University of Sydney

This course examines the field of mathematical analysis both with a careful theoretical framework as well as selected applications. It shows the utility of abstract concepts and teaches an understanding and construction of proofs in mathematics. The course starts with the foundations of calculus and the real numbers system. It goes on to study the limiting behavior of sequences and series of real and complex numbers. This leads naturally to the study of functions defined as limits and to the notion of uniform convergence. Returning to the beginnings of calculus and power series expansions leads to complex variable theory: elementary functions of complex variable, the Cauchy integral theorem, Cauchy integral formula, residues and related topics with applications to real integrals.

This course introduces students to the theoretical and practical aspects of sport and exercise coaching. Through active participation in lectures, tutorials and practical workshops, students learn how to create a positive sporting environment by utilizing athlete-centered coaching strategies. Students also learn how to evaluate and improve their own coaching performance by applying reflective and evaluative skills. Topics covered include coaching, training and management principles, coaching pedagogy, planning, skill learning and sports psychology. Students also complete the beginning coaching general principles course. At the completion of this course, students are more confident and knowledgeable in their coaching practice.

This course examines the online technologies, platforms and industries at the heart of constant economic and social changes. It covers key skills in analysis, evaluation and critique of these objects, situated in a historical context. It also interrogates the implications of emerging internet worked phenomena such as the internet of things, augmented reality and algorithmic cultures.