Prereq: Four years of high school mathematics Introduction to the mathematics of finite systems. Logic; Boolean algebra; induction and recursion; sets, functions, relations, equivalence, and partially ordered sets; elementary combinatorics; modular arithmetic and the Euclidean algorithm; group theory; permutations and symmetry groups; graph theory. Selected applications. The concept of a proof and development of the ability to recognize and construct proofs are part of the course.
Score: 6.7114224 Details | Listing | Web page
Prereq: Four years of high school mathematics Introduction to the mathematics of finite systems. Logic; Boolean algebra; induction and recursion; sets, functions, relations, equivalence, and partially ordered sets; elementary combinatorics; modular arithmetic and the Euclidean algorithm; group theory; permutations and symmetry groups; graph theory. Selected applications. The concept of a proof and development of the ability to recognize and construct proofs are part of the course.
Score: 6.7114224 Details | Listing | Web page
Prereq: One semester of calculus This course is an introduction to management science and the quantitative approach to decision making. Our focus will be on deterministic models, in which we assume that all problem parameters are known with certainty. The covered topics may include Linear and Integer Programming, Network Models, Inventory Models (Stationary Demand), Nonlinear Programming, Goal Programming, and Dynamic Programming. We emphasize model development and case studies, using spreadsheets and other computer software. The applications we study occur in manufacturing and transportation systems, as well as in finance and general management.
Score: 6.7114224 Details | Listing | Web page
Prereq: One semester of calculus This course is an introduction to management science and the quantitative approach to decision making. Our focus will be on deterministic models, in which we assume that all problem parameters are known with certainty. The covered topics may include Linear and Integer Programming, Network Models, Inventory Models (Stationary Demand), Nonlinear Programming, Goal Programming, and Dynamic Programming. We emphasize model development and case studies, using spreadsheets and other computer software. The applications we study occur in manufacturing and transportation systems, as well as in finance and general management.
Score: 6.7114224 Details | Listing | Web page
Prereqs: One year of Calculus, computing experience An introduction to the basic concepts of linear algebra, matrix theory, and differential equations that are used widely in modern engineering and science. Intended for engineering and science majors whose program does not permit taking both 110.201 and 110.302.
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Prereqs: One year of Calculus, computing experience An introduction to the basic concepts of linear algebra, matrix theory, and differential equations that are used widely in modern engineering and science. Intended for engineering and science majors whose program does not permit taking both 110.201 and 110.302.
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Prereq: one year of calculus. Recommended corequisite: multivariable calculus. - Students cannot receive credit for both 550.310 and 550.311. Students cannot receive credit for 550.310 after having received credit for 550.420 or 550.430. An introduction to probability and statistics at the calculus level, intended for engineering and science students planning to take only one course on the topics. This course will be at the same technical level as 550.311. Students are encouraged to consider 550.420-430 instead. Combinatorial probability, independence, conditional probability, random variables, expectation and moments, limit theory, estimation, confidence intervals, hypothesis testing, tests of means and variances, goodness-of-fit. Prerequisite: one year of calculus. Recommended corequisite: multivariable calculus.
Score: 6.7114224 Details | Listing | Web page
Prereq: one year of calculus. Recommended corequisite: multivariable calculus. - Students cannot receive credit for both 550.310 and 550.311. Students cannot receive credit for 550.310 after having received credit for 550.420 or 550.430. An introduction to probability and statistics at the calculus level, intended for engineering and science students planning to take only one course on the topics. This course will be at the same technical level as 550.311. Students are encouraged to consider 550.420-430 instead. Combinatorial probability, independence, conditional probability, random variables, expectation and moments, limit theory, estimation, confidence intervals, hypothesis testing, tests of means and variances, goodness-of-fit. Prerequisite: one year of calculus. Recommended corequisite: multivariable calculus.
