S. D. V. Stephens

notes /

Basic Neuroscience and Geometry of Neuroscience

Basic Neuroscience comprises: the minimal knowledge needed to operate in the academic world and should be standard knowledge for those wishing to engage in anything orbital to neuroscience; neurons and signalling, behavior, the senses, methods and disorders, from the PSY 212 (SSU) lecture slides and my notebook. Geometry of Neuroscience is much more ambitious, though I keep them together here: Matilde Marcolli’s Caltech course on dynamical, topological, geometric and categorical models of the brain, vision and language.

The notes come in two parts.

Basic Neuroscience (chapters 1–5) follows PSY 212. Each numbered lecture is written up from the course's lecture slides, with its review questions gathered at the end. My own notebook from the reading sits with the first chapter.

Geometry of Neuroscience (chapters 6–12) follows Matilde Marcolli's course Ma 191b, Geometry of Neuroscience at Caltech, winter 2026. Each section is written up from her slides, in the order of her schedule: structures in the brain, then vision, then language. The introduction also has the opening lecture of the 2017 course, which she taught with Doris Tsao.

Readings for Geometry of Neuroscience. The course's general references:

  • Jean Petitot, Neurogéométrie de la vision (2008)
  • David Spivak, Category Theory for the Sciences (MIT Press, 2014)
  • Eugene Izhikevich, Dynamical Systems in Neuroscience (MIT Press, 2007)
  • Mikhail Gromov, Structures, Learning and Ergosystems
  • Luciano da Fontoura Costa, Group Theory: A Primer

39 of 39 lectures and notes written

Basic Neuroscience

1Neurons and Signalling

  1. 1
    Meet the Nervous System
  2. 2
    The Action Potential
  3. 3
    Hormones and Neurotransmitters

From my notebook

  1. N1
    History of Neuroscience
  2. N2
    Levels of Analysis
  3. N3
    Neuroscientists and Research Practice
  4. N4
    Chapter 1 Review Questions
  5. N5
    Stains, Microscopes, and the Neuron Doctrine
  6. N6
    The Soma, the Nucleus, and Gene Expression
  7. N7
    Organelles of the Soma in progress
  8. N8
    Glia: Astrocytes, Microglia, and Oligodendrocytes

2Brain and Behavior

  1. 4
    Learning and Memory
  2. 5
    Social and Reproductive Behavior
  3. 6
    Sexual Development and Puberty

3The Senses

  1. 7
    Vision
  2. 8
    Hearing and Balance
  3. 9
    Touch, Taste, and Smell

4Methods and Technology

  1. 10
    Research Methods
  2. 11
    Machine Learning
  3. 12
    Therapies and Prosthetics

5Disorders

  1. 13
    Anxiety Disorders
  2. 14
    Depression

Geometry of Neuroscience

6Introduction

  1. G1
    A Mathematical Promenade and Gromov’s Ergobrain Program
  2. G2
    Geometry of Neuroscience: the 2017 Opening Lecture

7Neurons and Neural Codes

  1. G3
    The Neuron as a Dynamical System
  2. G4
    Neural Codes and Neural Rings: Topology and Algebraic Geometry

8Brain Networks

  1. G5
    Brain Networks and Topology
  2. G6
    Neurocortical Microcircuitry and Directed Algebraic Topology

9Learning and Categorical Models

  1. G7
    Coding and Learning in Networks
  2. G8
    Homotopy-Theoretic and Categorical Models of Neural Information Networks

10The Geometry of Vision

  1. G9
    The Visual System: Receptor Profiles and Gabor Frames
  2. G10
    Conformal Geometry of the Visual Cortex
  3. G11
    Contact Geometry of the Visual Cortex

11Image Segmentation

  1. G12
    Differential Topology of Image Segmentation and Invariance
  2. G13
    Image Segmentation: the Mumford–Shah Functional
  3. G14
    Algebraic Geometry of Segmentation and Tracking
  4. G15
    Pattern Theory

12Language

  1. G16
    Language and the Brain
  2. G17
    A Mathematical Model of Language