école Normale Supérieure Mathematics At The
Career PathsMathat the ENS“To rise above oneselfand to grasp the world”StudentFeedbackCampus LifeStudyingat the ENSécole Normale SupérieureHow to applyécole NormaleSupérieureMathematicsat theArchimedes
école NormaleSupérieureThe écoleNormale Supérieure (ENS)A World-Class University Builton French Excellence in EducationEstablished in 1794, the ENS is one of France’s most prestigious and selectiveinstitutions of higher learning and research in the arts and sciences, located inthe heart of one of the world’s greatest cities. It has trained generations of theworld’s most successful academic, research, business and civic leaders andcontinues to build on its heritage of intellectual innovation and excellence. Someof the most important names in the world’s scientific and cultural achievements- Henri Bergson, évariste Galois, Jacques Hadamard, Louis Pasteur, Jean-PaulSartre - made their intellectual start at the ENS. The ENS’s focus on research,interdisciplinary training, and intellectual creativity sets it apart from France’sother elite Grandes écoles and allows it to attract the most accomplishedstudents and professors from France and around the world.2 ENS DMA 2013Our campus in the heart of Paris2700 students1500 faculty (teaching and research)35 centers of research excellence300 foreign students from over 46 countries200 math students10 Fields Medal winners12 Nobel Prize winnersMathematics at the école Normale Supérieure ENS DMA 2013 3
Developing Multidisciplinary Expertiseécole NormaleSupérieureStudying at the ENSthe eNS is theonly school inFrance that trulyintegrates thesciences andthe humanities.DaviD bessisStudyingat the ENSThe ENS continues its proud tradition of training students to become leaders capable of bringingtheir creative vision and innovative solutions to bear on the increasingly complex and global issues oftoday’s world. It does this by assembling the world’s most distinguished experts to teach its studentsto conduct pioneering research that transcends the traditional boundaries between academicdisciplines.Student seminarMathematics at the école Normale Supérieure ENS DMA 2013 5Mathat the ENSCareer PathsENS students are trained to be international experts, ready to workanywhere in the world. Immersed in the cosmopolitan characterof a world capital like Paris, they are very quickly initiated into thebenefits of diversity and strongly encouraged to widen their horizonswith new languages and study abroad. Thanks to the ENS’s extensiveinternational network of alumni and academic partnerships, ENSstudents can work or study wherever they choose. For example, ENSgraduates now teach at Berkeley, Columbia, Harvard, the Institute ofMathematics at Beijing University, MIT and Oxford.StudentFeedbackNext-Generation Global LeadersHow to applyIn addition to the required courses in their fields, students are activelyencouraged to explore other disciplines to achieve new insightsinto their own research. Students work with tutors and academicadvisers to develop individualized study programs that are suited totheir interests and needs. The school provides a rich menu of seminars and study groups to supplement a student’s main academiccurriculum. Students also have the opportunity to conduct independent study programs away from the ENS on projects that aresometimes completely unrelated to their academic area of focus,whether it’s writing, film-making, music, learning a new languageor international field work. All of this is based upon the school’s fundamental belief in the creative power of multidisciplinary learning.Campus LifeA student room
école NormaleSupérieurewhat touchedme most about theENS was the trustand support fromour teachers6 ENS DMA 2013Mathematics at the école Normale Supérieure ENS DMA 2013 7Career PathsStudentFeedbackUnlike larger universities, the ENS provides an intimate settingfor students and teachers to live, work, and socialize together.The school’s relatively small size and large teacher-to-student ratiomean that each student receives individual attention and easy accessto professors. All students live on campus at least during their firstyear. They also take their meals together in on-campus dining hallsand can avail themselves of a variety of campus facilities, includingcomputer labs, a movie theater, music and dance practice spaces,dark rooms for photography, tennis courts and gymnasiums. Thiscreates a tight-knit community of students and teachers from diverse backgrounds and with different interests who learn from eachother. In addition to academic counseling, new students are pairedwith older students who help them navigate their new surroundingsand begin lifelong friendships. A variety of active student clubs andassociations means that it is not unusual to find physicists joiningphilosophers at film showings, geographers dancing with classicists,musicologists bumping into computer scientists at the photographylab, or economists facing off with archaeologists in rugby matches!And of course, the city of Paris awaits beyond the school’s formalboundaries, with its surfeit of cultural and academic offerings.How to applySuperlative Educationin a Personalized SettingMathat the ENSCampus LifeStudyingat the ENSJie Lin