Score: 6.7114224 Details | Listing | Web page
Prereq: one year of calculus. Recommended corequisite: multivariable calculus. - Students cannot receive credit for both 550.310 and 550.311. Students cannot receive credit for 550.310 after having received credit for 550.420 or 550.430. An introduction to probability and statistics at the calculus level, intended for engineering and science students planning to take only one course on the topics. This course will be at the same technical level as 550.311. Students are encouraged to consider 550.420-430 instead. Combinatorial probability, independence, conditional probability, random variables, expectation and moments, limit theory, estimation, confidence intervals, hypothesis testing, tests of means and variances, goodness-of-fit. Prerequisite: one year of calculus. Recommended corequisite: multivariable calculus.
Score: 6.7114224 Details | Listing | Web page
Prerequisite: One year of calculus; Corequisite: 110.202 recommended An introduction to probability and statistics at the calculus level, intended for students in the biological sciences planning to take only one course on the topics. This course will be at the same technical level as 550.310. Students are encouraged to consider 550.420-430 instead. Combinatorial probability, independence, conditional probability, random variables, expectation and moments, limit theory, estimation, confidence intervals, hypothesis testing, tests of means and variances, and goodness-of-fit will be covered. Students cannot receive credit for both 550.310 and 550.311. Students cannot receive credit for 550.311 after having received credit for 550.420 or 550.430.
Score: 6.7114224 Details | Listing | Web page
Prerequisite: One year of calculus; Corequisite: 110.202 recommended An introduction to probability and statistics at the calculus level, intended for students in the biological sciences planning to take only one course on the topics. This course will be at the same technical level as 550.310. Students are encouraged to consider 550.420-430 instead. Combinatorial probability, independence, conditional probability, random variables, expectation and moments, limit theory, estimation, confidence intervals, hypothesis testing, tests of means and variances, and goodness-of-fit will be covered. Students cannot receive credit for both 550.310 and 550.311. Students cannot receive credit for 550.311 after having received credit for 550.420 or 550.430.
Score: 6.7114224 Details | Listing | Web page
Prerequisites: 550.361 and multivariable calculus An introductory survey of optimization methods, supporting mathematical theory and concepts, and application to problems of planning, design, prediction, estimation, and control in engineering, management, and science. Study of varied optimization techniques including linear programming, network-problem methods, dynamic programming, integer programming, and nonlinear programming. Appropriate for undergraduate and graduate students without the mathematical background required for 550.661.
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Prerequisites: EN.550.171 (AS.110.204 with permission of instructor), linear algebra, computing experience. A first course in the mathematical theory of secure and reliable electronic communication. Cryptology is the study of secure communication: How can we ensure the privacy of messages? Coding theory studies how to make communication reliable: How can messages be sent over noisy lines? Topics include finite field arithmetic, error-detecting and error-correcting codes, data compressions, ciphers, one-time pads, the Enigma machine, one-way functions, discrete logarithm, primality testing, secret key exchange, public key cryptosystems, digital signatures, and key escrow
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Prerequisites: Calculus III, and 550.291 or approved alternative (e.g.,110.201) A first course on computational differential equations and applications. Topics include floating-point arithmetic, algorithms and convergence, root-finding (midpoint, Newton, and secant methods), numerical differentiation and integration, and numerical solution of initial value problems (RungeâKutta, multistep, extrapolation methods, stability, implicit methods, and stiffness). Theoretical topics such as existence, uniqueness, and stability of solutions to initial-value problems, conversion of higher order/ non-autonomous equations to systems, etc., will be covered as needed. Matlab is used to solve all numerical exercises; no previous experience with computer programming is required.
