International Selection in Sciences Selection procedure in Biology

The selection takes place in two phases: Application evaluation and Examinations

Application evaluation We consider several aspects: - Academic excellence. This is evaluated from examination marks and the teaching program of the University of origin. Report of activities like laboratory internships or participation to international contests is appreciated. - Adaptation to the teaching program proposed at the ENS. - Maturity of the project. Examinations As for other disciplines in Sciences, we perform written and oral examinations. Candidates will have to demonstrate good background knowledge in several Biology fields. However, since successful candidates will come into our teaching program at Master's level, examinations are adapted to the specialty closest to the candidate's project, i.e. Genetics and Genomics, Ecology, Developmental Biology, Neuroscience, Systems Biology... Written examinations evaluate the background knowledge in two different fields. At least part of the written examination is carried on interpretation and comment of figures and datasets extracted from research articles. Oral examination aims to evaluate the capacity of the candidate to present his/her knowledge in a structured manner as well as his/her capacity to react to examiners inquiries. We propose two subjects and the candidate will select one of them for a short presentation. This dissertation will be followed by a dynamic exchange with examiners on the proposed and other topics.

International Selection in Sciences Selection procedure in Chemistry

Report on the written component for scientific culture in Chemistry

The principle of the exam consists in evaluating to the greatest extent possible the candidates’ knowledge that is considered indispensable to the pursuit of studies at the highest level in chemistry for the Licence (3rd-year university degree) and the Master (5th-year university degree). Given the diversity of programs and the varied progression of coursework for different countries, the proposed exercises are not difficult, but they allow the jury to evaluate both the candidates’ mastery of the basics and their initiative skills.

The “chemist” candidates took up the two exercises proposed for “specialists”. The first exercise concerned the hydrolysis of an amide bond in the gas phase and in solution, as well as in biological systems (catalysis by the enzyme -chymotrypsine). This offered the possibility to question on subjects which are currently covered in the first university cycle (Licence): thermodynamic and kinetic aspects of a reaction, catalysis, coordination chemistry, and organic reactivity involving amide functions. The second exercise involved different aspects of the synthesis (reactivity including mechanisms with orbital-based analysis) of an organic alkaloid molecule (±)-cycloclavine.

Only one “non-chemist” candidate chose chemistry as a secondary subject and treated the third exercise, centered on the chemical reaction occurring in the Krebs cycle.

The test presented numerous easy questions designed to cover to the broadest degree possible the subjects of chemistry encompassed by the first cycle of French university studies (basic atomistics and electronic properties, solution chemistry, organic chemistry). Oral tests in chemistry ( either in French or English) Each candidate is asked a question dealing with a specific subject and is given 5-10 minutes to reflect on it. The jury’s questions first address the responses given by the candidate, and then quickly move on to address various points in chemistry, in an interactive and informal setting. The disparities of coursework already undertaken by the candidates as well as our philosophy of recruitment led us to evaluate the candidates’ reasoning skills and their reaction in face of unusual situations, rather than a level of knowledge attained.

International Selection in Sciences Selection procedure in Geosciences

The written examination is composed of three exercises, the two first being slightly more complex than the third. There will be at least one exercise focusing on solid Earth (geology, seismology, volcanology, hydrology) and one exercise on the external fluid envelopes (oceanography, atmospheric physics and dynamics, climate). The third exercise is recommended for candidates who chose geosciences as their minor field of study. The three exercises are conceived in such a way that only minimal knowledge in geosciences is necessary to solve them. Questions of progressive complexity will lead the candidate trough the problem, making use of basic principles of physics and mathematics that should be familiar to a second-year student of any scientific discipline. A specific knowledge in geoscience will however be of help. The oral examination takes place in a closed room with the candidate and two examiners. One question on solid Earth sciences and one on ocean/atmospheric sciences will be asked. The examination is not meant to test specific knowledge, but to assess the aptitude of the candidate to use scientific reasoning. The candidate will have to apply basic knowledge of physics and mathematics in order to reach the correct answer. Graphs or geophysical maps can be used to introduce the questions and the problems may be solved on a blackboard in front of the examiners.