école NormaleSupérieureThe ENS’slocation in themiddle of theLatin Quarteris an amazingassetStudyingat the ENSAlexandre MartinCampus LifeParis has been an intellectual center for centuries, with a remarkable concentration of poets,philosophers and scientists gathering there during the 18th century Age of Enlightenment.That cultural and intellectual tradition continues to this day and remains central to the city’senduring appeal for students and teachers alike. In 2012 Paris was named the best city in theworld for students by QS World University Rankings, based on the quality of life and educational offerings.“To study in Parisis to be born in Paris.”Campus LifeStudying in the City of LightNight event for students in main courtyardCédric Villani, Fields Medal winner, with studentThe school is located in the heart of Paris’traditional student area, the Latin Quarter,whose name refers to its origins as a student haven when Latin was the universallanguage of learning. This is one of the mostvibrant parts of Paris, filled with interestingrestaurants of every ethnic origin, cafés, cinémas, dance clubs and bookstores. Paris isa feast for the eyes, the mind and the soul.Mathematics at the école Normale Supérieure ENS DMA 2013 9Career PathsStudentFeedbackDances at ENSHow to applyThe ENS is surrounded by top universities and research institutes like the Sorbonne, the Collège de France, and the CurieInstitute. Students are spoiled for choicewith some of the best cultural offerings inthe world: museums like the Louvre, theMusée d’Orsay, and Pompidou Center aswell as opera houses, concert halls, countless cinemas, historical theaters and cafés.Mathat the ENSVictor Hugo
France has a long and proud tradition in mathematics. The century of Louis XIV was also that ofDescartes, Fermat and Pascal. Today greater Paris has the largest concentration of mathematicians in the world, with more than 1,000 researchers breaking new ground in pure and appliedmathematics.The Paris Mathematical Sciences Foundation (FSMP) and the Jacques Hadamard Mathematical Foundation (FMJH) bring together a number of mathematical research institutions in Paris,including the ENS, Pierre and Marie Curie University (UPMC), Paris-Diderot University, theNational Center for Scientific Research (CNRS), Paris-Dauphine University, the Collège deFrance, the Orsay University, the Institut des Hautes études Scientifiques (IHES), the écolePolytechnique, Paris-Descartes University and Paris-Nord University. The foundations fundprograms to attract the international elite, support the mathematicians of tomorrow and takemathematical research to a new level of excellence. This effort is firmly supported by the Frenchgovernment, which recognizes the strategic importance of investing in the country’s uniquecapabilities in math.Mathematicsat the ENSécole NormaleSupérieureStudyingat the ENSGreater Paris as a Center of MathematicsCampus LifeMarcel Berger, pioneerin differential geometryMathat the ENSMore than anyother city on theplanet, Paris is theworld’s center formathematics .Cédric Villani (2010),Bao Châu Ngô (2010)A Curriculum Cultivating Innovation and CreativityWendelin Werner (2006)Laurent Lafforgue (2002)International students studying pure and applied math at the ENS follow a three-year programworking toward a master’s degree and possibly continuing on to their doctoral degree. Mostdoctoral students will receive a three-year teaching scholarship to support their doctoral studies.As with all courses of study at the ENS, the emphasis in the math department is on training byresearch and on providing a broad range of specialties within mathematics and beyond. Whetheryou’re interested in algebraic geometry or stochastic calculus - or anything else - you will findan unparalleled concentration of mathematical talent to help you develop your expertise.The Math and Computer Science LibraryPierre-Louis Lions (1994)StudentFeedbackMathematicians who trained at the ENS have received more Fields Medals, mathematics’ highestaward, than those from any other institution. Since 1936, when the award was first introduced,10 of the 53 recipients have come from the ENS, and many of them are still working in Paris:Career PathsInternational DistinctionsJean-Christophe Yoccoz (1994)René Thom (1958)Jean-Pierre Serre (1954)Laurent Schwartz (1950)A tutorial on knots and linksMathematics at the école Normale Supérieure ENS DMA 2013 11How to applyAlain Connes (1982)
