Interfacial Phenomena

keywords:
Engineering
Mathematics
Mechanical Engineering
Applied Mathematics
Fluid Mechanics

de: Maschinenbau/Verfahrenstechnik

uk: Машинобудування/Технологія

en: Mechanical Engineering / Process Engineering

uk: Математика, природничі науки

description: This graduate-level course covers fluid systems dominated by the influence of interfacial tension. The roles of curvature pressure and Marangoni stress are elucidated in a variety of fluid systems. Particular attention is given to drops and bubbles, soap films and minimal surfaces, wetting phenomena, water-repellency, surfactants, Marangoni flows, capillary origami and contact line dynamics.

uk: вхід без авторизації


Random Walks and Diffusion

Massachusetts Institute of Technology

addressCountry: US

addressLocality: Cambridge

addressRegion: Massachusetts

type: Organization

Martin Bazant

honorificPrefix: Prof.

type: Person

keywords:
Engineering
Mathematics
Mechanical Engineering
Probability and Statistics
Applied Mathematics
Transport Processes
Fluid Mechanics
Chemical Engineering

cs: Matematika

de: Mathematik

fi: matematiikka

uk: Математика

en: Mathematics

fr: Mathématiques

da: Matematik

es: Matemáticas

nl: Wiskunde

cs: Technické vědy

de: Ingenieurwissenschaften

fi: tekniikka

uk: Інженерія

en: Engineering Sciences

fr: Ingénierie

da: Ingeniørvidenskab

es: Ingeniería

nl: Engineering

uk: Машинобудування/Технологія

uk: Хімічна інженерія/Інженерія хімічних процесів

en: Chemical Engineering/Chemical Process Engineering

de: Mathematik, Naturwissenschaften

uk: Математика, природничі науки

en: Mathematics, Natural Sciences

description: This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.

MIT OpenCourseWare

type: Service

type: WebContent

@language: en

cs: přihlášení není vyžadováno

de: keine Anmeldung erforderlich

uk: вхід без авторизації

en: no login required

nl: geen login vereist

cs: Kurz

de: Kurs

fi: Kurssi

uk: Курс

en: Course

fr: Cours

da: Kursus

nl: Cursus

es: Curso


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This resource provides solutions to exam 1 on random walks and diffusion.

uk: вхід без авторизації

cs: Cvičení

de: Übung

fi: Harjoitus

uk: Практика

en: Drill and Practice

fr: Apprentissage par Répétition

da: Øvelse

nl: Oefenen

es: Práctica


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: An exam on topics multivariate normal random walk, student random walk, and the largest step.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This resource provides solutions to exam 2 on random walks and diffusion.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: An exam including problems on electrochemical?equilibrium, first passage?of?a?set?of?random?walkers, and escape?from?a?symmetric?trap.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This resource contains midterm exam.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This resource contains solution to the midterm exam.

uk: вхід без авторизації


Mathematical Methods in Nanophotonics

keywords:
Engineering
Science
Physics
Mathematics
Nanotechnology
Applied Mathematics
Atomic, Molecular, Optical Physics
Quantum Mechanics
Linear Algebra

de: Physik

uk: Фізика

en: Physics

uk: Математика, природничі науки

de: Physik, Astronomie

fi: fysiikka, tähtitiede

uk: Фізика, Астрономія

en: Physics, Astronomy

fr: Physique, Astronomie

da: Fysik, Astronomi

es: Física, Astronomía

nl: Natuurkunde, Astronomie

description:
Find out what solid-state physics has brought to Electromagnetism in the last 20 years. This course surveys the physics and mathematics of nanophotonics—electromagnetic waves in media structured on the scale of the wavelength.

Topics include computational methods combined with high-level algebraic techniques borrowed from solid-state quantum mechanics: linear algebra and eigensystems, group theory, Bloch's theorem and conservation laws, perturbation methods, and coupled-mode theories, to understand surprising optical phenomena from band gaps to slow light to nonlinear filters.

