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Course Criteria
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3.00 Credits
Newtonian Mechanics, spectacular as it is in describing planetary motion and a wide range of other phenomena, only hints at the richness of behaviors seen in the universe. Special relativity has extended physics into the realm of high speeds and high energies and requires us to rethink our basic notions of space and time. Quantum mechanics successfully describes atoms, molecules, and solids while at the same time calling into question our notions of what can be predicted by a physical theory. Statistical physics reveals new behaviors that emerge when many particles are present in a system. This course covers the same basic material as Physics 142 but in a small seminar format for students with strong prior preparation in physics.
Prerequisite:
Placement by the department (see "advanced placement" section in the description about the department). Students may take either Physics 142 or Physics 151 but not both
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3.00 Credits
In this course, we study electromagnetic phenomena and their mathematical description. Topics include electrostatics, magnetic fields, and electromagnetic induction, DC and AC circuits, and the electromagnetic properties of matter. We also introduce Maxwell's equations, which express the essence of the theory in remarkably succinct form.
Prerequisite:
Physics 142, Mathematics 105 or 106
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3.00 Credits
Waves and oscillations characterize many different physical systems, including vibrating strings, springs, water waves, sound waves, electromagnetic waves, and gravitational waves. Quantum mechanics even describes particles with wave functions. Despite these diverse settings waves exhibit several common characteristics, so that the understanding of a few simple systems can provide insight into a wide array of phenomena. In this course we begin with the study of oscillations of simple systems with only a few degrees of freedom. We then move on to study transverse and longitudinal waves in continuous media in order to gain a general description of wave behavior. The rest of the course focuses on electromagnetic waves and in particular on optical examples of wave phenomena. In addition to well known optical effects such as interference and diffraction, we will study a number of modern applications of optics such as short pulse lasers and optical communications. Throughout the course mathematical methods useful for higher-level physics will be introduced.
Prerequisite:
Physics 201; co-requisite: Physics/Mathematics 210 or permission of instructor
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3.00 Credits
This course covers a variety of mathematical methods used in the sciences, focusing particularly on the solution of ordinary and partial differential equations. In addition to calling attention to certain special equations that arise frequently in the study of waves and diffusion, we develop general techniques such as looking for series solutions and, in the case of nonlinear equations, using phase portraits and linearizing around fixed points. We study some simple numerical techniques for solving differential equations. A series of optional sessions in Mathematica will be offered for students who are not already familiar with this computational tool.
Prerequisite:
Mathematics 105 or 106 and familiarity with Newtonian mechanics at the level of Physics 131
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3.00 Credits
The cancer death rate scales like (age)6 so it was thought that a proliferating cancer cell must have acquired 6 mutations. The probability of having had N sexual partners scales like N2.4. Body Mass Index = Mass / Length2. The heart rate is proportional to the organism's mass0.75. The number of policemen scales like population1.15. Power-law relationships often describe emergent phenomena of self-organizing systems. In this course we will learn how to obtain data and plot it in an informative way, including estimates of the errors of fits. We will learn how to describe phenomena with differential equations and to find analytic and numerical solutions. With those tools we will study the human experience: births, body size, sex, death rates (by cause, by age, by gender), metrics of cities, distributions of common names, population growth rates, per capita use of energy, the spread of disease, etc. Projects will involve applying the methods to new phenomena.
Prerequisite:
MATH 105
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3.00 Credits
This course serves as a one-semester introduction to the history, formalism, and phenomenology of quantum mechanics. We begin with a discussion of the historical origins of the quantum theory, and the Schroedinger wave equation. The concepts of matter waves and wave-packets are introduced. Solutions to one-dimensional problems will be treated prior to introducing the system which serves as a hallmark of the success of quantum theory, the three-dimensional hydrogen atom. In the second half of the course, we will develop the important connection between the underlying mathematical formalism and the physical predictions of the quantum theory. We then go on to apply this knowledge to several important problems within the realm of atomic and nuclear physics.
Prerequisite:
Physics 202 and Physics 210
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3.00 Credits
Properties like temperature, pressure, magnetization, heat capacity, conductivity, etc describe the material world. Macroscopic objects are made up of huge numbers of fundamental particles interacting in simple ways--obeying the Schr?dinger equation, Newton's and Coulomb's Laws. In this course we will develop the tools of statistical physics, which will allow us to predict the cooperative phenomena that emerge in large ensembles of interacting particles. We will apply those tools to a wide variety of physical questions, including the behavior of gasses, polymers, heat engines, magnets, and electrons in solids.
Prerequisite:
Required: Physics 201, Physics 210; recommended: Physics 202, Physics 301
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3.00 Credits
No course description available.
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3.00 Credits
This course will provide an overview of Computational Biology, the application of computational, mathematical, and physical problem-solving techniques to interpret the rapidly expanding amount of biological data. Topics covered will include database searching, DNA sequence alignment, phylogeny reconstruction, RNA and protein structure prediction, methods of analyzing gene expression, networks, and genome assembly using techniques such as string matching, dynamic programming, suffix trees, hidden Markov models, and expectation-maximization.
Prerequisite:
Programming experience (e.g., CSCI 136), mathematics (PHYS 210 or MATH 105), and physical science (PHYS 142 or 151, or CHEM 151 or 153 or 155), or permission of the instructor
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3.00 Credits
Living in the early decades of the information age, we find ourselves depending more and more on codes that protect messages against either noise or eavesdropping. This course examines some of the most important codes currently being used to protect information, including linear codes, which in addition to being mathematically elegant are the most practical codes for error correction, and the RSA public key cryptographic scheme, popular nowadays for internet applications. We also study the standard AES system as well as an increasingly popular cryptographic strategy based on elliptic curves. Looking ahead by a decade or more, we show how a "quantum computer" could crack any RSA code scheme in short order, and how quantum cryptographic devices will achieve security through the Heisenberg uncertainty principleinherent unpredictability of quantum events.
Prerequisite:
Physics 210 or Mathematics 211 (possibly concurrent) or permission of the instructors; students not satisfying the course prerequisites but who have completed Mathematics 209 or Mathematics 251 are particularly encouraged to ask to be admitted
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