école NormaleSupérieureMathat the ENS“If one thing is clear about the ENS, it’s that it gives its students nearlytotal freedom to choose their own paths. I wanted to devote myselfentirely to mathematics, so the ENS was a kind of paradise for me.In addition to my regular classes, I was able to meet researcherswho helped me sort through my choices, which turned out to be anextraordinary bit of luck for me. Since I’d arrived at the ENS with a fairly precise idea ofthe sort of mathematics that I wanted to go into, it was great to be able to count on a tutorto put me in contact with foreign mathematicians whose research fields corresponded tomy own interests. This is how I managed to spend five months in Edinburgh while writingmy master’s thesis. I was also able to find my future PhD advisor and move to Strasbourg,where I have since begun a dissertation in topology and in geometric group theory. Finally,in addition to the academic benefits, the ENS’s location in the middle of the Latin Quarteris an amazing asset, so you can have an exceptional course of study combined with thenumerous opportunities offered by living in the heart of Paris.”Career PathsAlexandre Martin / STUDENTCampus LifeStudyingat the ENSFarouk BoucekkineStudentFeedback“What drew me to the ENS was its intellectualfreedom: all disciplines are available, and eachstudent has enormous freedom in designinga curriculum. After obtaining under-graduatedegrees in classics and math, and a master’sdegree in philosophy, I’m currently working on on a master’s degreein math at Cambridge University through an exchange with the ENS.However, this tremendous freedom does not mean that you are lefttotally on your own: thanks to the small size of the ENS, I’ve alwayshad the good fortune to find teachers who knew me well enoughto really listen to me, advise me or warn me. But the intellectualopportunities the ENS gave me go far beyond the mere freedomto choose my courses and degrees freely.The greatest riches of the ENS are, forme, the students: the way the dormitoriesand student life are organized allowed meto meet many remarkable people from alldifferent fields and, thanks to them, to getto know their work and their perspectivesup close. Now I know I can make a fullyinformed decision about the field I go into,whether it’s the philosophy of science,mathematics or any other discipline.”what I owemost to the ENSis that it taughtme to make myown choices.Mathematics at the école Normale Supérieure ENS DMA 2013 13How to applyDavid Waszek / student
école NormaleSupérieure“I was a student at the ENS and stayed on as ateaching assistant (TA) because I like studyingand teaching. I’ve never regretted my choice!I have wonderful memories of my student years at the ENS: freedom, diverse courseofferings, high-quality education and life in one of the most interesting parts of Paris. Iwas able to try out a lot of different fields like physics, economics, biology and a greatvariety of mathematics before I decided to focus on probabilities. As I started my PhD, I wasoffered a teaching position as a tutor for the probabilities team in the math department.That means I’m now on the other side of the desk so to speak. There are currently sevenTAs in the math department, mostly in charge of the seminars for first-year students. It’s apleasure but also a bit daunting to be in front of a roomful of bright ENS students who aren’tshy about asking the mathematically difficult questions, the same questions we ourselvesposed a few years ago as students! But as young alumni and future researchers, we arealso intermediaries between the professors and the students. We consider our students asour future colleagues and the relatively small size of the classes makes it possible for usto attend to students individually: every professor/researcher/working group teacher actsas a tutor for a small number of students.“Studyingat the ENSTeaching AssistantCampus LifeNicolas Curien /Career PathsStudentFeedbackMathematics at the école Normale Supérieure ENS DMA 2013 15How to apply“When one of the best students in my high school in Shanghai, China, wasadmitted to the ENS seven years ago, my math teacher was so happy hecarefully wrote the name of the école Normale Supérieure on the blackboardand told us the school had the best mathematics department in the world.That was the first time I heard of the ENS. When I was in the math departmentat Tsinghua University, I discovered that the ENS had a very long and storiedhistory as the training ground for top mathematicians in the world. At the same time, I wastaking several courses with some French professors who had graduated from the ENS. I wasimpressed by their achievements in math and their kindness toward the students. So I appliedfor the International Selection in 2010 and was