International Selection in Sciences Selection procedure in Computer Sciences

The first step of the admission process is a selection of students according to their transcripts and recommendation letters. Candidates submit the form available on the website between January, 10 th and March, 4th 2013. In May, candidates will be informed of the results of the preselection process. The preselected candidates are asked to come to Paris, where they will take written tests and will be interviewed by the examination panel immediately afterwards. There is a written test and an oral examination which evaluate the candidate knowledge of basic computer science concepts and algorithmic tools, including recursivity, controle structures, running time analysis. This includes classical algorithm design paradigms with data structures such as trees and graphs. Prior experience in computer programming is needed. The candidates must also be familiar with logic (propositional calculus, truth tables, language theory) and discrete mathematics (combinatorics, basic graph theory, algebraic structures). The written examination will focus on basic computer science knowledge on these topics. During the oral, the candidate will be asked less classical questions, which require no more knowledge but some ingenuity.

International Selection in Sciences

Selection procedure inMathematics

Either in the major field of study or in the minor field, written and oralexams can be done in French or in English.

1 Mathematics as a major field of study

1.1 Written exam

The written part of the test consists in two problems in Mathematics : onein Analysis and one in Algebra. They both include easy questions and counttowards one half of the grade. It is therefore a bad strategy to focus on only oneof the two problems. Examples of questions are given on the internet web site.

1.2 Oral exam

The oral examination lasts one hour and fifteen minutes : 15 minutes ofpreparation and one hour of discussion with the jury.

More precisely, the candidate is given one exercise at the beginning of theoral test, goes in a separate room to prepare on his own and try to find ideasor a strategy to solve the exercise. After 15 minutes, he is brought in anotherroom to meet the jury for one hour. Since many of the exercises are difficult,the jury does not expect a complete solution after the 15’ preparation. Once infront of the jury, the candidate explains his ideas about the exercise and triesto solve the exercise in front of the blackboard. Most of the time, it will takea substantial amount of time (in some cases it may even be a full hour) anddiscussion with the jury before the exercise is completed. The jury might askintermediate questions or questions on related problems. Sometimes the jurymay ask another problem if enough time is remaining (often in a different areaof mathematics to test various skills).

We do want to stress the following points

1. The most important word above is ”discussion”. It is crucial to spell outyour ideas on the blackboard and to explain your strategy for solving theexercise.

2. It is important to listen to the jury’s hints and questions (they are al-ways directed to help the candidate). Usually the jury will ask manyquestions and try to discuss with the candidate. Nevertheless, sometimesthe jury stays quiet because it feels that the candidate is progressing inan interesting direction

1

3. Exercises are of various difficulties. Some can be solved in a short timeand others require longer period of time and the jury is well aware of it.

4. After one hour with the jury, the examination stops ; most of the time itwill be in the middle of an exercise and the candidate should not worryabout this.

1.3 Examples

To be definite, let us gives some examples of exercises of various difficultiesthat were given in 2013.

Exercise 1. Let A ∈Mn(C) be a square n× n-matrix. The exponential of A isby definition the matrix

exp(A) :=∑n≥0

An

n!.

Let Unin(C) ⊂ Mn(C) be the subset of unipotent matrices, that is matriceswhose only eigenvalue is 1.

1. Prove that exp : Mn(C)→Mn(C) is well-defined and continuous.

2. Prove that Unin(C) ⊂ exp(Mn(C)), that is, that every unipotent matrixis in the image of the exponential function.

3. Prove that exp(Mn(C)) = GLn(C).

4. What is the image of exp(Mn(R)) ?

Exercise 2. Consider the series

f(x) =

+∞∑n=0

sin(n!πx).

Prove that the series converges for x = m sin(1) where m is an integer.

Exercise 3 (difficult). Let E be the vector space of C∞(R,C) functions thatare 1-periodic. Let T ∈ L(E) be the endomorphism defined by

Tf(x) = f(x+3√

2)− f(x).

Find the kernel and the image of T .

2

2 Mathematics as a minor field

2.1 Written exam

The problem is, sometimes, quite long and we do not expect the candidateto finish it. It is composed of different parts with varying difficulties.