Note: An earlier version of this course was published on OCW as 18.325 Topics in Applied Mathematics: Mathematical Methods in Nanophotonics, Fall 2005.

uk: вхід без авторизації


2005 Midterm

uk: Математика, природничі науки

uk: Фізика, Астрономія

description: Midterm exam on 2d metallic electromagnetic cavities, reflected and transmitted light, Hermitian matrix, and band diagrams.

uk: вхід без авторизації


2007 Midterm

uk: Математика, природничі науки

uk: Фізика, Астрономія

description: Midterm exam on hexagons, band diagrams, and operators.

uk: вхід без авторизації


2008 Midterm

uk: Математика, природничі науки

uk: Фізика, Астрономія

description: Midterm exam on waveguide gaps, symmetry, and projected bands.

uk: вхід без авторизації


Nonlinear Dynamics and Chaos

keywords:
Mathematics
Applied Mathematics
Topology and Geometry
Differential Equations

uk: Математика, природничі науки

description: This graduate level course focuses on nonlinear dynamics with applications. It takes an intuitive approach with emphasis on geometric thinking, computational and analytical methods and makes extensive use of demonstration software.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Exam Number 1 for 18.385j/2.036j.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Exam Number 2 for 18.385j/2.036j

uk: вхід без авторизації


uk: Математика, природничі науки

description: This resource consists of problem statement on balancing a broom.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Balancing a Broom

uk: вхід без авторизації


uk: Математика, природничі науки

description: This resource consists of Coastline Fractal construction.

uk: вхід без авторизації


uk: Математика, природничі науки

description: This resource consists of problem set for deriving equation for pendulum.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Variable Length Pendulum

uk: вхід без авторизації


Theory of Computation

keywords:
Engineering
Computer Science
Mathematics
Computation
Theory of Computation
Discrete Mathematics

name: 18.404J F2006 Sample Final Exam Solutions

name: Lecture 2: Nondeterminism, Closure Properties, Regular Expressions → Finite Automata

name: Lecture 5: CF Pumping Lemma, Turing Machines

name: Lecture 7: Decision Problems for Automata and Grammars

name: Lecture 1: Introduction, Finite Automata, Regular Expressions

name: Lecture 14: P and NP, SAT, Poly-Time Reducibility

name: Lecture 17: Space Complexity, PSPACE, Savitch's Theorem

name: Lecture 19: Games, Generalized Geography

name: Lecture 22: Provably Intractable Problems, Oracles

name: Lecture 23: Probabilistic Computation, BPP

name: Lecture 24: Probabilistic Computation (cont.)

name: Lecture 25: Interactive Proof Systems, IP

name: Lecture 3: Regular Pumping Lemma, Finite Automata → Regular Expressions, CFGs

name: Lecture 6: TM Variants, Church-Turing Thesis

cs: Informatika

de: Informatik

fi: tietojenkäsittelytiede

uk: Комп'ютерні науки

en: Computer Science

fr: Informatique

da: Datalogi

es: Ciencias de la Computación

nl: Informatica

uk: Математика, природничі науки

description: This course emphasizes computability and computational complexity theory. Topics include regular and context-free languages, decidable and undecidable problems, reducibility, recursive function theory, time and space measures on computation, completeness, hierarchy theorems, inherently complex problems, oracles, probabilistic computation, and interactive proof systems.

uk: вхід без авторизації


uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації

cs: Video

de: Video

fi: Video

uk: Відео

en: Video

fr: Vidéo

da: Video

nl: Video

es: Video


uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 10: Computation History Method

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 11: Recursion Theorem and Logic

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 12: Time Complexity

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 15: NP-Completeness

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 16: Cook-Levin Theorem

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 18: PSPACE-Completeness

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 20: L and NL, NL = coNL

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 21: Hierarchy Theorems

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 26: coNP ⊆ IP

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 8: Undecidability

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 9: Reducibility

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


18.404J F2006 Sample Final Exam

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


18.404J F2001 Sample Midterm Exam

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


18.404J F2006 Sample Midterm Exam

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 4: Pushdown Automata, CFG ↔ PDA

