# Mathematics & Physics

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Physics is the quantitative description and explanation of inanimate nature, and encompasses length scales ranging from the atomic nucleus and to the size of the entire universe. If one were to use only two words to describe physics research activity, the verbs "modeling" and "measuring" would be the most appropriate.

In its decidedly analytical and reductionist approach, physics is the ongoing quest for creating a scientific world-view based on first principles. The mathematical formulation of these principles gives rise to the explanation of known experimental facts, and delivers predictions of new phenomena. Physical models are constantly challenged by confrontation with reality in experiments and observations which aim to confirm or infirm predictions and to measure universal physical quantities. In the mutual interplay between models and measurements, the quantitative evaluation of the incertitude of the predictions is an integral part in the practice of physics as in all scientific activity.

In this creative process paved with revolutions and discoveries, physicists are now seeking and finding answers to fundamental questions like: What is the history and the future of our universe? How comes that the particles composing our universe have so strongly differing masses? Why does time have a privileged direction? What is the mechanism that causes certain materials to exhibit superconductivity at high temperatures? Do black holes produce thermal radiation? Is there a “theory of everything” that would encompass all the observed physical phenomena? We ignore if and when answers to these hot open questions will be found but we are certain that "modeling" and "measuring" are the only methods to attempt to tackle these problems.

Fundamental discoveries are also the footing of the applied sciences and engineering. Uncountable everyday commodities are based on physical phenomena that have been discovered by fundamental research: Space exploration is based on classical mechanics; the global positioning system relies on the precise measurement of time by atomic clocks; lasers are ubiquitous in communication, machining, and medicine; wireless communication was invented after the discovery of electromagnetic waves; solid state physics has given us powerful computers, cheap smartphones and solar power; quantum physics will revolutionize computing and cryptography. These few examples illustrate that the unforeseen technological innovations of this century will be based on the fundamental discoveries made today.

Following the steps of Galileo, Newton, Maxwell, Einstein, Schrödinger... and many others, the students will be taken on a journey through the concepts that have shaped our modern vision of the world. What is matter made of? What is the nature of light? What is the fabric of space and time? Not only they will get answers to these questions, but they will also get a hand-on approach to these modern in the lab.

**Core scientific studies**

In the first year, all students will be familiarized with the basic concepts of modern physics, learn to master the tools to describe most phenomena of classical physics, and acquire the two principal skills of experimental sciences: measuring and modeling. The course "Introduction To Modern Physics" will introduce the mathematical description of the basic phenomena of the movement of matter exposed to forces (mechanics and relativity), of the behavior of light and radiation (optics), the laws of electricity and magnetism, the nature of heat energy (thermodynamics), and the structure of matter. In tutorials (small classes), the students will apply their knowledge to solve concrete problem sets and sharpen their critical thinking. In the beginners' lab sessions students will actively discover the experimental approach to physics, and acquire basic skills of scientific practice.

Thanks to a close coordination with the mathematics course, students will be able to immediately apply their freshly acquired mathematical skills to physics. The most powerful concept here will be «linearity» which is central to both disciplines. Advanced mathematical tools for physics and other experimental sciences will be taught in a dedicated course that will put the focus on applications in physics and mechanics.

In the second semester, an elective course will treat in more depth fundamental physical notions, potentially broaden the scope to mechanics or applied physics, and consolidate the student's problem-solving skills.

**Double major in Mathematics & Physics and Mechanics**

The mathematics, physics and mechanics track will provide the students with the required knowledge and skills for further studies in all three fields.

In the second year, advanced courses on classical mechanics and classical electrodynamics as well as introductory courses on statistical physics and quantum physics will provide the necessary theoretical background for mastering the concepts of motion, energy, fields, waves, multi-body systems. Building on the knowledge acquired in the first year, students will put to work their expanding mathematical toolbox, and exercise their capability for abstract thinking.

In the advanced lab sessions students will hone their practical skills, and progressively acquire the means to interrogate nature in a controlled manner in more sophisticated experiments. Through both experimental and theoretical practice students will develop physical judgment and the capacity of methodical scientific work.

In the third year of the double major students will continue to discover the concepts of modern physics and expand their horizon of knowledge to the frontiers of modern physics. Courses in mechanics of the deformable solid body and on fluid mechanics will offer the opportunity to study more complex modeling situations in detail. Well prepared for guided scientific production the student will conclude this track by a guided research work of approximately two months in a team of the Ecole polytechnique research center (bachelor's thesis).

**Optional courses**

As part of their curriculum, students following this double major will have the opportunity, if they wish, to study a minor in Biology or Chemistry. This option gives the opportunity to students to broaden their knowledge outside of their chosen field.

**Biology option**

Life sciences and their applications are undergoing a complete revolution. The amount of available data has tremendously scaled up, bringing exciting opportunities but also new challenges, which require skills and techniques from sciences, like informatics, physics or mathematics.

The Bachelor program provides excellent formation in these areas. The biology option offers the opportunity to add a strong corpus of knowledge in modern biology, paving the way to carriers in bioengineering or biotechnology. During the two years of major, students will follow courses on molecular biology, cellular biology and its integration at the organism level, genomics.

**Courses built on experimental approaches**

Experimentation is at the heart of progress in biology. The biology option is thus built around experimentation. Half of classes will be practical work, performed over weeks. This allows students to build their knowledge, acquire a sound scientific reasoning, and get familiar with the main techniques of modern biology.

**Second year Syllabus - Mathematics and Physics**

For more information on the second year curriculum for the double major in Mathematics and Physics (i.e. courses, ECTS credits, etc.), please consult the syllabus.

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