2.2 Oral exam

The oral examination lasts forty fives minutes. There is no preparation.The candidate is given an exercise directly on the blackboard, by the jury.Then the candidate explains his ideas about the exercise and tries to solve theproblem. The jury does not expect the candidate to solve the question rightaway. Indeed, often, it will take a substantial amount of time (in some casesthe full examination) and some discussion with the jury before the exercise iscompleted. The jury might ask intermediate questions or questions on relatedproblems. Sometimes the jury may ask another problem if there is enough timeleft.

We do stress the following points

1. It is crucial to write ideas on the blackboard and to explain the strategyadopted.

2. It is important to listen to the jury’s points and questions (they arealways directed to help the candidate).

3. Exercises are of various difficulties.

4. After forty five minutes with the jury, the examination stops ; most ofthe time it will be in the middle of an exercise and the candidate shouldnot worry about that.

2.3 Examples

To be definite, let us gives some examples of exercises of various difficultiesthat were given in 2013.

Q1. Which is the largest number : eπ ou πe.Q2. Compute an approximate value of∫ 1/2

0

sinx

xdx.

Q3 (difficult) Consider a compactly supported function f : R → C. Provethat

1

4

(∫|f(x)|2 dx

)2≤(∫

x2|f(x)|2 dx)(∫

|f ′(x)|2 dx).

3

International Selection in Sciences Selection procedure in Physics

In Physics, the oral examination is organized as follows: - For the major, a first exercise is given to the candidate who has 15 minutes to prepare it in a separate room. During these 15 minutes, the candidate has generally enough time to prepare the first questions of the exercise. When the 15 minutes are over, the candidate is invited to describe the exercise to the jury and to solve it on a blackboard. The jury asks questions to the candidate when further explanation is needed. A second exercise is always given to the candidate without any preparation time. The candidate has again to explain and to solve the exercise in front of the jury. In total, the oral examination lasts 1 hour with 15 minutes preparation included. - The minor examination is similar to the major one but no preparation time is given to the candidate. The candidate is invited to solve two exercises on the blackboard during 45 minutes. In both cases, the program of the oral examination is not defined in advance. The exercises that are given to the candidate always fit to the program that he (she) studied. For example, the jury can give an exercise on quantum physics only if the candidate already studied this topic. During the oral interrogation, the committee feels free to deepen some question if it feels the candidate is on the right track. In this respect the oral examination should not be considered as a mere recitation of some physical notion by the candidate. The committee is free to ask questions that are not necessarily related to the exercise. This is in particular true if it happens that a bright candidate has gone fast.

International Selection in Sciences Selection procedure in Sciences cognitives

Écrit, épreuve de spécialité principale : (Written test for applicants applying for the cognitive science master’s program) This test will consist of two or three independent exercises. These exercises can bear on any sub-discipline of cognitive science (from the philosophy of mind to cognitive neuroscience), but they will be adjusted to the applicants’ background. We do not expect applicants to have in depth knowledge of every sub-field of cognitive science, but to show an ability to seriously engage with scientific results and theorizing in cognitive science. The exercises will contain both theoretical and experimental aspects. In one of the exercises, the applicant may be asked to answer questions about a short scientific article. Another exercise may ask the applicant to analyze and interpret some experimental results. Finally, there may be a somewhat more general question whose aim will be to test the applicant’s familiarity with some of the major theoretical questions of cognitive science. Écrit, épreuve de spécialité secondaire : (Written test for applicants not applying primarily for the cognitive science’s master’s program) This test is similar to the one described above, except that it will be much shorter and somewhat less technical. It will consist of a single exercise that will be divided into sub-questions. Oral en sciences cognitives, spécialité principale (Oral test for applicants applying for the cognitive science Master’s program) The test will involve two or three examiners from various sub-fields of cognitive science (e.g. cognitive psychology, cognitive neuroscience, philosophy, linguistics, etc.). The applicant will prepare for the oral test for 30 minutes. The oral test itself will last 45 minutes. The applicant will have to comment on a short scientific article, and then will discuss with examiners a few questions (not necessarily related to the article) whose goal will be to assess the applicant’s motivation and his/her ability to engage with some of the current debates in cognitive science. Oral en sciences cognitives, spécialité secondaire (Oral test for applicants who do not apply fo the cognitive science Master’s program).

The applicant will prepare for the oral test for 15 minutes, and the oral test itself will last 30 minutes. The applicant will have to analyze and discuss some experimental results. This will be followed by a general discussion with examiners.