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In this unit we use the geometric concept of symmetry to introduce some of the basic ideas of group theory, including group tables, and the four properties, or axioms, that define a group.
We discuss intuitive ideas of symmetry for a two-dimensional figure, and define the set of symmetries of such a figure. We then view these symmetries as functions that combine under composition, and show that the resulting structure has properties known as closure, identity, inverses and associativity.
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This is a free excel 2007 tutorial with explanations and examples
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Equilibria and the solution of linear and linear least squares problems. Dynamical systems and the eigenvalue problem with the Jordan form and Laplace transform via complex integration
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Course Aims:
Develop a theory which can characterize the behavior of real-world Random Signals and Processes.
Use standard Probability Theory for this.
Random signal theory is important for
Analysis of signals,
Inference of underlying system parameters from noisy observed data,
Design of optimal systems (digital and analogue signal recovery, signal classification, estimation ...),
Predicting system performance (error-rates, signal-to-noise ratios, ...),
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- Ensemble theory; noninteracting classical and quantum systems;
- cluster expansion for interacting systems, many body quantum mechanics, phase transitions, scaling, renormalisation;
- nonequilibrium thermodynamics;
- Boltzmann transport equation
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This resource contains notes about exploring distance-time graphs as a mathematical model of a journey.
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Continuation of Quantum Mechanics I (introduction to quantum mechanics and quantum mechanics in one-dimension) including study of symmetries and perturbation theory. Applications to orbital angular momentum, spherical symmetric potentials (three-dimension square well potential, hydrogen like atom, three-dimension harmonic oscillator etc.), spin angular momentum, spin-orbit interaction and composition of angular momentum. A concept of symmetries is characterized by orbital angular momentum, spin angular momentum and interchange of the two particles.
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This course is an introduction to game theory and strategic thinking. Ideas such as dominance, backward induction, Nash equilibrium, evolutionary stability, commitment, credibility, asymmetric information, adverse selection, and signaling are discussed and applied to games played in class and to examples drawn from economics, politics, the movies, and elsewhere.
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Physics for Humanists is intended for those who are intellectually and emotionally curious but do not intend to specialize in the natural sciences. The course covers facts and concepts of classical and modern physics; eminent scientists and the emotions that have impelled them; nuclear energy and nuclear bombs; and the interaction, both constructive and destructive, between science and society.
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This course explores the basic principles of chemistry and their application to engineering systems. It deals with the relationship between electronic structure, chemical bonding, and atomic order. It also investigates the characterization of atomic arrangements in crystalline and amorphous solids: metals, ceramics, semiconductors, and polymers (including proteins). Topics covered include organic chemistry, solution chemistry, acid-base equilibria, electrochemistry, biochemistry, chemical kinetics, diffusion, and phase diagrams.
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