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.

The following topics will be covered:

1.Mathematical theories for ion channels and membrane potential.

2.Computational models for single neurons at different levels of details.

3.Analyzing behavior of single neurons using theories of dynamical systems

(attractors, bifurcation etc).

4.Dynamics and functions of neural circuits.

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 of neural simulations.

五、教學進度(Syllabus)

[09/18] Introduction

[09/25] Membrane potential, nernst equation & leaky integrate-and-fire model

[10/02] Leaky Integrate-and-fire model & synapse

[10/09] Channel dynamics & Hodgkin-Huxley model

[10/23] Signal propagation in single neurons, Poisson noise

[10/30] Neural network simulators: current state & issues

[11/06] Dynamical systems – introduction

[11/13] Single neuron dynamics: stability, attractor & bifurcation

[11/20] Matrix algebra, eigenfunction & eigenvalues

[11/27] Binary model, rate-based model and simple networks

[12/04] Recurrent network: states and stability

[12/11] Oscillation

[12/18] Memory

[12/25] Synaptic plasticity & Hebbian learning

[01/08] Conditioning & reinforcement learning

六、成績考核(Evaluation)

1.Attendance, preparation, participation

2.Homeworks (bi-weekly) (60%)

3.Final project (40%)