Score: 6.7114224 Details | Listing | Web page
Prerequisites: ( EN.550.310 or EN.550.311 or EN.550.420 or EN.550.430 ) and EN.550.361 Formulation, analysis, interpretation, and evaluation of mathematical models. Synthesis of ideas, techniques, and models from mathematical sciences, science, and engineering.Case studies to illustrate basic features of the modeling process. Project-oriented practice and guidance in modeling techniques, research techniques, and written and oral communication of mathematical concepts. The focus of this version of the course is on applied statistics, that is, using statistics to solve real-world problems. The R statistical package will be introduced. No previous knowledge of computing is necessary.Formulation, analysis, interpretation, and evaluation of mathematical models. Synthesis of ideas, techniques, and models from mathematical sciences, science, and engineering. Case studies to illustrate basic features of the modeling process. Project-oriented practice and guidance in modeling techniques, research techniques and written and oral commucation of mathematical concepts.
Score: 6.7114224 Details | Listing | Web page
Prereq: (110.106 or 110.108) and (110.107 or 110.109) or AP Credit for Calculus I and II Recommended corequisite: multivariable calculus. Probability and its applications, at the calculus level. Emphasis on techniques of application rather than on rigorous mathematical demonstration. Probability, combinatorial probability, random variables, distribution functions, important probability distributions, independence, conditional probability, moments, covariance and correlation, limit theorems. Students initiating graduate work in probability or statistics should enroll in 550.620.
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Prereq: (110.106 or 110.108) and (110.107 or 110.109) or AP Credit for Calculus I and II Recommended corequisite: multivariable calculus. Probability and its applications, at the calculus level. Emphasis on techniques of application rather than on rigorous mathematical demonstration. Probability, combinatorial probability, random variables, distribution functions, important probability distributions, independence, conditional probability, moments, covariance and correlation, limit theorems. Students initiating graduate work in probability or statistics should enroll in 550.620.
Score: 6.7114224 Details | Listing | Web page
Mathematical theory of stochastic processes. Emphasis on deriving the dependence relations, statistical properties, and sample path behavior including random walks, Markov chains (both discrete and continuous time), Poisson processes, martingales, and Brownian motion. Applications that illuminate the theory. Prerequisite: 550.420.
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Prerequisite: 550.420 or approved alternative. Introduction to the basic principles of statistical reasoning and data analysis. Emphasis on techniques of application. Classical parametric estimation, hypothesis testing, and multiple decision problems; linear models, analysis of variance, and regression; nonparametric and robust procedures; decision-theoretic setting, Bayesian methods.
Score: 6.7114224 Details | Listing | Web page
Prerequisite: 550.420 or approved alternative. Introduction to the basic principles of statistical reasoning and data analysis. Emphasis on techniques of application. Classical parametric estimation, hypothesis testing, and multiple decision problems; linear models, analysis of variance, and regression; nonparametric and robust procedures; decision-theoretic setting, Bayesian methods.
Score: 6.7114224 Details | Listing | Web page
Prerequisite: 550.420 or approved alternative. Introduction to the basic principles of statistical reasoning and data analysis. Emphasis on techniques of application. Classical parametric estimation, hypothesis testing, and multiple decision problems; linear models, analysis of variance, and regression; nonparametric and robust procedures; decision-theoretic setting, Bayesian methods.
Score: 6.7114224 Details | Listing | Web page
By surveying legal cases from various parts of the world, this course brings the tools of anthropology to examine how universal human rights discourses and institutions have interlocked with cultural norms, social relations and national politics.
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Anthropology of the Self. This course examines various cultures, histories, and philosophies of selfhood, focusing especially on questions of desire, pleasure, emotion, embodiment, morality, sensuality, and the emergence of the modern self. Cross-listed with Humanities Center
Score: 6.7114224 Details | Listing | Web page
What kind of activity is prayer? Are we talking to God(s), to our ancestors, to ourselves? What are the differences between choosing our own words and repeating the words of an established prayer? The course will explore these and similar questions with particular attention to the language of prayers across a number of religious traditions.
Score: 6.7114224 Details | Listing | Web page
This course will follow the life of the image in both religious and secular contexts in South Asia and ask how the image functions at the level of the domestic and the political.
Score: 6.7114224 Details | Listing | Web page
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