delighted to be admitted. The first year at theENS was challenging, because I had a lot of courses that year, but they gave me much a richunderstanding of different areas in mathematics. A big advantage of studying math at the ENSis the ability to draw on the resources of all the universities in Paris. We can select courses andchoose our thesis advisors from other universities. Besides the high quality of the curriculum,what touched me most about the ENS was the trust and support from our teachers. We all havea tutor who helps us select courses and find thesis advisors. We also receive help in learninghow to write papers and give lectures, working with young mathematicians as well as seniorprofessors. I also learned a lot from my fellow talented schoolmates. Workshops provideda really quick way to learn something with other students who shared the same interest.Their enthusiasm and curiosity for all things mathematical kept me motivated throughout mycourse of studies. The ENS has been like abig family for me, not only supporting meacademically with my math studies butalso helping me develop as a person. Itis truly a wonderful experience to studymath at the ENS and to live “la vie enNicolas Curien lecturingrose” in this beautiful city!”Mathat the ENSJie Lin / from Tsinghua University, Beijing (China), 3rd year ENS student
école NormaleSupérieureCampus LifeStudyingat the ENSSylvia Serfaty16 ENS DMA 2013Working in the DMA loungeMathematics at the école Normale Supérieure ENS DMA 2013 17How to applyStudentFeedbackCareer Paths“After two years at the University in Pisa, I appliedto the ENS as part of the International Selectioncompetition in 2011, based on the enthusiasticaccounts from friends from Pisa who had taken thesame route. Once there, my expectations weren’tdisappointed: on the one hand, there were the incredible academicofferings at other universities in Paris, probably the largest centerof mathematical research in Europe, if not the world. On the otherhand, there was the advantage of being at a school that encouragesstudents to expand their horizons by attending courses in differentsubjects. Because the ENS is a relatively small university, I’ve had theopportunity to have direct contact with my professors, who willinglyspend their time helping and advising their students. Despite somelinguistic challenges at first, life in the student dormitory helped meget to know my fellow French and foreign students well, even if I hada different personal background. Indeed one of the most interestingaspects of my life at the ENS has been living and working with openminded students, who are always willing to share their points of viewon different subjects. Beyond the ENS, I’ve enjoyed the rich theaterscene and the huge number of museums and exhibitions Paris has tooffer as one of the most culturally active cities in Europe. On the whole,I strongly recommend this opportunity to anybody who’s looking for anenriching experience abroad as well as a first-class education.”.the school’shistoric role hasbeen in trainingthe Frenchintellectualelite.Mathat the ENSPietro Vertechi / from Pisa (Italy), ENS student
école NormaleSupérieureStudyingat the ENSAmong the students enrolled in the first year of the math programin 1999, here’s where they landed 10 years later:Life after the ENS13 researchers with positions outside France5 researchers with the CNRS or INRIADiscussion with François Loeser and Wendelin Werner,Fields Medal winnerCampus LifeCareer Choices Made by ENS Students7 university professors5 graduates of civil-service training schools6 corporate executives1 research engineer4 teachers dedicated to preparing studentsfor the Grandes écolesCareer Snapshot of All ENS GraduatesCareer PathsLaure Saint-Raymond, professorMathat the ENS(French state-funded research centers)In addition to offering a universal language for abstract ideas, mathematics forms the basis of nearlyevery science, from biology to economics, cryptography, oceanography, and sociology. Not surprisingly,ENS mathematics graduates have a variety of possible paths open to them, aided by the internationalprestige and distinction that comes from an ENS degree. While many ENS students remain in academia, continuing on to become professors and researchers at major universities and research institutions around the world, others choose to go into business or government or other technical fields.5%Higher education and researchSecondary school teachingPublic service other than teachingPrivate sectorPursuing further studies (or did not participatein the survey)5%15 %65 %A ceremony for awarding Honorary DegreesMathematics at the école Normale Supérieure ENS DMA 2013 19How to applyCareer Paths(Source: Lehmann report, 2008)10 %StudentFeedbackThe career paths of ENS alumni from all fields,three to nine years after graduation.
