Courses tagged with "Calculus I" (279)

The level of popularity you experienced in childhood and adolescence is still affecting you today in ways that you may not even realize. Learn about how psychologists study popularity and how these same concepts can be used in adulthood to be more successful at work, become better parents, and have a happier life.

How can you tell a secret when everyone is able to listen in? In this course, you will learn how to use quantum effects, such as quantum entanglement and uncertainty, to implement cryptographic tasks with levels of security that are impossible to achieve classically.

This interdisciplinary course is an introduction to the exciting field of quantum cryptography, developed in collaboration between QuTech at Delft University of Technology and the California Institute of Technology.

By the end of the course you will

• Be armed with a fundamental toolbox for understanding, designing and analyzing quantum protocols.
• Understand quantum key distribution protocols.
• Understand how untrusted quantum devices can be tested.
• Be familiar with modern quantum cryptography – beyond quantum key distribution.

This course assumes a solid knowledge of linear algebra and probability at the level of an advanced undergraduate. Basic knowledge of elementary quantum information (qubits and simple measurements) is also assumed, but if you are completely new to quantum information additional videos are provided for you to fill in any gaps.

Already know something about quantum mechanics, quantum bits and quantum logic gates, but want to design new quantum algorithms, and explore multi-party quantum protocols? This is the course for you!

In this advanced graduate physics course on quantum computation and quantum information, we will cover:

• The formalism of quantum errors (density matrices, operator sum representations)
• Quantum error correction codes (stabilizers, graph states)
• Fault-tolerant quantum computation (normalizers, Clifford group operations, the Gottesman-Knill Theorem)
• Models of quantum computation (teleportation, cluster, measurement-based)
• Quantum Fourier transform-based algorithms (factoring, simulation)
• Quantum communication (noiseless and noisy coding)
• Quantum protocols (games, communication complexity)

Research problem ideas are presented along the journey.

Learner Testimonial

“This course is hard!” 
-- Anonymous MIT graduate student

This is an introduction to quantum computation, a cutting edge field that tries to exploit the exponential power of computers based on quantum mechanics. The course does not assume any prior background in quantum mechanics, and can be viewed as a very simple and conceptual introduction to that field.

Quantum computation is a remarkable subject building on the great computational discovery that computers based on quantum mechanics are exponentially powerful. This course aims to make this cutting-edge material broadly accessible to undergraduate students, including computer science majors who do not have any prior exposure to quantum mechanics. The course starts with a simple introduction to the fundamental principles of quantum mechanics using the concepts of qubits (or quantum bits) and quantum gates. This treatment emphasizes the paradoxical nature of the subject, including entanglement, non-local correlations, the no-cloning theorem and quantum teleportation. The course covers the fundamentals of quantum algorithms, including the quantum fourier transform, period finding, Shor's quantum algorithm for factoring integers, as well as the prospects for quantum algorithms for NP-complete problems. It also discusses the basic ideas behind the experimental realization of quantum computers, including the prospects for adiabatic quantum optimization and the D-Wave controversy.

Before your course starts, try the new edX Demo where you can explore the fun, interactive learning environment and virtual labs. Learn more.

Do I need a textbook for this class?
No. Notes will be posted each week. If you wish to consult other references, a list of related textbooks and online resources will be provided.

What is the estimated effort for course?
About 5-12 hrs/week.

Why is the work load range so wide?
How long you spend on the course depends upon your background and on the depth to which you wish to understand the material. The topics in this course are quite open ended, and will be presented so you can understand them at a high level or can try to follow it at a sophisticated level with the help of the posted notes.

How much does it cost to take the course?
Nothing! The course is free.

Will the text of the lectures be available?
Yes. All of our lectures will have transcripts synced to the videos.

Do I need to watch the lectures live?
No. You can watch the lectures at your leisure.

Quantum Mechanics for Everyone is a four-week long MOOC that teaches the basic ideas of quantum mechanics with a method that requires no complicated math beyond taking square roots (and you can use a calculator for that). Quantum theory is taught without “dumbing down” any of the material, giving you the same version experts use in current research. We will cover the quantum mystery of the two-slit experiment and advanced topics that include how to see something without shining light on it (quantum seeing in the dark) and bunching effects of photons (Hong-Ou-Mandel effect).

To get a flavor for the course and see if it is right for you, watch "Let's get small", which shows you how poorly you were taught what an atom looks like, and "The fallacy of physics phobia." 

