Theoretical Neuroscience

Course Description

Are you fascinated by the intricate workings of the human brain? Do you want to unravel the mysteries behind decision-making, memory recall, and perception? Welcome to the cutting-edge world of Theoretical Neuroscience! This advanced course delves deep into the mathematical and computational models that explain how our brain functions at a neural level. You'll explore the collective dynamics of thousands of interacting neurons and learn how to analyze these complex systems using sophisticated mathematical techniques.

What Students Will Learn

  • Analyzing connected networks in the mean-field limit
  • Formalizing biological facts into mathematical models
  • Understanding simple mathematical models of memory formation in the brain
  • Comprehending mathematical models of decision processes
  • Grasping cortical field models of perception

Pre-requisites

To succeed in this course, you should have a strong foundation in:

  • Calculus
  • Differential equations

These should be at the level typically acquired in a bachelor's degree in physics, mathematics, or electrical engineering.

Course Content

  • Associative Memory and Hopfield Model
  • Attractor networks and spiking neurons
  • Neuronal populations and mean-field theory
  • Perception and cortical field models
  • Decision making and competitive dynamics
  • Synaptic Plasticity and learning

Who This Course Is For

  • Graduate students in neuroscience, physics, mathematics, or computer science
  • Researchers looking to expand their knowledge in theoretical neuroscience
  • Professionals in fields such as artificial intelligence or cognitive science seeking to understand brain-inspired computing

Real-World Applications

  • In neuroscience research, to develop more accurate models of brain function
  • In artificial intelligence, to create more brain-like algorithms and neural networks
  • In medicine, to better understand neurological disorders and potential treatments
  • In cognitive science, to model and predict human behavior and decision-making
  • In data science, to apply advanced mathematical techniques to complex systems

Syllabus

Textbook: "Neuronal Dynamics - from single neurons to networks and models of cognition" by W. Gerstner, W.M. Kistler, R. Naud and L. Paninski, Cambridge Univ. Press. 2014

Online version available at: http://neuronaldynamics.epfl.ch/

The course is based on Chapters 12 and 16-19 and is structured over 6 weeks:

Week 1: Associative Memory and Hopfield Model
Week 2: Attractor networks and spiking neurons
Week 3: Neuronal populations and mean-field theory
Week 4: Perception and cortical field models
Week 5: Decision making and competitive dynamics
Week 6: Synaptic Plasticity and learning

Each week includes:

  • 5-8 video lectures (60-90 minutes viewing time)
  • 90 minutes of self-learning time
  • Online exercises and quizzes

The course concludes with a final exam.

Total duration: 6 weeks

Weekly workload: Approximately 2.5-3 hours

Join us on this exciting journey into the mathematical foundations of brain function and unlock the secrets of cognition!