Neuroscience

A comprehensive graduate-level course on neuroscience—from neural coding and synaptic transmission through systems neuroscience, computational models, brain imaging, and brain-computer interfaces.

Course Overview

Neuroscience spans the study of individual neurons to the emergent properties of neural circuits and whole-brain systems. This course integrates cellular, systems, and computational perspectives to provide a unified understanding of how the brain processes information, generates behavior, and gives rise to cognition.

What You'll Learn

  • • Neural coding and information processing
  • • Synaptic transmission and plasticity
  • • Neural circuits and sensory processing
  • • Motor systems, learning, and memory
  • • Decision making and consciousness
  • • Computational models of neural systems
  • • Brain imaging and connectomics
  • • Brain-computer interfaces and neural engineering

Prerequisites

  • • Biology fundamentals (cell biology)
  • • Basic chemistry and biochemistry
  • • Calculus and linear algebra
  • • Probability and statistics
  • • Programming basics (helpful)

References

  • • E. R. Kandel et al., Principles of Neural Science (6th ed.)
  • • P. Dayan & L. F. Abbott, Theoretical Neuroscience
  • • W. Gerstner et al., Neuronal Dynamics
  • • M. F. Bear, B. W. Connors & M. A. Paradiso, Neuroscience: Exploring the Brain

Course Structure

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Part I: Neural Basics

Neural coding, synaptic transmission, neural circuits, and sensory processing.

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Part II: Systems Neuroscience

Motor systems, learning and memory, decision making, and attention and consciousness.

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Part III: Computational

Computational models, neural networks, brain imaging, and connectomics.

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Part IV: Applied Neuroscience

Neurological disorders, neuropharmacology, brain-computer interfaces, and neural engineering.

Key Equations

Hodgkin-Huxley Equation

$$C_m \frac{dV}{dt} = -g_{\text{Na}} m^3 h (V - E_{\text{Na}}) - g_{\text{K}} n^4 (V - E_{\text{K}}) - g_L (V - E_L) + I_{\text{ext}}$$

Describes action potential generation in neurons

Cable Equation

$$\lambda^2 \frac{\partial^2 V}{\partial x^2} - \tau \frac{\partial V}{\partial t} = V$$

Passive signal propagation along dendrites and axons

Spike Train Information

$$I = \int P(r) \log_2 \frac{P(r)}{P_0(r)} \, dr$$

Mutual information between stimulus and neural response

STDP Learning Rule

$$\Delta w = \begin{cases} A_+ e^{-\Delta t / \tau_+} & \text{if } \Delta t > 0 \\ -A_- e^{\Delta t / \tau_-} & \text{if } \Delta t < 0 \end{cases}$$

Spike-timing-dependent plasticity: synaptic weight change

Drift-Diffusion Model

$$dx = A \, dt + c \, dW$$

Accumulation of evidence for perceptual decision making

BOLD Signal Model

$$y(t) = (h * u)(t) + \epsilon = \int_0^t h(\tau) \, u(t - \tau) \, d\tau + \epsilon$$

Hemodynamic response convolution in fMRI