I am a mathematics graduate with a first-class degree (with honours), and I run my own tutoring business whilst completing my master's degree in pure mathematics at the University of Melbourne. I am also a tutor in the mathematics department at the University of Melbourne, running white-board tutorials for Calculus 2 and Linear Algebra. So far I have tutored over 15 separate university mathematics subjects, as well as many high school students. I am deeply passionate about mathematics education as evidenced by my numerous talks and interactive classes I have given to undergraduate students, high school students and even the general public. I have self-learned the computer programming language Python to create 3-D animations that I utilised as a part of these talks to help visual learners. Throughout my first three years at university, I got A's in all of my 12 mathematics subjects. However, I found this to be very difficult and I felt that I had to constantly work hard to reach this goal. I had actually been out of higher education for over 5 years and had a poor high school mathematics education, so reaching this goal was quite difficult for me. As such, I had to relearn all of high school mathematics on my own, before returning to university. Once at university I always felt behind the curve, and that I had to work twice as hard as other students. Whilst this might not sound like the ideal path for becoming a tutor, on the contrary; I feel it has put me in a great position for tutoring, especially for students that find the subject naturally difficult. Since I have approached my own learning from the perspective of a struggling student, then I am readily able to recognise and even anticipate where issues of understanding and learning can come from, and how exactly to overcome them. I am currently employed by the school of mathematics and statistics as a mathematics tutor for Calculus 2 and Linear Algebra at the University of Melbourne. I have also been employed as a summer school mathematics tutor at the University of Glasgow in the UK. I have tutored high school mathematics for seven years, but for the past three years I have been tutoring the following university subjects: MAST10005 Calculus 1 MAST10006 Calculus 2 MAST10007 Linear Algebra Complex Analysis (MTH328 Charles Stuart University) Differential Equations and Mechanics (MATH 314 ACU) Advanced Mathematics for Economics and Social Science (20136 Bocconi University, Italy) Engineering Mathematics 3B (MTH20014 Swinburne University) Number Theory and Cryptography (MATH308 ACU) Linear Algebra for Data Analysis (SIT292 Deakin University) Discrete Mathematics (RMIT) Mathematics for Economics Linear Algebra for Data Analysis (SIT292 Deakin University) MAST30021 Complex Analysis MGMT90239 Business Analytics for Decision Making MAST20026 Real Analysis MAST30021 Complex Analysis MAST30024 Geometry I will be the volunteer subject coordinator for VCE specialist mathematics at the summer school organised by the University of Melbourne Student Union (UMSU) I have also given a 90-minute talk to high school students about university mathematics entitled "How to explore higher dimensions" and have written for the undergraduate mathematics magazine, introducing higher maths to interested undergraduates. I am giving a public talk/seminar aimed at the general public also on "How to explore higher dimensions". I have also had experience as a volunteer mathematics and English teacher in India for 4 months which developed my communication skills since many of the students had little to no knowledge of these subjects. Tutoring Approach: I believe that strong academic performance can be obtained through hard work together with good instruction. "Inherent ability" is nothing, I believe, but a result of these two important aspects. I pride myself on being able to both quickly identify the gaps in a students understanding, as well as how to effectively communicate these gaps to the student in a multitude of ways. For example, one can explain a concept visually with pictures, algebraically, by analogy with the real world, purely verbally or just in terms of other mathematics that one already knows. The key idea though is to patch each of these explanations together, showing how one relates to the other, as well as honing in on the way that makes the most sense for each student. Usually, there are at most one or two pieces of information that a student needs in order to understand a concept in mathematics. I believe that I am very good at identifying those missing pieces of information that the student needs in order to 'get it'. This skill came to me during my own degree where it took me a lot of work on my own before identifying the missing pieces for each concept. Whilst tutoring students I attempt to keep a 40:60 ratio of student speaking/writing to tutor instructing. Keeping the student interacting and speaking provides a perfect way to do two things simultaneously: 1) checking the student understands the material on the spot, and 2) as the student interacts with the material then they reinforce what we are covering to help with recall afterwards. I also emphasise mathematical spoken language, since writing and speaking involve two different parts of the brain. Interacting with the student via both mediums allows for the student to become a lot more comfortable with the abstract symbols, both in writing and reading. Once the student understands how to properly ‘talk’ mathematics, then reading it on their own (sub-vocalisation) becomes possible, and hence the symbols become much easier to handle and less daunting. I believe this is one of the (many) major aspects left out in high school education and can make the difference between being intimidated by the symbols or feeling comfortable with them.