一、課程說明(Course Description)
<br>Being the most complex matter in the universe, the brain is a dynamical system 
<br>consisting of more than 100 billion interaction neurons. To understand  how 
<br>brain works, it is essential to understand mathematical theories and 
<br>computational models developed for neurons and neural circuits. This course will 
<br>provide an introduction to theories and models in neuron- and circuit-level 
<br>neuroscience for beginning graduate students. The goal is to understand how 
<br>individual neurons work and how functions of neural circuits are achieved 
<br>through interacting neurons. 
<br>
<br>The following topics will be covered: 
<br>1.Mathematical theories for ion channels and membrane potential.
<br>2.Computational models for single neurons at different levels of details.
<br>3.Analyzing behavior of single neurons using theories of dynamical systems 
<br>(attractors, bifurcation etc). 
<br>4.Dynamics and functions of neural circuits.
<br>
<br>Students should have basic knowledge in calculus, physics and  differential 
<br>equations.
<br>
<br>
<br>二、指定用書(Text Books)
<br>
<br>1.Peter Dayan & L. F. Abbott. Theoretical Neuroscience: Computational and 
<br>Mathematical Modeling of Neural Systems.  The MIT Press (2005)
<br>2.Eugene M. Izhikevich. Dynamical Systems in Neuroscience: The Geometry of 
<br>Excitability and Bursting. The MIT Press (2006)
<br>
<br>
<br>三、參考書籍(References)
<br>
<br>1.Christof Koch and Idan Segev. Methods in Neuronal Modeling: From Ions to 
<br>Networks. The MIT Press (1998).
<br>2.Wulfram Gerstner, Werner M. Kistler. Spiking Neuron Models. Cambridge 
<br>University Press (2002)
<br>3.Fred Rieke, David Warland, Rob de Ruyter van Steveninck, William Bialek. 
<br>Spikes: Exploring the Neural Code. The MIT Press (1996) 
<br>
<br>
<br>四、教學方式(Teaching Method)
<br>1.Lecture supplemented with computer demonstrations of neural simulations. 
<br>
<br>
<br>五、教學進度(Syllabus)
<br>
<br> [09/18] Introduction
<br> [09/25] Membrane potential, nernst equation & leaky integrate-and-fire model
<br> [10/02] Leaky Integrate-and-fire model & synapse
<br> [10/09] Channel dynamics & Hodgkin-Huxley model
<br> [10/23] Signal propagation in single neurons, Poisson noise
<br> [10/30] Neural network simulators: current state & issues
<br> [11/06] Dynamical systems – introduction
<br> [11/13] Single neuron dynamics: stability, attractor & bifurcation
<br> [11/20] Matrix algebra, eigenfunction & eigenvalues
<br> [11/27] Binary model, rate-based model and simple networks
<br> [12/04] Recurrent network: states and stability
<br> [12/11] Oscillation
<br> [12/18] Memory
<br> [12/25] Synaptic plasticity & Hebbian learning
<br> [01/08] Conditioning & reinforcement learning
<br>
<br>
<br>六、成績考核(Evaluation)
<br>1.Attendance, preparation, participation
<br>2.Homeworks (bi-weekly) (60%)
<br>3.Final project (40%)
<br>