My name is John Connell and at present I am in my third year of a Bachelor of Teaching with a Bachelor of Mathematics and Computer Science at the University of Adelaide. I hope to graduate as a high school Maths and Physics teacher at the end of 2015. In 2014 I worked to complete a Pure Maths major with a strong focus on analysis, one of my courses being Complex Analysis. After obtaining at ATAR of 99.95 in Year 12 and merits in Mathematical Studies, Chemistry, Physics and Specialist Mathematics, I was awarded an Adelaide Undergraduate Scholarship. My first year university results led me to being invited to join the Golden Key International Society. Ever since Year 12 I have been fascinated with complex numbers and especially visualizing functions of the complex variable. My other area of interest and passion is using technology to stimulate interest and engage all students in Mathematics and Science classrooms.
Visualising Complex Functions
Complex Functions have always held a fascination to the mathematical world as they contain properties, such as Cauchy’s theorem that are not present among real functions. Visualising these functions creates problems as they are a subset of a 4 dimensional space. However, some of the methods to overcome this problems include, dropping one of the variables to look at the projection in 3 space, using domain colouring in a two dimensional graph or using conformal mapping in two dimensions. These techniques form the basis for most types of mapping of complex valued functions.