answers to difficult questions throughout the course of this summer research project. When not ...

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#### Time-Series Analysis

Thomas McCarthy McCann

The University of Newcastle

A time series is a collection of random variables indexed according to the order in which they are observed in ...

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#### Symmetry Actions

Jack Berry

The University of Newcastle

The concept of symmetry gives rise to a pervasive field of interest within the mathematical community with direct applications to ...

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#### Connected Graphs

Aditya Joshi

The University of Newcastle

A graph is a collection of nodes (called vertices), some of which are joined together by edges. Connected simple graphs ...

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#### Approximation

Zhou Dai

University of New England

Maths is about approximation. Starting by Calculus, Maclaurin and Taylor series are about how to approach or estimate a function ...

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#### Curve-Shortening Flow and Grayson’s Theorem

Nicholas Garrett

University of New England

Over the course of my project, what I found was most interesting was all the unexpected interconnections and relations that ...

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#### Modelling Language Representations

Ana-Maria Vintila

University of New England

Vast amounts of knowledge are trapped in presentation media such as videos, html, PDFs, and paper as opposed to being ...

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#### Research Project Takeaways

Yee Chin

The University of Sydney

Hello! This project was my first real Mathematics research project, so I’m excited to tell you about my experience working ...

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#### What Is Mathematical Research, Anyway?

Tony Wang

The University of Sydney

For many years, and even now, the world of mathematical research was shrouded in mystery. What do people work on ...

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#### Permutations

Steven Condell

The University of Sydney

Permutations are interesting mathematical objects, with many different applications. One use of permutations is as a tool for encrypting secret ...

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#### Mademoiselle Who Bid Science Farewell Back to Sell Single Cell

Samantha Chew

The University of Sydney

Having given up all science subjects since the beginning of university, doing a research project about precision medicine was quite ...

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#### The Emotive Qualities of Mathematics

Martin Gossow

The University of Sydney

The abstract artist Agnes Martin once lamented: ‘from music people accept pure emotion, but from art they demand explanation’. A ...

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#### Not Everyone Dreams in Mathematics

Kenneth Guo

The University of Sydney

Not once have I ever drifted off while thinking about a problem and woke up with the solution. Not once ...

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#### A Short Journey Through My VRS Project

Cameron Eggins

The University of Sydney

A short journey through my VRS project, including all my difficulties and achievements. While the project did not go as ...

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#### Modelling T-Cell Proliferation

Holly Casey

Swinburne University

Over the summer I was given the opportunity to study T-cell proliferation using an original model I wrote in MATLAB ...

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#### Human Computer

Stephanie Fuser

RMIT University

I just heard the news that Katherine Johnson had died a few days before writing. For those who are not ...

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#### Why I Am Learning as Much Mathematics as Possible

Bayan Khalili

RMIT University

We live in an era of “fake news” and false advertising. But then again, fake news has a LONG history, ...

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#### My Journey Through Mathematics

Stefano Giannini

Queensland University of Technology

I have always been interested in mathematics, as a young primary school student mathematics was simple arithmetic, that is, addition, ...

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#### Lattice Frames for Artificial Skin

Reuben Hill

Queensland University of Technology

3D printing is a relatively new invention that could prove to be the next printing press when it comes to ...

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#### Advanced Bayesian Statistical Inference Methods for Simulation-Based Models in Cell Biology

Michael Carr

Queensland University of Technology

Understanding the parameters which govern the cell cycle and spread of cells has wide impacts in many areas. One being ...

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#### The Journey to Enlightenment Through Mathematics

Joshua Wilson

Queensland University of Technology

What does mathematics mean to me and my life? I discuss how my journey with mathematics has led me to ...

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#### Diffusion-Decay Problems

Jonah Klowss

Queensland University of Technology

You might wonder why your coffee cools down more in the first 5 minutes after you’ve made it than it ...

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#### My Journey Towards Research

Caren Rattray

Queensland University of Technology

I chose the Bachelor of Mathematics at QUT for several reasons. Primarily because my OP was above the prerequisite, and ...

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#### How to Get the Most Out of Electropherograms

Louise Branch-Smith

Murdoch University

A DNA profile is valuable to eliminate certain persons of interest from a forensic case. They do not prove that ...

