Category Archives: Mathematics

Mathematics

  • 12.006J / 18.353J Nonlinear Dynamics I: Chaos, Fall 2005
    This course provides an introduction to the theory and phenomenology of nonlinear dynamics and chaos
  • 6.042J / 18.062J Mathematics for Computer Science, Fall 2005
    This is an introductory course in Discrete Mathematics oriented toward Computer Science and Engineer
  • 6.042J / 18.062J Mathematics for Computer Science (SMA 5512), Fall 2002
    This is an introductory course in Discrete Mathematics oriented toward Computer Science and Engineer
  • 6.042J / 18.062J Mathematics for Computer Science, Spring 2005
    This course is offered to undergraduates and is an elementary discrete mathematics course oriented t
  • 6.045J / 18.400J Automata, Computability, and Complexity, Spring 2005
    This course is offered to undergraduates and introduces basic mathematical models of computation and
  • 6.046J / 18.410J Introduction to Algorithms (SMA 5503), Fall 2005
    This course teaches techniques for the design and analysis of efficient algorithms, emphasizing meth
  • 6.852J / 18.437J Distributed Algorithms, Fall 2005
    This course intends to provide a rigorous introduction to the most important research results in the
  • 6.854J / 18.415J Advanced Algorithms, Fall 2005
    This course is a first-year graduate course in algorithms. Emphasis is placed on fundamental algorit
  • 6.854J / 18.415J Advanced Algorithms, Fall 2001
    This is a graduate course on the design and analysis of algorithms, covering several advanced topics
  • 6.856J / 18.416J Randomized Algorithms, Fall 2002
    This course examines how randomization can be used to make algorithms simpler and more efficient via
  • 6.876J / 18.426J Advanced Topics in Cryptography, Spring 2003
    The topics covered in this course include interactive proofs, zero-knowledge proofs, zero-knowledge
  • 18.013A Calculus with Applications, Spring 2005
    This is an undergraduate course on differential calculus in one and several dimensions. It is intend
  • 18.014 Calculus with Theory I, Fall 2002
    18.014, Calculus with Theory, covers the same material as 18.01 (Calculus), but at a deeper and more
  • 18.01 Single Variable Calculus, Fall 2005
    This introductory calculus course covers differentiation and integration of functions of one variabl
  • 18.022 Calculus, Fall 2005
    This is an undergraduate course on calculus of several variables. It covers all of the topics covere
  • 18.024 Calculus with Theory II, Spring 2003
    This course is a continuation of 18.014. It covers the same material as 18.02 (Calculus), but a
  • 18.02 Multivariable Calculus, Spring 2006
    This course covers vector and multi-variable calculus. It is the second semester in the freshman cal
  • 18.034 Honors Differential Equations, Spring 2004
    This course covers the same material as 18.03 with more emphasis on theory. Topics include first ord
  • 18.03 Differential Equations, Spring 2006
    Differential Equations are the language in which the laws of nature are expressed. Understanding pro
  • 18.04 Complex Variables with Applications, Fall 1999
    The following topics are covered in the course: complex algebra and functions; analyticity; contour
  • 18.04 Complex Variables with Applications, Fall 2003
    This course explored topics such as complex algebra and functions, analyticity, contour integration,
  • 18.05 Introduction to Probability and Statistics, Spring 2005
    This course provides an elementary introduction to probability and statistics with applications. Top
  • 18.06CI Linear Algebra – Communications Intensive, Spring 2004
    This is a communication intensive supplement to Linear Algebra (18.06). The main emphasis is on the
  • 18.06 Linear Algebra, Spring 2005
    This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will b
  • 18.075 Advanced Calculus for Engineers, Fall 2004
    This course analyzes the functions of a complex variable and the calculus of residues. It also cover
  • 18.085 Mathematical Methods for Engineers I, Fall 2005
    This course provides a review of linear algebra, including applications to networks, structures, and
  • 18.086 Mathematical Methods for Engineers II, Spring 2006
    This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topic
  • 18.091 Mathematical Exposition, Spring 2005
    This course provides techniques of effective presentation of mathematical material. Each section of
  • 18.100B Analysis I, Fall 2002
    Analysis I covers fundamentals of mathematical analysis: convergence of sequences and series, contin
  • 18.100C Analysis I, Spring 2006
    This course is meant as a first introduction to rigorous mathematics; understanding and writing of p
  • 18.101 Analysis II, Fall 2005
    This course continues from Analysis I (18.100B), in the direction of manifolds and global analysis.