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


Advanced Complexity Theory

keywords:
Engineering
Computer Science
Mathematics
Computation
Theory of Computation

uk: Комп'ютерні науки

uk: Математика, природничі науки

description: This graduate-level course focuses on current research topics in computational complexity theory. Topics include: Nondeterministic, alternating, probabilistic, and parallel computation models; Boolean circuits; Complexity classes and complete sets; The polynomial-time hierarchy; Interactive proof systems; Relativization; Definitions of randomness; Pseudo-randomness and derandomizations;Interactive proof systems and probabilistically checkable proofs.

uk: вхід без авторизації


keywords:
Engineering
Computer Science
Mathematics
Algorithms and Data Structures
Algebra and Number Theory
Discrete Mathematics

uk: Комп'ютерні науки

uk: Математика, природничі науки

description: In this course, we will present the theory of Probabilistically Checkable Proofs (PCPs), and prove some fundamental consequences of it as well as more recent advances. More specifically, the first half of the course will be devoted to the (algebraic) proof of the basic PCP Theorem and basic relation to approximation problems. We will then move on to more advanced topics, such as hardness amplification, the long-code framework, the Unique-Games Conjecture and its implications, and the 2-to-2 Games Theorem.

uk: вхід без авторизації

name: Topics in Theoretical Computer Science: Probabilistically Checkable Proofs


Algorithmic Aspects of Machine Learning

keywords:
Engineering
Computer Science
Mathematics
Applied Mathematics
Algorithms and Data Structures
Theory of Computation
Discrete Mathematics

uk: Комп'ютерні науки

uk: Математика, природничі науки

description: This course is organized around algorithmic issues that arise in machine learning. Modern machine learning systems are often built on top of algorithms that do not have provable guarantees, and it is the subject of debate when and why they work. In this class, we focus on designing algorithms whose performance we can rigorously analyze for fundamental machine learning problems.

uk: вхід без авторизації


Behavior of Algorithms

keywords:
Engineering
Computer Science
Mathematics
Computation
Algorithms and Data Structures
Theory of Computation
Mathematical Analysis

uk: Комп'ютерні науки

uk: Математика, природничі науки

description: This course is a study of Behavior of Algorithms and covers an area of current interest in theoretical computer science. The topics vary from term to term. During this term, we discuss rigorous approaches to explaining the typical performance of algorithms with a focus on the following approaches: smoothed analysis, condition numbers/parametric analysis, and subclassing inputs.

uk: вхід без авторизації


keywords:
Engineering
Computer Science
Mathematics
Applied Mathematics
Algorithms and Data Structures
Theory of Computation
Topology and Geometry
Linear Algebra

uk: Комп'ютерні науки

uk: Математика, природничі науки

description: This course covers a collection of geometric techniques that apply broadly in modern algorithm design.

uk: вхід без авторизації

name: Topics in Theoretical Computer Science: An Algorithmist's Toolkit


Error-Correcting Codes Laboratory

keywords:
Engineering
Computer Science
Mathematics
Computation
Algorithms and Data Structures
Cryptography
Theory of Computation

uk: Комп'ютерні науки

uk: Математика, природничі науки

description: This course introduces students to iterative decoding algorithms and the codes to which they are applied, including Turbo Codes, Low-Density Parity-Check Codes, and Serially-Concatenated Codes. The course will begin with an introduction to the fundamental problems of Coding Theory and their mathematical formulations. This will be followed by a study of Belief Propagation--the probabilistic heuristic which underlies iterative decoding algorithms. Belief Propagation will then be applied to the decoding of Turbo, LDPC, and Serially-Concatenated codes. The technical portion of the course will conclude with a study of tools for explaining and predicting the behavior of iterative decoding algorithms, including EXIT charts and Density Evolution.

uk: вхід без авторизації


keywords:
Engineering
Science
Mathematics
Biological Engineering
Biology
Computation
Computational Biology
Molecular Biology

de: Biotechnologie

uk: Біотехнологія

en: Biotechnology

de: Biologie

uk: Біологія

en: Biology

uk: Математика, природничі науки

description: This course introduces the basic computational methods used to understand the cell on a molecular level. It covers subjects such as the sequence alignment algorithms: dynamic programming, hashing, suffix trees, and Gibbs sampling. Furthermore, it focuses on computational approaches to: genetic and physical mapping; genome sequencing, assembly, and annotation; RNA expression and secondary structure; protein structure and folding; and molecular interactions and dynamics.

