N J Wildberger


School of Maths UNSW Sydney 2052 Australia


Tel:61 (02) 9385 7098

Fax:61 (02) 9385 7123


Yale, Stanford and Toronto

As an undergraduate at the University of Toronto I tutored first year maths (Calculus and Algebra) in both my third and fourth years. As a PhD student at Yale University I taught several classes of Calculus. I taught for two years at Stanford University (1984-1986) and for three years at the University of Toronto (1986-1989), where besides calculus and linear algebra, I taught group theory, differential equations, vector calculus and algebra. In 1990 I arrived at UNSW in Sydney Australia, where I am currently Associate Professor.


I have been teaching at UNSW since 1990, generally have excellent teaching evaluations, and have played an important role in structuring courses in Pure mathematics at UNSW.

To lower years I have taught Calculus, Linear Algebra (Higher and Ordinary), Discrete Mathematics, Vector Calculus, Higher Geometry, Differential Geometry, Logic and Computability, Higher Real Analysis, Higher Complex Analysis and probably some others I can't remember.

Fourth year (honours) courses I have designed and taught here over the years include Algebraic Number Theory, Advanced Combinatorics, Information theory and Codes, Lie groups, Algebraic Topology, Representation theory, and Themes of Classical Mathematics and Geometry.

In 2007 I taught (and was in charge of) the engineering course MATH2069 Maths 2A which includes Complex Analysis and Vector Calculus. I taught the Complex Analysis strand, using Saff and Snider as a textbook.

I also taught MATH5785 Geometry, which was a special treat for me, as I used my recent book `Divine Proportions: Rational Trigonometry to Universal Geometry' as a text. We did Euclidean geometry (the correct way, using quadrance and spread so that all theorems hold over a general field), projective geometry, spherical/elliptic geometry and hyperbolic geometry. Even these latter subjects can be described purely algebraically, and doing so clarifies them considerably. This is a very important point that anyone interested in geometry should attempt to understand.

Next session I will be teaching MATH1241 Higher Linear Algebra.

Teaching ideas

In my opinion here are the keys to successful mathematics teaching at the university level, in order of importance. These might be useful to young lecturers who are starting out on their teaching careers.

  • Content
    The fundamental requirement for succesful teaching (actually at any level) is to have something to teach. In mathematics, this means content that is accessible, useful and interesting. Material should be aimed at the appropriate level for students, it should be seen to be useful by them, and it should stimulate them at the same time. All three aspects are necessary, and getting the balance right is not easy. Well chosen examples are particularly important for mathematics teaching.

  • Preparation
    The second most important factor for succesful mathematics teaching is careful preparation. You must know the material, have your examples worked out beforehand, and have thought about how best to structure the content, both at the global and local levels.

  • Delivery
    The third most important factor is effective delivery. Without distorting your natural self, you should strive to be enthusiastic, friendly, and to talk and write clearly. There are many specific skills to be learnt in this direction.

  • Action
    Mathematics is an active subject. Students learn not only by reading and listening, but also by writing and more crucially by doing. It is thus valuable to structure mathematics learning so as to provide opportunities for students to take lecture notes, work actively in solving problems, and to write up and discuss solutions.

  • Resources
    The right tools make any job easier. A well-designed book is an important aid in succesful long term learning, particularly if written by an expert who has thought deeply about how to best structure the subject. Be skeptical about the merit of quickly put together notes, especially common on the web.

sure you have prepared and worked these out carefully.