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Math 679 is a graduate level mathematics course whose purpose is to prove Mazur's theorem (link is external). Mazur's theorem is a well-known and important result, however it is not often taught in classroom settings. The course is divided into three parts: elliptic curves and abelian varieties, moduli of elliptic curves, and proof of Mazur’s theorem.
- Keywords:
- Abelian varieties Curves Algebraic Curves Elliptic
- Resource Type:
- Courseware
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Courseware
CHEM 216 builds on the experimental approach started in CHEM 211. Students participate in planning exactly what they are going to do in the laboratory by being given general goals and directions that have to be adapted to fit the specific project they will be working on. They use microscale equipment, which requires them to develop manual dexterity and care in working in the laboratory. They also evaluate the results of their experiments by checking for identity and purity using various chromatographic and spectroscopic methods.
- Subjects:
- Laboratory Techniques and Safety and Chemistry
- Keywords:
- Chemical laboratories Chemistry Organic Chemical laboratories -- Technique Organic compounds -- Synthesis
- Resource Type:
- Courseware
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Courseware
The focus of this guided inquiry laboratory is to foster critical thinking that allows students to design, perform, and interpret experiments. In addition, the student acquires technical skills that are required for further advancement in experimental sciences. Although an ability to collect and analyze data in a quantitative manner is developed, the emphasis of the course is to provide a qualitative understanding of the basic concepts of chemistry. This is accomplished by demonstrating that chemical principles are derived from experimental data. The goal is to provide students both with a more accurate picture of the scientific process and with skills that are relevant to solving real life problems.
- Subjects:
- Laboratory Techniques and Safety and Chemistry
- Keywords:
- Chemical laboratories Chemical laboratories -- Technique Chemistry
- Resource Type:
- Courseware
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Courseware
In electrical engineering, solid-state materials and the properties play an essential role. A thorough understanding of the physics of metals, insulators and semiconductor materials is essential for designing new electronic devices and circuits. After short introduction of the IC fabrication process, the course starts with the crystallography. This will be followed by the basic principle of the quantum mechanics, the sold-state physics, band-structure and the relation with electrical properties of the solid-state materials. When the material physics has been throughly understood, the physics of the semiconductor device follows quite naturally and can be understood quickly and efficiently.
- Subjects:
- Physics and Electrical Engineering
- Keywords:
- Semiconductors Solid state physics Matter -- Properties
- Resource Type:
- Courseware
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Courseware
In this nuclear energy course, we will tackle provocative questions such as: -Is nuclear energy a good substitute for fossil fuels to reduce our CO2 emission or not? -Can nuclear reactors operate safely without any harm to the public and environment? -How much nuclear waste is produced and how long does it need to be stored safely? -How can we make nuclear energy clean and more sustainable? -How much are nuclear energy costs? You will learn the physics behind nuclear science, how to gain energy from nuclear fission, how nuclear reactors operate safely, and the life cycle of nuclear fuel: from mining to disposal. In the last part of the course, we will focus on what matters most in the public debate: the economic and social impact of nuclear energy but also the future of energy systems. Practically, we will: -Teach you about nuclear science and technology (radiation and radioactivity, nuclear reactions, nuclear reactors and fuel cycle, economics of nuclear energy, and the sociality aspects) -Show you short videos about the theory and practical implementation of nuclear energy -Stimulate discussion and debate about nuclear energy -Ask you to formulate your own opinion about nuclear energy and its role in society The GENTLE consortium has sponsored and prepared this course. GENTLE is focused on maintaining the current high level of nuclear safety, and developing a highly skilled and well informed nuclear workforce, following the conclusion of the Council of the EU that it “it is essential to maintain in the European Union a high level of training in the nuclear field” to deal with reactor fleet safely, decommission obsolete plants, be involved in new builds where policy dictates, and deal with the legacy and future radioactive wastes.
- Subjects:
- Physics and Electrical Engineering
- Keywords:
- Nuclear engineering Nuclear physics Nuclear energy
- Resource Type:
- Courseware
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Courseware
The focus of this course: - Applications of topology in condensed matter based on bulk-edge correspondence. - Special attention to the most active research topics in topological condensed matter: theory of topological insulators and Majorana fermions, topological classification of “grand ten” symmetry classes, and topological quantum computation - Extensions of topology to further areas of condensed matter, such as photonic and mechanical systems, topological quantum walks, topology in fractionalized systems, driven or dissipative systems.
- Keywords:
- Condensed matter Topology
- Resource Type:
- Courseware
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Courseware
The lectures are at a beginning graduate level and assume only basic familiarity with Functional Analysis and Probability Theory. Topics covered include: Random variables in Banach spaces: Gaussian random variables, contraction principles, Kahane-Khintchine inequality, Anderson’s inequality. Stochastic integration in Banach spaces I: γ-Radonifying operators, γ-boundedness, Brownian motion, Wiener stochastic integral. Stochastic evolution equations I: Linear stochastic evolution equations: existence and uniqueness, Hölder regularity. Stochastic integral in Banach spaces II: UMD spaces, decoupling inequalities, Itô stochastic integral. Stochastic evolution equations II: Nonlinear stochastic evolution equations: existence and uniqueness, Hölder regularity.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Stochastic partial differential equations Evolution equations
- Resource Type:
- Courseware
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Courseware
Quantum Information Processing aims at harnessing quantum physics to conceive and build devices that could dramatically exceed the capabilities of today’s “classical” computation and communication systems. In this course, we will introduce the basic concepts of this rapidly developing field.
- Subjects:
- Physics
- Keywords:
- Quantum computing Quantum theory -- Data processing
- Resource Type:
- Courseware
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Courseware
Mesoscopic physics is the area of Solid State physics that covers the transition regime between macroscopic objects and the microscopic, atomic world.The main goal of the course is to introduce the physical concepts underlying the phenomena in this field.
- Subjects:
- Physics
- Keywords:
- Mesoscopic phenomena (Physics)
- Resource Type:
- Courseware
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Courseware
How do populations grow? How do viruses spread? What is the trajectory of a glider? Many real-life problems can be described and solved by mathematical models. In this course, you will form a team with another student and work in a project to solve a real-life problem. You will learn to analyze your chosen problem, formulate it as a mathematical model (containing ordinary differential equations), solve the equations in the model, and validate your results. You will learn how to implement Euler’s method in a Python program. If needed, you can refine or improve your model, based on your first results. Finally, you will learn how to report your findings in a scientific way. This course is mainly aimed at Bachelor students from Mathematics, Engineering and Science disciplines. However it will suit anyone who would like to learn how mathematical modeling can solve real-world problems.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical models
- Resource Type:
- Courseware