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#### Refining Clinical Thresholds for Diagnosing Equine Pituitary Gland Dysfunction

George Malone

Murdoch University

After a spur-of-the-moment decision to apply for the AMSI Vacation Research Scholarship, this student learned about a long-known condition in ...

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#### What Is the Dimension of a Network?

Will Veenman

Monash University

My research focused on answering what the typical metric dimension of a network is by probabilistic methods. Networks are structures ...

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#### Four Vertex Theorem and Its Converse

Jia Jia Qian

Monash University

Curves are fundamental objects in differential geometry. The simplest examples are ones which lie in a plane; curves that we ...

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#### The Finite Element Method

Connor Mallon

Monash University

This blog intends to introduce the general ideas behind the finite element method as a means of finding numerical solutions ...

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#### Game Theory

Baihe Zhang

Monash University

As a student now embarking on the way to researching in mathematics, I gradually find that I would not make ...

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#### Modelling Gene Expression Data

Yong See Foo

The University of Melbourne

My summer research consisted of comparing the performance of different statistical methods for sparse factor models. Sparse factor models are ...

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#### How I Came to Study Fluid Mechanics

Matthew Walker

The University of Melbourne

To quote the great David Byrne, ‘how did I get here?’ Did mathematicians always want to be mathematicians? Well, some ...

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#### My Research Project

Kulunu Dharmakeerthi

The University of Melbourne

A brief introductory note into the contents of my AMSI research. We discuss the motivation for the project, as well ...

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#### Betting on Maths

Matthew Hanna

Macquarie University

Everyone has their lovingly reminisced tale of their first love with mathematics. Mine is a little different. A bet made ...

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#### The Rewards of Maths

Grace Klimek

La Trobe University

My research project was on Group Theory and tiling problems. I had quite a bit of fun working on it, ...

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#### There Is Always a Faster Way to Perform Your Calculations

Daniel Roberts

La Trobe University

My project looked at the risks of refusing vaccination. One of the things I came to appreciate was the importance ...

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#### The VRS Journey

An Ky Duy Nguyen

La Trobe University

Mathematics has not always been my passion; in fact, quite to the opposite. I used to hate Maths during my ...

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#### My VRS Experience

Aidan Brohm

La Trobe University

Last year I finished my 2nd year of studies and up until that point I had never had an experience ...

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#### Programming and Mathematics

Duong Thuy Dung Le

Deakin University

Mathematics was a nightmare for me when I was in secondary and high school. I have chosen programming as my ...

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#### The Stable Marriage Problem

James Morgan

The Australian National University

Can we always pair two groups of people together in such a way that there is no mutual incentive for ...

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#### A Topos? Puzzles!

Yuchen Jiang

The University of Adelaide

Take a moment and think about your childhood science classes. Remember how your teacher showed you how to make batteries ...

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#### PDE Discovery with Machine Learning

Sean McGowan

The University of Adelaide

In science, engineering and mathematics we often seek models of real-life dynamics to better our understanding and help predict behaviour ...

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#### Entropy, Elvish and the New Testament

Megan Crossing

The University of Adelaide

Abstract: Have you ever wondered how realistic Tolkien’s languages really are? Or how might they differ statistically from natural languages? ...

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#### Fixing Sore Knees: Mechanics of Articular Cartilage

Lin Jiang

The University of Adelaide

Articular cartilage is a mechanically strong tissue found in joints (knee, hip) that acting as a lubricating surface to prevent ...

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#### Modelling Electrospun Fibres Using Differential Equations

Jesse Tonkin

The University of Adelaide

Mathematical modelling involves an incredible range of powerful techniques that can be used to describe and predict real-world phenomena. One ...

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#### Mathematical Modelling of Post-Transcriptional Regulation of Gene Expression

Eunice Blessica Yuwono

The University of Adelaide

Mathematical Modelling of Post-Transcript…”, what does the title even mean? Read on to decipher the title as well as to ...

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#### Using Mathematics to Untangle World War One Documents

Christina Tait

The University of Adelaide

Abstract As a student who has studied both mathematics and history it has become quite apparent that the two subjects ...

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#### Do the rich get richer on Reddit?

Alexander Lai De Oliveira

University Of Adelaide

Until starting the Vacation Research Scholarship, I had only used MATLAB and R when writing code. At the recommendation of ...

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