  • 18.103 Fourier Analysis – Theory and Applications, Spring 2004
    18.103 picks up where 18.100B (Analysis I) left off. Topics covered include the theory of
  • 18.112 Functions of a Complex Variable, Fall 2005
    This is an advanced undergraduate course dealing with calculus in one complex variable with geometri
  • 18.117 Topics in Several Complex Variables, Spring 2005
    This course covers harmonic theory on complex manifolds, the Hodge decomposition theorem, the Hard L
  • 18.125 Measure and Integration, Fall 2003
    This graduate-level course covers Lebesgue\’s integration theory with applications to analysis, incl
  • 18.152 Introduction to Partial Differential Equations, Fall 2004
    This course analyzes initial and boundary value problems for ordinary differential equations and the
  • 18.152 Introduction to Partial Differential Equations, Fall 2005
    This course provides a solid introduction to Partial Differential Equations for advanced undergradua
  • 18.155 Differential Analysis, Fall 2004
    This is the first semester of a two-semester sequence on Differential Analysis. Topics include funda
  • 18.156 Differential Analysis, Spring 2004
    The main goal of this course is to give the students a solid foundation in the theory of elliptic an
  • 18.175 Theory of Probability, Spring 2005
    This course covers the laws of large numbers and central limit theorems for sums of independent rand
  • 18.238 Geometry and Quantum Field Theory, Fall 2002
    Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to p
  • 18.303 Linear Partial Differential Equations, Fall 2005
    This course covers the classical partial differential equations of applied mathematics: diffusion, L
  • 18.305 Advanced Analytic Methods in Science and Engineering, Fall 2004
    Advanced Analytic Methods in Science and Engineering is a comprehensive treatment of the advanced me
  • 18.306 Advanced Partial Differential Equations with Applications, Spring 2004
    This course presents the concepts and techniques for solving partial differential equations (pde), w
  • 18.307 Integral Equations, Spring 2006
    This course emphasizes concepts and techniques for solving integral equations from an applied mathem
  • 18.310 Principles of Applied Mathematics, Fall 2004
    Principles of Applied Mathematics is a study of illustrative topics in discrete applied mathematics
  • 18.311 Principles of Applied Mathematics, Spring 2006
    This course introduces fundamental concepts in \”continuous\’\’ applied mathematics, with an emphasi
  • 18.312 Algebraic Combinatorics, Spring 2005
    This course analyzes the applications of algebra to combinatorics and conversely. The topics discuss
  • 18.314 Combinatorial Analysis, Fall 2005
    This course analyzes combinatorial problems and methods for their solution. Prior experience with ab
  • 18.315 Combinatorial Theory: Hyperplane Arrangements, Fall 2004
    This is a graduate-level course in combinatorial theory. The content varies year to year, accor
  • 18.315 Combinatorial Theory: Introduction to Graph Theory, Extremal and Enumerative Combinatorics, Spring 2005
    This course serves as an introduction to major topics of modern enumerative and algebraic combinator
  • 18.318 Topics in Algebraic Combinatorics, Spring 2006
    The course consists of a sampling of topics from algebraic combinatorics. The topics include the mat
  • 18.319 Geometric Combinatorics, Fall 2005
    This course offers an introduction to discrete and computational geometry. Emphasis is placed on tea
  • 18.325 Topics in Applied Mathematics: Mathematical Methods in Nanophotonics, Fall 2005
    This course covers algebraic approaches to electromagnetism and nano-photonics. Topics include photo
  • 18.327 / 1.130 Wavelets, Filter Banks and Applications, Spring 2003
    Wavelets are localized basis functions, good for representing short-time events. The coefficients at
  • 18.330 Introduction to Numerical Analysis, Spring 2004
    This course analyzed the basic techniques for the efficient numerical solution of problems in scienc
  • 18.335J Introduction to Numerical Methods, Fall 2004
    The focus of this course is on numerical linear algebra and numerical methods for solving ordinary d
  • 18.335J / 6.337J Numerical Methods of Applied Mathematics I, Fall 2001
    IEEE-standard, iterative and direct linear system solution methods, eigendecomposition and model-ord
  • 18.336 Numerical Methods of Applied Mathematics II, Spring 2005
    This graduate-level course is an advanced introduction to applications and theory of numerical metho
  • 18.337J / 6.338J Applied Parallel Computing (SMA 5505), Spring 2005
    Applied Parallel Computing is an advanced interdisciplinary introduction to applied parallel computi
  • 18.338J / 16.394J Infinite Random Matrix Theory, Fall 2004
    In this course on the mathematics of infinite random matrices, students will learn about the tools s
  • 18.366 Random Walks and Diffusion, Spring 2005
    This graduate-level subject explores various mathematical aspects of (discrete) random walks and (co
  • 18.404J / 6.840J Theory of Computation, Fall 2002
    A more extensive and theoretical treatment of the material in 18.400J, Automata, Computability, and
