The class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models.

Explores a variety of models and optimization techniques for the solution of airline schedule planning problems. Schedule design, fleet assignment, aircraft maintenance routing, crew scheduling, robust planning, passenger mix, integrated schedule planning, and other topics. Solution techniques involving decomposition, e.g., Lagrangian relaxation, column generation and partitioning, and state-of-the-art applications of these techniques to airline problems. Explores a variety of models and optimization techniques for the solution of airline schedule planning and operations problems. Schedule design, fleet assignment, aircraft maintenance routing, crew scheduling, passenger mix, and other topics are covered. Recent models and algorithms addressing issues of model integration, robustness, and operations recovery are introduced. Modeling and solution techniques designed specifically for large-scale problems, and state-of-the-art applications of these techniques to airline problems are detailed.

This course covers the fundamental notions and results about algebraic varieties over an algebraically closed field. It also analyzes the relations between complex algebraic varieties and complex analytic varieties.

Two options offered, both covering fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Both options show the utility of abstract concepts and teach understanding and construction of proofs. Option A chooses less abstract definitions and proofs, and gives applications where possible. Option B is more demanding and for students with more mathematical maturity. Places greater emphasis on point-set topology.

Focuses on modeling, quantification, and analysis of uncertainty by teaching random variables, simple random processes and their probability distributions, Markov processes, limit theorems, elements of statistical inference, and decision making under uncertainty. This course extends the discrete probability learned in the discrete math class. It focuses on actual applications, and places little emphasis on proofs. A problem set based on identifying tumors using MRI (Magnetic Resonance Imaging) is done using Matlab.

Physics, modeling, application, and technology of compound semiconductors (primarily III-Vs) in electronic, optoelectronic, and photonic devices and integrated circuits. Topics: properties, preparation, and processing of compound semiconductors; theory and practice of heterojunctions, quantum structures, and pseudomorphic strained layers; metal-semiconductor field effect transistors (MESFETs); heterojunction field effect transistors (HFETs) and bipolar transistors (HBTs); and optoelectronic devices.

Covers computational and data analysis techniques for environmental engineering applications. First third of subject introduces MATLAB and numerical modeling. Second third emphasizes probabilistic concepts used in data analysis. Final third provides experience with statistical methods for analyzing field and laboratory data. Numerical techniques such as Monte Carlo simulation are used to illustrate the effects of variability and sampling. Concepts are illustrated with environmental examples and data sets. This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environmental Applications (1.017) and Uncertainty in Engineering (1.010), are being jointly offered and taught as a single course.

This lesson begins a 4 lesson review about adding whole numbers, carrying in addition, and place value. [Developmental Math playlist: Lesson 10 of 196]

This is the second lesson that reviews the addition of whole numbers, carrying in addition, and place value. [Developmental Math playlist: Lesson 11 of 196]

This is the fourth lesson that reviews the addition of whole numbers, carrying in addition, and place value. [Developmental Math playlist: Lesson 12 of 196]

This is the fourth lesson that reviews the addition of whole numbers, carrying in addition, and place value.[[Developmental Math playlist: Lesson 13 of 196]

This is the first lesson of a 6-part review of the division of whole numbers. [Developmental Math playlist: Lesson 26 of 196]

This is the 2nd part of a 6-part review of the division of whole numbers. [Developmental Math playlist: Lesson 27 of 196]

This is part 3 of a 6-part review of the division of whole numbers. [Developmental Math playlist: Lesson 28 of 196]

This is lesson 4 of a 6-part review of the division of whole numbers. [Developmental Math playlist: Lesson 29 of 196]

This is lesson 5 of the 6-part review of the division of whole numbers. [Developmental Math playlist: Lesson 30 of 196]

This is the final lesson of the 6-part review of the division of whole numbers. [Developmental Math playlist: Lesson 31 of 196]

This lesson begins a 6-part review of multiplication of whole numbers. [Developmental Math playlist: Lesson 20 of 196]

This is the 2nd part of a 6-part review of the multiplication of whole numbers. [Developmental Math playlist: Lesson 21 of 196]