it stays with you,for Paris is a moveable feast.”Ernest Hemingway, A Moveable FeastMathematics at the école Normale Supérieure ENS DMA 2013 21Campus Lifefor the rest of your life,Mathat the ENSthen wherever you goCareer Pathsin Paris as a young person,StudentFeedback“If you are lucky enough to have lived“I started at the ENS in 1991. It wasmade me travel indeed: two yearseasy for me to choose between theat Yale, one in Moscow, severalENS and the École Polytechniquelong stays in China and Japan. Myfor a lot of superficial reasonsyears at Yale were very enriching.(the campus was pret
Mathematics at the école Normale Supérieure eNS dma 2013_ 9 écol E Nor MA l E Su P ér IE ur E S T udy IN g AT T h E ENS c ampu S l ife M AT h AT T h E ENS cA r EE r P AT h S S T ud ENT ck F EE db A h ow T o APP ly Campus Life The ENS is surrounded by top universi-ties and research institutes like the Sor-bonne, the Collège de France, and .
SUP.6 Product evaluation A SUP.7 Documentation A H SUP.8 Configuration management A H SUP.9 Problem resolution management A H SUP.10 Change request management Support Process Group (SUP) A H SUP.1 Quality assurance A SUP.2 Verification SUP.3 Validation A SUP.4 Joint review SUP.5 Audit SUP.6 Product evaluation A SUP.7 Documentation
t. The log-normal distribution is described by the Cole-Cole a, and the mode of the distribution is the time constant of relaxation [Cole and Cole, 1941]. If the Cole-Cole distribution parameter, a, is unity, then there is a single time constant of relaxation and the Cole
The Cole-Cole (II is a number that is often used to describe the divergence of a measured dielectric dispersion from the ideal dispersion exhibited by a Debye type of dielectric relaxation, and is widely . [27] equation, introduced by the Cole brothers [28] in which an additional parameter, the Cole-Cole (Y, is used to characterise the fact .
Annales ScientiÞques de lÕ cole Normale Sup”rieure, 45, rue dÕUlm, 75230 Paris Cedex 05, France. T”l. : (33) 1 44 32 20 88. Fax : (33) 1 44 32 20 80. annales@ens.fr dition et abonnements / Publication and subscriptions Soci”t” Math”matique de France Case 916 - Luminy
Le mod ele de la loi normaleCalculs pratiques Param etres de la loi normale Pour chaque ; , il existe une loi normale de moyenne et d' ecart-type . On la note N( ; ). Cas particulier 0 et 1 : loi normale centr ee/r eduite. Lorsque l'on suppose qu'une variable X suit le mod ele de la loi normale N( ; ), on ecrit X N( ; ):
the Cole–Cole and PLS models, the latter technique giving more satisfactory results. Keywords On-line biomass monitoring In-situ spectroscopy Scanning capacitance (dielectric) spectroscopy Cole–Cole equation PLS Calibration model robustness Introduction Over the last few decades, the field of biotechnology has
Equation 20 is the prove of equation 1 which relate water saturation to cole cole time; maximum cole cole time and fractal dimension. The capillary pressure can be scaled as logSw (Df 3) logPc constant 21 Where Sw the water saturation, Pc the capillary pressure and
and Owner's Manual SUP-1.5B, SUP-1.5B, SUP-6.5WF SUP-6WE, SUP-8WE, SUP-10WE Indicates a potentially hazardous situation, which, if not avoided, could result in death or serious injury. Indicates a potentially hazardous situation, which, if not avoided, may result in minor or moderate injury. Information Step-by-step Instructions FOR YOUR SAFETY
