Being the most complex matter in the universe, the brain is a dynamical system consisting of more than 100 billion interaction neurons. To understand how brain works, it is essential to understand mathematical theories and computational models developed for neurons and neural circuits. This course will provide an introduction to theories and models in neuron- and circuit-level neuroscience for beginning graduate students. The goal is to understand how individual neurons work and how functions of neural circuits are achieved through interacting neurons.

Continuing what we have covered in the previous semester, the following topics will be covered this semester:

1.Analyzing behavior of single neurons using theories of dynamical systems (attractors, bifurcation etc).

2.Dynamics and functions of neural circuits.

3.Examples of neural network models from several representative research papers.

Students should have basic knowledge in calculus, physics and differential equations.

二、指定用書(Text Books)

1.Peter Dayan & L. F. Abbott. Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems. The MIT Press (2005)

2.Eugene M. Izhikevich. Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. The MIT Press (2006)

三、參考書籍(References)

1.Christof Koch and Idan Segev. Methods in Neuronal Modeling: From Ions to Networks. The MIT Press (1998).

2.Wulfram Gerstner, Werner M. Kistler. Spiking Neuron Models. Cambridge University Press (2002)

3.Fred Rieke, David Warland, Rob de Ruyter van Steveninck, William Bialek. Spikes: Exploring the Neural Code. The MIT Press (1996)

四、教學方式(Teaching Method)

1.Lecture supplemented with computer demonstrations for neural simulation.

2.Oral presentations for selected research papers and term projects by students.

3.Offered in English.

六、成績考核(Evaluation)

1.Attendance, preparation, participation

2.Homeworks (30%)

3.Oral presentations (30%)

4.Final project (40%)