Courses tagged with "Information control" (59)
This course continues the content covered in 18.100 Analysis I. Roughly half of the subject is devoted to the theory of the Lebesgue integral with applications to probability, and the other half to Fourier series and Fourier integrals.
This subject offers an interactive introduction to discrete mathematics oriented toward computer science and engineering. The subject coverage divides roughly into thirds:
- Fundamental concepts of mathematics: Definitions, proofs, sets, functions, relations.
- Discrete structures: graphs, state machines, modular arithmetic, counting.
- Discrete probability theory.
On completion of 6.042J, students will be able to explain and apply the basic methods of discrete (noncontinuous) mathematics in computer science. They will be able to use these methods in subsequent courses in the design and analysis of algorithms, computability theory, software engineering, and computer systems.
Interactive site components can be found on the Unit pages in the left-hand navigational bar, starting with Unit 1: Proofs.
Game Theory, also known as Multiperson Decision Theory, is the analysis of situations in which the payoff of a decision maker depends not only on his own actions but also on those of others. Game Theory has applications in several fields, such as economics, politics, law, biology, and computer science. In this course, I will introduce the basic tools of game theoretic analysis. In the process, I will outline some of the many applications of Game Theory, primarily in economics.
This course provides an elementary introduction to probability and statistics with applications. Topics include: basic combinatorics, random variables, probability distributions, Bayesian inference, hypothesis testing, confidence intervals, and linear regression.
The Spring 2014 version of this subject employed the residential MITx system, which enables on-campus subjects to provide MIT students with learning and assessment tools such as online problem sets, lecture videos, reading questions, pre-lecture questions, problem set assistance, tutorial videos, exam review content, and even online exams.
This course offers a rigorous treatment of linear algebra, including vector spaces, systems of linear equations, bases, linear independence, matrices, determinants, eigenvalues, inner products, quadratic forms, and canonical forms of matrices. Compared with 18.06 Linear Algebra, more emphasis is placed on theory and proofs.
This calculus course covers differentiation and integration of functions of one variable, and concludes with a brief discussion of infinite series. Calculus is fundamental to many scientific disciplines including physics, engineering, and economics.
Course Format
This course has been designed for independent study. It includes all of the materials you will need to understand the concepts covered in this subject. The materials in this course include:
- Lecture Videos with supporting written notes
- Recitation Videos of problem-solving tips
- Worked Examples with detailed solutions to sample problems
- Problem sets with solutions
- Exams with solutions
- Interactive Java Applets ("Mathlets") to reinforce key concepts
Content Development
David Jerison
Arthur Mattuck
Haynes Miller
Benjamin Brubaker
Jeremy Orloff
This is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but assumes a familiarity with linear algebra and finite groups. Topics were chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected.
This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts and teaches an understanding and construction of proofs. MIT students may choose to take one of three versions of Real Analysis; this version offers three additional units of credit for instruction and practice in written and oral presentation.
The three options for 18.100:
- Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible.
- Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology.
- Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication. This fulfills the MIT CI requirement.
Other Versions
Related Content
This is a undergraduate course. It will cover normed spaces, completeness, functionals, Hahn-Banach theorem, duality, operators; Lebesgue measure, measurable functions, integrability, completeness of L-p spaces; Hilbert space; compact, Hilbert-Schmidt and trace class operators; as well as spectral theorem.
This is an advanced undergraduate course dealing with calculus in one complex variable with geometric emphasis. Since the course Analysis I (18.100B) is a prerequisite, topological notions like compactness, connectedness, and related properties of continuous functions are taken for granted.
This course offers biweekly problem sets with solutions, two term tests and a final exam, all with solutions.
This is a communication intensive supplement to Linear Algebra (18.06). The main emphasis is on the methods of creating rigorous and elegant proofs and presenting them clearly in writing. The course starts with the standard linear algebra syllabus and eventually develops the techniques to approach a more advanced topic: abstract root systems in a Euclidean space.
18.311 Principles of Continuum Applied Mathematics covers fundamental concepts in continuous applied mathematics, including applications from traffic flow, fluids, elasticity, granular flows, etc. The class also covers continuum limit; conservation laws, quasi-equilibrium; kinematic waves; characteristics, simple waves, shocks; diffusion (linear and nonlinear); numerical solution of wave equations; finite differences, consistency, stability; discrete and fast Fourier transforms; spectral methods; transforms and series (Fourier, Laplace). Additional topics may include sonic booms, Mach cone, caustics, lattices, dispersion, and group velocity.
This course is a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics include: hypothesis testing and estimation, confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, correlation, decision theory, and Bayesian statistics.
The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number of ways to write a positive integer n as a sum of positive integers, taking order into account, is 2n-1. We will be concerned primarily with bijective proofs, i.e., showing that two sets have the same number of elements by exhibiting a bijection (one-to-one correspondence) between them. This is a subject which requires little mathematical background to reach the frontiers of current research. Students will therefore have the opportunity to do original research. It might be necessary to limit enrollment.
Trusted paper writing service WriteMyPaper.Today will write the papers of any difficulty.