analytical methods
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Statistics 110 (Probability), which has been taught at Harvard University by Joe Blitzstein (Professor of the Practice, Harvard Statistics Department) each year since 2006. Lecture videos, review materials, and over 250 practice problems with detailed solutions are provided. This course is an introduction to probability as a language and set of tools for understanding statistics, science, risk, and randomness. The ideas and methods are use...more
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Note: This course is offered by Stanford as an online course for credit. It can be taken individually, or as part of a master’s degree or graduate certificate earned online through the Stanford Center for Professional Development. This course provides a broad introduction to machine learning and statistical pattern recognition. Topics include: supervised learning (generative/discriminative learning, parametric/non-parametric learnin...more
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This course explores the physical processes that control Earth's atmosphere, ocean, and climate. Quantitative methods for constructing mass and energy budgets. Topics include clouds, rain, severe storms, regional climate, the ozone layer, air pollution, ocean currents and productivity, the seasons, El Niño, the history of Earth's climate, global warming, energy, and water resources.
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Concentrates on recognizing and solving convex optimization problems that arise in engineering. Topics include: Convex sets, functions, and optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interiorpoint methods. Applications to signal proc...more
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Analysis and optimized design of monolithic operational amplifiers and wide-band amplifiers; methods of achieving wide-band amplification, gain-bandwidth considerations; analysis of noise in integrated circuits and low noise design. Precision passive elements, analog switches, amplifiers and comparators, voltage reference in NMOS and CMOS circuits, Serial, successive-approximation, and parallel analog-to-digital converters. Switched-...more
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Topics include: Advanced memory management features of C and C++; the differences between imperative and object-oriented paradigms; the functional paradigm (using LISP) and concurrent programming (using C and C++); brief survey of other modern languages such as Python, Objective C, and C#. Prerequisites: Programming and problem solving at the Programming Abstractions level. Prospective students should know a reasonable amount of C++. Yo...more
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Continuation of Convex Optimization I. Topics include: Subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Alternating projections. Exploiting problem structure in implementation. Convex relaxations of hard problems, and global optimization via branch & bound. Robust optimization. Selected applications in areas such as control, circuit design, signal processing, and com...more
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This course teaches techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics covered include: sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; amortized analysis; graph algorithms; shortest paths; network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing.
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This is a continuation of Fundamentals of Physics, I (PHYS 200), the introductory course on the principles and methods of physics for students who have good preparation in physics and mathematics. This course covers electricity, magnetism, optics and quantum mechanics. Course Structure: 75 minute lectures, twice per week
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This course provides a thorough introduction to the principles and methods of physics for students who have good preparation in physics and mathematics. Emphasis is placed on problem solving and quantitative reasoning. This course covers Newtonian mechanics, special relativity, gravitation, thermodynamics, and waves.
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Under the guidance of Professor Lisa Anderson, Conceptual Foundations of International Politics is a graduate course at Columbia's School of International and Public Affairs which examines many of the central concepts, theories, and analytical tools used in contemporary social science to understand and explain international affairs.
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This graduate-level course is a continuation of Computational Science and Engineering I. Topics include numerical methods; initial-value problems; network flows; and optimization.