  • 18.405J / 6.841J Advanced Complexity Theory, Fall 2001
    The topics for this course cover various aspects of complexity theory, such as the basic
  • 18.409 Behavior of Algorithms, Spring 2002
    This course is a study of Behavior of Algorithms and covers an area of current interest in theoretic
  • 18.413 Error-Correcting Codes Laboratory, Spring 2004
    This course introduces students to iterative decoding algorithms and the codes to which they are app
  • 18.417 Introduction to Computational Molecular Biology, Fall 2004
    This course introduces the basic computational methods used to understand the cell on a molecular le
  • 18.433 Combinatorial Optimization, Fall 2003
    Combinatorial Optimization provides a thorough treatment of linear programming and combinatorial opt
  • 18.440 Probability and Random Variables, Fall 2005
    This course introduces students to probability and random variables. Topics include distribution fun
  • 18.441 Statistical Inference, Spring 2002
    Reviews probability and introduces statistical inference. Point and interval estimation. The maximum
  • 18.443 Statistics for Applications, Fall 2003
    This course provides a broad treatment of statistics, concentrating on specific statistical techniqu
  • 18.465 Topics in Statistics: Statistical Learning Theory, Spring 2004
    The main goal of this course is to study the generalization ability of a number of popular machine l
  • 18.465 Topics in Statistics: Nonparametrics and Robustness, Spring 2005
    This graduate-level course focuses on one-dimensional nonparametric statistics developed mainly from
  • 18.466 Mathematical Statistics, Spring 2003
    This graduate level mathematics course covers decision theory, estimation, confidence intervals, and
  • 18.700 Linear Algebra, Fall 2005
    This course offers a rigorous treatment of linear algebra, including vector spaces, systems of linea
  • 18.701 Algebra I, Fall 2003
    The subjects to be covered include groups, vector spaces, linear transformations, symmetry grou
  • 18.702 Algebra II, Spring 2003
    The course covers group theory and its representations, and focuses on the Sylow theorem, Schur\’s l
  • 18.704 Seminar in Algebra and Number Theory: Rational Points on Elliptic Curves, Fall 2004
    This is a seminar for mathematics majors, where the students present the lectures. No prior experien
  • 18.725 Algebraic Geometry, Fall 2003
    This course covers the fundamental notions and results about algebraic varieties over an algebraical
  • 18.727 Topics in Algebraic Geometry: Intersection Theory on Moduli Spaces, Spring 2006
    The topics for this course vary each semester. This semester, the course aims to introduce technique
  • 18.755 Introduction to Lie Groups, Fall 2004
    This course is devoted to the theory of Lie Groups with emphasis on its connections with Differentia
  • 18.781 Theory of Numbers, Spring 2003
    This course provides an elementary introduction to number theory with no algebraic prerequisites. To
  • 18.786 Topics in Algebraic Number Theory, Spring 2006
    This course is a first course in algebraic number theory. Topics to be covered include number fields
  • 18.901 Introduction to Topology, Fall 2004
    This course introduces topology, covering topics fundamental to modern analysis and geometry. It als
  • 18.904 Seminar in Topology, Fall 2005
    In this course, students present and discuss the subject matter with faculty guidance. Topics presen
  • 18.906 Algebraic Topology II, Spring 2006
    In this second term of Algebraic Topology, the topics covered include fibrations, homotopy groups, t
  • 18.950 Differential Geometry, Spring 2005
    This course is an introduction to differential geometry of curves and surfaces in three dimensional
  • 18.965 Geometry of Manifolds, Fall 2004
    Geometry of Manifolds analyzes topics such as the differentiable manifolds and vector fields and for
  • 18.994 Seminar in Geometry, Fall 2004
    In this course, students take turns in giving lectures. For the most part, the lectures are based on
  • 18.996A Simplicity Theory, Spring 2004
    This is an advanced topics course in model theory whose main theme is simple theories. We treat simp
  • 18.996 / 16.399 Random Matrix Theory and Its Applications, Spring 2004
    This course is an introduction to the basics of random matrix theory, motivated by engineering and s
  • 18.996 Topics in Theoretical Computer Science : Internet Research Problems, Spring 2002
    We will discuss numerous research problems that are related to the internet. Sample topics include:
  • 18.996VP General Relativity and Gravitational Radiation, Fall 2002
    In this Special Topics course we discuss current theoretical and experimental developments towards t
  • 18.997 Topics in Combinatorial Optimization, Spring 2004
    In this graduate-level course, we will be covering advanced topics in combinatorial optimization. We
  • 18.S34 Problem Solving Seminar, Fall 2004
    This course,which is geared toward Freshmen, is an undergraduate seminar on mathematical proble
  • 18.S66 The Art of Counting, Spring 2003
    The subject of enumerative combinatorics deals with counting the number of elements of a finite set.