uk: вхід без авторизації

name: Introduction to Computational Molecular Biology


Combinatorial Optimization

keywords:
Engineering
Computer Science
Mathematics
Systems Engineering
Computation
Algorithms and Data Structures
Theory of Computation
Systems Optimization

uk: Комп'ютерні науки

uk: Математика, природничі науки

description: Combinatorial Optimization provides a thorough treatment of linear programming and combinatorial optimization. Topics include network flow, matching theory, matroid optimization, and approximation algorithms for NP-hard problems.

uk: вхід без авторизації


Quantum Computation

keywords:
Engineering
Science
Computer Science
Physics
Mathematics
Computation
Algorithms and Data Structures
Cryptography
Theory of Computation
Quantum Mechanics
Discrete Mathematics

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: Фізика, Астрономія

description: This course provides an introduction to the theory and practice of quantum computation. Topics covered include: physics of information processing, quantum logic, quantum algorithms including Shor's factoring algorithm and Grover's search algorithm, quantum error correction, quantum communication, and cryptography.

uk: вхід без авторизації


midterm.pdf

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: Фізика, Астрономія

description: This resource deals with midterm exam.

uk: вхід без авторизації


midtermsol.pdf

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: Фізика, Астрономія

description: This resource contains solutions of midterm exam.

uk: вхід без авторизації


uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: Фізика, Астрономія

description: Quiz problems.

uk: вхід без авторизації


uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: Фізика, Астрономія

description: Solutions to quiz problems.

uk: вхід без авторизації


Probability and Random Variables

keywords:
Mathematics
Probability and Statistics
Discrete Mathematics

name: 18.440 Practice Midterm 2 Partial Solutions

uk: Математика, природничі науки

description: This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

uk: вхід без авторизації


18.440 Final Exam Solutions

uk: Математика, природничі науки

description: This resource contains information related to final exam solutions.

uk: вхід без авторизації


Fall 2012 18.440 Final Exam Solutions

uk: Математика, природничі науки

description: This resource contains information related to fall 2012 final exam solutions.

uk: вхід без авторизації


Spring 2014 18.440 Final Exam Solutions

uk: Математика, природничі науки

description: This resource contains information related to spring 2014 final exam solutions.

uk: вхід без авторизації


18.440 Final Exam

uk: Математика, природничі науки

description: This resource contains information related to final exam.

uk: вхід без авторизації


Fall 2012 18.440 Final Exam

uk: Математика, природничі науки

description: This resource contains information related to fall 2012 final exam.

uk: вхід без авторизації


Spring 2014 18.440 Final Exam

uk: Математика, природничі науки

description: This resource contains information related to spring 2014 final exam.

uk: вхід без авторизації


18.440 Midterm 1, Fall 2009

uk: Математика, природничі науки

description: This resource contains information related to midterm 1, fall 2009.

uk: вхід без авторизації


18.440 Midterm 1, Spring 2011

uk: Математика, природничі науки

description: This resource contains information related to midterm 1, spring 2011.

uk: вхід без авторизації


18.440 Midterm 1 Solutions, Spring 2011

uk: Математика, природничі науки

description: This resource contains information related to midterm 1 solutions, spring 2011.

uk: вхід без авторизації


18.440 Midterm 1, Spring 2014

uk: Математика, природничі науки

description: This resource contains information related to midterm 1, spring 2014.

uk: вхід без авторизації


18.440 Midterm 1 Solutions, Spring 2014

uk: Математика, природничі науки

description: This resource contains information related to midterm 1 solutions, spring 2014.

uk: вхід без авторизації


18.440 Midterm 2, Fall 2009

uk: Математика, природничі науки

description: This resource contains information related to midterm 2, fall 2009.

uk: вхід без авторизації


18.440 Midterm 2 Solutions, Fall 2009

uk: Математика, природничі науки

description: This resource contains information related to midterm 2 solutions, fall 2009.

