Cogmaster, Course CA6a

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Academic year 2017-2018
Site updated on September 4, 2017.
If you want to attend this Course, even if you do not intend to pass the exam,
register with the secretariat of the Cogmaster.
First Lecture: Thursday Oct 5, 2017, 1pm, ENS Physics Department, room L363/L365.



Vincent Hakim (01 44 32 37 68, hakim[at]

Gianluigi Mongillo (01 42 86 38 13, gianluigi.mongillo[at]

Jean-Pierre Nadal (01 44 32 32 75, nadal[at]

Srdjan Ostojic (01 44 32 26 44, srdjan.ostojic[at]

TA: Charlotte Le Mouel (charlotte.le-mouel [at]




            This course introduces quantitative approaches to three central questions in neuroscience: How is the brain made up? What functions and computations does it accomplish? By which mechanisms? The brain is a highly complex object; its function is also highly complex and at the same time extremely refined. Because of this, it is often impossible to establish direct links between the biochemistry, on the one hand, and brain function, on the other. Theoretical or computational neuroscience attempts to provide bridges between the two, by suggesting possible mechanisms that the brain may use in perception, learning, memory, motor control,… Furthermore, in recent years an enormous amount of neurobiological data has been collected with high precision. The sheer volume of data begs for computational principles that may help organize and understand it, and the unprecedented precision of the data is now allowing for detailed comparisons with mathematical theories.


            The scope of the course is threefold. First, to present a number of questions for which a quantitative approach is relevant. Second, to introduce quantitative or mathematical tools necessary to the study of these questions, as well as to the study of similar questions in related fields (psychophysics, computer science, biophysics, bioengineering,...). Third, and maybe most importantly, to discuss concrete examples relevant to brain function in which one can make progress through quantitative thinking. Questions and examples that will be discussed include: How do neurons code inputs to the brain? Is ‘function’ carried out by single neurons or by groups of neurons? How can vision be so precise? Where do the brain rhythms come from? How can one model the learning and storage of memories? How does the brain generate outputs such as motor outputs?




This course belongs to the Master in Cognitive Science ('Cogmaster', ENS, EHESS, University Paris Descartes), and hence appears in the curriculum of students in Cognitive Science (“Advanced Course CA6a”, 6 ECTS).

The course is also open to L3, M1, and M2 physics students; the course can be taken for credit as a non-specialty (non-physics) course by physics students at ENS, but may be taken for credit as well as a specialty (physics) course upon agreement by the Head of Teaching in the Department of Physics.

L3, M1, and M2 biology students at ENS can also take the course for credit as a non-specialty (non-biology) course.

We more specifically recommend the course for credit for M2 cognitive science and biology students, and M1 math, physics, and computer science students.

PhD students from Ecole doctorale Physique en Ile de France (ED PIF) can take the course as one of the optionnal courses. Other Ecoles doctorales allow to take this course among those which have to be taken during the thesis (do not hesitate to ask).

All L3, M1, and M2 students, from any department, are welcome as (non-credit) listeners.

All graduate students, postdocs, visitors, and researchers are welcome as listeners.


Time: The classes of the Course "Theoretical Neuroscience" take place
every Thursday (not including holidays) from 1pm to 4:30pm, with a 30mn break,
with class 1 on Thursday, 5th of October 2017, and last class of the term on Thursday, the 11th of January 2018.

Place: The Course (and the TDs) will be hosted by the Ecole Normale Supérieure (ENS), room L363/L365, third floor of the Physics Department of ENS (24, rue Lhomond, Paris 5).




Starting October the 12th, problem sets will be discussed on Thursdays, from 5pm to 6:30pm, same room as the Course. The exercises topics will essentially correspond to the ones of the Lecture of the preceding week.
Problem sets for the current year are/will be posted here - access with password.



For students taking the course for credit, the exam will be:
- partly based on a (small) project based on an article given in advance, students working in pairs or groups of three.
- partly written: this written part will take place on Thursday, the 25th of January 2018.
Detailed instructions will be posted here.
The exam modalities and the projects topics will be presented on Tursday October 5, following the first Lecture (same place, after a break) (to be confirmed)




The course has few prerequisites. However, a good familiarity with elementary mathematics in analysis, linear algebra and probability is mandatory. Some knowledge of neurobiology, and of dynamical systems and statistical mechanics, will be helpful but not necessary.
For students of the Cogmaster: the course prerequisites correspond more or less to the UEs AMS (Introductory course in mathematics and statistics for cognitive scientists) : AMS S1, and courses labeled "Maths 2" (linear algebra, probabilities) of AMS S2.
For the projects (TDs, part of the exam), some basic knowledge in programming, preferably in python, is strongly recommended.





Informative and reference material for the course will be posted on this web page, .





Course CA6a – Academic year 2017/2018

Location (Lectures, TDs and exam): Physics Department of the ENS, 24 rue Lhomond, room L363/L365 (third floor).

Lecture 1- 05/10/17,
                Vincent Hakim - Overview & Neurons I: Hodgkin Huxley

Lecture 2- 12/10/17,
                Vincent Hakim - Neurons II

Lecture 3- 19/10/17,
                Gianluigi Mongillo - Synapses

Lecture 4- 26/10/17,
                Srdjan Ostojic - Balanced networks

[2/11/17 -- holidays]

Lecture 5- 09/11/17,
                Srdjan Ostojic - Rate models

Lecture 6- 16/11/17,
                Jean-Pierre Nadal - Learning I (Intro - supervised - unsupervised)

Lecture 7- 23/11/17,
                Gianluigi Mongillo - Learning II: Behavioural learning

Lecture 8- 30/11/17,
                Jean-Pierre Nadal - Coding

Models of specific cognitive systems

Lecture 9- 07/12/17,
                Srdjan Ostojic - Vision

Lecture 10- 14/12/17,
                Vincent Hakim - Navigation

Lecture 11- 21/12/17,
                Gianluigi Mongillo - Memory

[28/12/17 -- holidays]
[04/01/18 -- holidays]

Lecture 12- 11/01/18,
                Jean-Pierre Nadal - Decision

[ 18/01/18 no lecture, only oral exam ]

25/01/18       Written exam   (2pm-4pm)

See also the course material page.


This Course has been created in 2005 at the Physics Department of the ENS, with as initial faculty team: Rava Azeredo da Silveira, Nicolas Brunel, Vincent Hakim and Jean-Pierre Nadal. Romain Brette joined the team during several years. A PhD student or postdoc in computational neuroscience is in charge of the problem sets/TDs (most often a former student of this Course). For the current teaching team, see above.

You may have a look at the course material of the last years, 2016-2017, 2015-2016, 2014-2015,


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