Please note: the four sections of this course will be released on a weekly basis from April 18, 2017 to May 9, 2017, when all the course material will be available and the course will become fully self-paced.

Knowing the geometrical structure of the molecules around us is one of the most important and fundamental issues in the field of chemistry. This course introduces the two primary methods used to determine the geometrical structure of molecules: molecular spectroscopy and gas electron diffraction.

In molecular spectroscopy, molecules are irradiated with light or electric waves to reveal rich information, including:

• Motions of electrons within a molecule (Week 1),
• Vibrational motions of the nuclei within a molecule (Week 2), and
• Rotational motions of a molecule (Week 3).

In the gas electron diffraction method, molecules are irradiated with an accelerated electron beam. As the beam is scattered by the nuclei within the molecule, the scattered waves interfere with each other to generate a diffraction pattern. In week 4, we study the fundamental mechanism of electron scattering and how the resulting diffraction images reveal the geometrical structure of molecules.

By the end of the course, you will be able to understand molecular vibration plays an important role in determining the geometrical structure of molecules and gain a fuller understanding of molecular structure from the information obtained by the two methodologies.

FAQ

Do I need to buy a textbook?

No, you can learn the contents without any textbooks. However, if you hope to learn more on the subjects treated in this course, you are recommended to read the textbook introduced below:

Kaoru Yamanouchi, “Quantum Mechanics of Molecular Structures,” Springer-Verlag, 2012.

In this quantum physics course you will learn the basic concepts of scattering – phase-shifts, time delays, Levinson’s theorem, and resonances – in the simple context of one-dimensional problems. We then turn to the study of angular momentum and the motion of particles in three-dimensional central potentials. We learn about the radial equation and study the case of the hydrogen atom in detail.

This is the final course in a series which includes:

• Quantum Mechanics: Wavefunctions, Operators, and Expectation Values
• Quantum Mechanics: Quantum Physics in 1D Potentials
• Quantum Mechanics: 1D Scattering and Central Potentials

The series is based on the MIT 8.04: Quantum Mechanics I. At MIT, 8.04 is the first of a three-course sequence in Quantum Mechanics, a cornerstone in the education of physics majors that prepares them for advanced and specialized studies in any field related to quantum physics.

After completing the 8.04x series, you will be ready to tackle the Mastering Quantum Mechanics course series on edX, which will be available in Spring 2018.

In this quantum physics course you will acquire concrete knowledge of quantum mechanics by learning to solve the Schrodinger equation for important classes of one-dimensional potentials. We study the associated energy eigenstates and bound states. The harmonic oscillator is solved using the differential equation as well as algebraically, using creation and annihilation operators. We discuss barrier penetration and the Ramsauer-Townsend effect.

This is the second course in a series which includes:

• Quantum Mechanics: Wavefunctions, Operators, and Expectation Values
• Quantum Mechanics: Quantum Physics in 1D Potentials
• Quantum Mechanics: 1D Scattering and Central Potentials

The series is based on the MIT 8.04: Quantum Mechanics I. At MIT, 8.04 is the first of a three-course sequence in Quantum Mechanics, a cornerstone in the education of physics majors that prepares them for advanced and specialized studies in any field related to quantum physics.

After completing the 8.04x series, you will be ready to tackle the Mastering Quantum Mechanics course series on edX, which will be available in Spring 2018.

In this quantum physics course you will learn the basics of quantum mechanics. We begin with de Broglie waves, the wavefunction, and its probability interpretation. We then introduce the Schrodinger equation, inner products, and Hermitian operators. We also study the time-evolution of wave-packets, Ehrenfest’s theorem, and uncertainty relations.

This is the first course in a series which includes:

• Quantum Mechanics: Wavefunctions, Operators, and Expectation Values
• Quantum Mechanics: Quantum Physics in 1D Potentials
• Quantum Mechanics: 1D Scattering and Central Potentials

The series is based on MIT 8.04: Quantum Mechanics I. At MIT, 8.04 is the first of a three-course sequence in Quantum Mechanics, a cornerstone in the education of physics majors that prepares them for advanced and specialized studies in any field related to quantum physics.

After completing the 8.04x series, you will be ready to tackle the Mastering Quantum Mechanics course series on edX, which will be available in Spring 2018.

