Naturally Reductive Metrics on Homogeneous Spaces

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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Why Maths?

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

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?

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

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

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

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

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

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

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

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

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

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

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

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

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!

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

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

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

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

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

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

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

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?

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

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

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?

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

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

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

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

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

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

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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Kanellos Antonopoulos

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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Julian Ceddia

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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Rohan Hitchcock

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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Daniel Stratti

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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Luke Robinson

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

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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David Adams

Nexting

David Adams
University of Western Australia
I find it inspiring how Mathematicians distill down aspects of real life in to an applicable and usually generalizable understanding ...
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Timothy Chapman

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

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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Rory Jacques

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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Alexander Hiller

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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Alexander Oakley

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

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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Jonathan Wilton

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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Dylan Green

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

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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Dion Nikolic

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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Amelia Lee

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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Thomas Vandenberg

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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Mikayla Goodwin

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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Luke Yerbury

“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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Thomas McCarthy McCann

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

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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Aditya Joshi

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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Zhou Dai

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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Nicholas Garrett

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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Ana-Maria Vintila

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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Yee Chin

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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Tony Wang

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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Steven Condell

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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Samantha Chew

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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Martin Gossow

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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Kenneth Guo

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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Cameron Eggins

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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Holly Casey

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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Stephanie Fuser

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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Bayan Khalili

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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Stefano Giannini

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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Reuben Hill

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

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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Joshua Wilson

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

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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Caren Rattray

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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Louise Branch-Smith

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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George Malone

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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Will Veenman

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

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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Connor Mallon

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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Baihe Zhang

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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Yong See Foo

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

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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Kulunu Dharmakeethi

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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Matthew Hanna

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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Grace Klimek

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

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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An Ky Duy Nguyen

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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Aidan Brohm

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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Duong Thuy Dung Le

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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James Morgan

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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node-with-self-loop

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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Sean McGowan

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

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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Lin Jiang

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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Jesse Tonkin

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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Eunice Blessica Yuwono

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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Christina Tait

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?

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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