Quantitative Course Descriptions

MIT Mathematics Courses

18.01 Calculus (5 semester credits)

Differentiation and integration of functions of one variable, with applications. Concept of function, limits, and continuity. Differentiation rules, application to graphing, rates, approximations, and extremum problems. Mean-value theorem. Definite and indefinite integration. Fundamental theorem of calculus. Applications of integration to geometry and science. Elementary functions. Techniques of integration. Approximation of definite integrals, infinite series, improper integrals, Taylor’s formula and l’Hopital’s rule.

18.02 Calculus (5 semester credits)

Prereq.: 18.001 or 18.01. Functions of several variables, with elementary linear algebra. Vector algebra in 3-space and n-space. Matrices, row-reduction, systems of linear equations. Vector-valued functions of one variable; space motion. Scalar functions of two and three variables; partial differentiation, gradient, approximation techniques. Double and triple integration, with applications. Vector fields, line integrals, exact differentials. Green’s theorem, Divergence theorem. Stokes’ theorem.

18.03 Differential Equations (4 semester credits)

Prereq.: 18.002 or 18.02. Examples of initial value problems in science and engineering associated with single equations and with systems of first order equations. Methods of solution include graphical constructions, similarity transformations, series, Laplace transforms, matrices, numerical integration and the phase plane. Emphasis on formulation of natural phenomena in terms of differential equations and on interpretation of the solutions.

18.05 Introduction to Probability and Statistics (3 semester credits)

Prereq.: 18.001, 18.01 or 18.012. A one semester introduction, covering both basic probability and statistics, with applications to the social, physical, and life sciences. The treatment of statistics is less formal than that in 18.441 and 18.443, making only limited use of calculus, but is more oriented towards theory and concepts than that in 18.055J. Relative frequency. Probability models. Combinatorics. Binomial and Poisson experiments. Normal approximation. Descriptive level of significance. Composite models. Chi-square approximation. Contingency tables. Hypothesis testing. Confidence regions. Random variables. Distribution-free methods, t-tests. Regression. Elements of decision theory.

18.700 Linear Algebra (3 semester credits)

Prereq.: 18.002 or 18.02. Basic subject on matrix theory and linear algebra, emphasizing the topics most useful in other disciplines. Covers the fundamental theory: systems of equations, vector spaces, determinants, eigenvalues, similarity, positive definite matrices and quadratic forms. Applications given to such topics as Gauss elimination with pivoting, least squares approximations, stability of systems of differential equations, and Rayleigh-Ritz variational techniques. Compared with 18.710 this subject is oriented more towards linear algebra as used in applications, and less towards theorems and proofs.

UC Berkeley Public Policy Courses

PP 240A/240B Decision Analysis, Modeling and Quantitative Methods in Policy Analysis (8 quarter credits)

This course integrates the theories of modeling, using linear and non-linear, static and sequential, and deterministic and stochastic models. Designed for the beginning student, the course encourages questions.

UC Berkeley Industrial Engineering and Operations Research Courses

The three courses marked with an asterisk would have been accepted for the Applied Mathematics major at UC Berkeley (letter from Department of Mathematics Acting Chair).

IEOR S162 Linear Programming (5 quarter credits)

Two 2-hour lectures and one 2-hour laboratory per week. Prerequisite: Mathematics 51A. An introduction to linear programming with emphasis on formulation, the simplex method, duality theory, post-optimization problems, network models and applications to industrial systems.

IEOR 220 Economics and Dynamics of Production (4 semester credits)

Three hours of lecture and one hour of discussion per week. Prerequisites: 262A (may be taken concurrently), Statistics 134. Modeling and analysis of production-service systems and engineering projects. Engineering economics, including project evaluation and risk analysis. Econometric and programming models of production, dynamic systems and production networks for analyses of resource utilization and output possibilities. (Instructor’s lecture schedule – first five weeks.)

*IEOR 231 Forecasting Models and Time Series Analysis (4 semester credits)

Two 1 1/2-hour lectures and one 2-hour laboratory per week. Prerequisites: 263A; Statistics 135. Forecasting Models and Time Series Analysis of discrete time series. The course includes a review of Minimum Mean Squared Error Predictors, Linear Predictors, and the use of Regression Models. Identification and estimation of parameters in autoregressive and moving average processes; linear stationary and non-stationary models; Kalman filters, Bayes estimation and Bayesian forecasting techniques. Updating algorithms for on-line adaptive forecasting. (Instructor’s course topics list.)

IEOR 254 Process Planning and Scheduling (3 semester credits)

Three hours of lecture per week. Prerequisites: 262A and 220. Mathematical and computer methods for production planning, scheduling, and control. Topics treated include: aggregate capacity planning, manufacturing requirements planning, lot size models, job shop scheduling; hierarchical linkage of production planning and control.

*IEOR 262A Mathematical Programming I (4 semester credits)

Three hours of lecture and one hour discussion per week. Prerequisites: Mathematics 111. Basic graduate course in linear programming and introduction to network flows and non-linear programming. Formulation and model building. The simplex method and its variants. Duality theory. Sensitivity analysis, parametric programming, convergence (theoretical and practical). Special structures such as upper bounds and decomposition.

*IEOR 263A Applied Stochastic Processes I (4 semester credits)

Three hours of lecture and one hour of discussion per week. Prerequisites: Statistics 134A or Statistics 200A. Conditional Expectation. Poisson and renewal processes. Renewal reward processes with application to inventory, congestion, and replacement models. Discrete and continuous time Markov chains; with applications to various stochastic systems – such as exponential queueing systems, inventory models and reliability systems.