The Kohonen self organizing mapping algorithms. Nearest neighbor algorithms. One current topic includes the use of a neural network to learn elementary arithmetic. Research project in neural modelling. This is the most important part of the course and will form the major part of your grade, if such things concern you.
Neural networks are tools to be applied to problems.
You should be thinking about what you want to do all during the term. An Introduction to Neural Networks, James A. Anderson, MIT Press. A good book on linear algebra is useful. There are any number of good text books. This book is designed for graduate level engineers and is difficult but very good on the mathematical analysis of algorithms.