This is the first course in the undergraduate Quantum Physics sequence. It introduces the basic features of quantum mechanics. It covers the experimental basis of quantum physics, introduces wave mechanics, Schrödinger's equation in a single dimension, and Schrödinger's equation in three dimensions.

This presentation of 8.04 by Barton Zwiebach (2016) differs somewhat and complements nicely the presentation of Allan Adams (2013). Adams covers a larger set of ideas; Zwiebach tends to go deeper into a smaller set of ideas, offering a systematic and detailed treatment. Adams begins with the subtleties of superpostion, while Zwiebach discusses the surprises of interaction-free measurements. While both courses overlap over a sizable amount of standard material, Adams discussed applications to condensed matter physics, while Zwiebach focused on scattering and resonances. The different perspectives of the instructors make the problem sets in the two courses rather different.
 

Together, this course and 8.06 Quantum Physics III cover quantum physics with applications drawn from modern physics. Topics covered in this course include the general formalism of quantum mechanics, harmonic oscillator, quantum mechanics in three-dimensions, angular momentum, spin, and addition of angular momentum.

8.06 is the third course in the three-sequence physics undergraduate Quantum Mechanics curriculum. By the end of this course, you will be able to interpret and analyze a wide range of quantum mechanical systems using both exact analytic techniques and various approximation methods. This course will introduce some of the important model systems studied in contemporary physics, including two-dimensional electron systems, the fine structure of Hydrogen, lasers, and particle scattering.

8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement.

8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

Have you ever wondered how you can apply math and science skills to real life? Do you wish you could go beyond what you've learned in the classroom? This science course will advance your knowledge as we unpack some important scientific thinking skills using real-world examples. By completing this course, you will be better prepared to continue studying math and science at the high school level and beyond.

In this course, a collaboration between The University of Queensland and Brisbane Grammar School, we will cover key scientific concepts related to:

• Measurement
• Estimation
• The validity of evidence
• The difference between logic and opinion
• Misconceptions
• Modeling
• Prediction
• Extrapolation

Each concept will be explored through real world examples and problems that will help you visualize how math and science work in your life.

This course is ideal for high school students looking to challenge themselves and further develop an interest in math and science. It is also applicable to high school science teachers looking for additional materials for teaching.

Clique aqui​ para a versão em português.

How much can we know of the physical world? Can we know everything? Or are there fundamental limits to how much we can explain? If there are limits, to what extent can we explain the nature of physical reality? RealityX investigates the limits of knowledge and what we can and cannot know of the world and ourselves.

We will trace the evolution of ideas about the nature of reality in philosophy and the natural sciences through the ages. Starting with the philosophers of Ancient Greece and ending with cutting edge theories about the universe, quantum physics, and the nature of consciousness.

Learners who complete this course will be able to:

A. Communicate with others about the latest scientific discoveries in various disciplines including cosmology, quantum physics, mathematics, machine intelligence and cognitive science.

B. Identify key points in history where scientific advances changed humanity’s philosophy and understanding of the nature of reality and our place in the Universe.

C. Reflect on and examine their own worldview and identify if any changes occurred during this course.

D. Confidently argue about scientific evidence, philosophical viewpoints, and others’ interpretations of both.

E. Demonstrate how the scientific method works, its limitations, and how scientists use it to construct knowledge about physical reality.

Join world-renowned physicist and author Marcelo Gleiser and leading experts as we explore how philosophers and physicists from Plato to Einstein and many others have attempted to explain the nature of the world and of reality.

This course will be offered in both English and Portuguese. Videos will have subtitles,discussions will be supported in both languages, as will all assignments.

This course is a project of the Institute for Cross-Disciplinary Engagement at Dartmouth (ICE), dedicated to transforming the dialogue between the sciences and the humanities in academia and in the public sphere in order to explore fundamental questions where a cross-disciplinary exchange is essential.

This is an Exploratorium Teacher Institute professional development course open to any middle or high school science teacher. This course is designed to help science teachers infuse their curriculum with hands-on STEM activities that support the NGSS engineering practices.

8.323, Relativistic Quantum Field Theory I, is a one-term self-contained subject in quantum field theory. Concepts and basic techniques are developed through applications in elementary particle physics, and condensed matter physics.

This course is the second course of the quantum field theory trimester sequence beginning with Relativistic Quantum Field Theory I (8.323) and ending with Relativistic Quantum Field Theory III (8.325). It develops in depth some of the topics discussed in 8.323 and introduces some advanced material.