uk: вхід без авторизації


18.440 Midterm 2, Fall 2012

uk: Математика, природничі науки

description: This resource contains information related to midterm 2, fall 2012.

uk: вхід без авторизації


18.440 Midterm 2 Solutions, Fall 2012

uk: Математика, природничі науки

description: This resource contains information related to midterm 2 solutions, fall 2012.

uk: вхід без авторизації


18.440 Midterm 2, Spring 2014

uk: Математика, природничі науки

description: This resource contains information related to midterm 2, spring 2014.

uk: вхід без авторизації


18.440 Midterm 2 Solutions, Spring 2014

uk: Математика, природничі науки

description: This resource contains information related to midterm 2 solutions, spring 2014.

uk: вхід без авторизації


18.440 Midterm 2 Solutions, Fall 2011

uk: Математика, природничі науки

description: This resource contains information related to midterm 2 solutions, fall 2011.

uk: вхід без авторизації


18.440 Midterm 2, Spring 2011

uk: Математика, природничі науки

description: This resource contains information related to midterm 2, spring 2011.

uk: вхід без авторизації


18.440 Midterm 2 Solutions, Spring 2011

uk: Математика, природничі науки

description: This resource contains information related to midterm 2 solutions, spring 2011.

uk: вхід без авторизації


18.440 Practice Final Exam

uk: Математика, природничі науки

description: This resource contains information related to practice final exam.

uk: вхід без авторизації


18.440 Practice Final Exam Solutions

uk: Математика, природничі науки

description: This resource contains information related to practice final exam solutions.

uk: вхід без авторизації


18.440 Practice Midterm 1 Solutions

uk: Математика, природничі науки

description: This resource contains information related to practice midterm 1 solutions.

uk: вхід без авторизації


18.440 Practice Midterm Two

uk: Математика, природничі науки

description: This resource contains information related to practice midterm two.

uk: вхід без авторизації


uk: Математика, природничі науки

description: This resource contains information related to practice midterm 2 partial solutions.

uk: вхід без авторизації


18.440 Practice Midterm 1

uk: Математика, природничі науки

description: This resource contains information related to practice midterm 1.

uk: вхід без авторизації


Statistics for Applications

keywords:
Mathematics
Probability and Statistics
Applied Mathematics
Discrete Mathematics

uk: Математика, природничі науки

description:
This course offers 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, and correlation.

OCW offers an earlier version of this course, from Fall 2003. This newer version focuses less on estimation theory and more on multiple linear regression models. In addition, a number of Matlab examples are included here.

uk: вхід без авторизації


uk: Математика, природничі науки

description: This resource contains practice test on sample mean, sample standard deviation and Matlab commands.

uk: вхід без авторизації


uk: Математика, природничі науки

description: This resource contains problem test on Poisson distribution and variance analysis.

uk: вхід без авторизації


Peter Kempthorne

honorificPrefix: Dr.

name: Statistics for Applications Exam 1 Solution

name: Statistics for Applications Exam 2 Solution

name: Statistics for Applications Exam 3 Solution

uk: Математика, природничі науки

description: 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.

uk: вхід без авторизації


Statistics for Applications Exam 1

uk: Математика, природничі науки

description: This is a file that contains information regarding exam 1.

uk: вхід без авторизації


uk: Математика, природничі науки

description: This is a file that contains information regarding exam 1 solution.

uk: вхід без авторизації


Statistics for Applications Exam 2

uk: Математика, природничі науки

description: This is a file that contains information regarding exam 2.

uk: вхід без авторизації


uk: Математика, природничі науки

description: This is a file that contains information regarding exam 2 solution.

uk: вхід без авторизації


Statistics for Applications Exam 3

uk: Математика, природничі науки

description: This is a file that contains information regarding exam 3.

uk: вхід без авторизації


uk: Математика, природничі науки

description: This is a file that contains information regarding exam 3 solution.

uk: вхід без авторизації


uk: Математика, природничі науки

description: This is a file that contains information regarding exam 3 table.

uk: вхід без авторизації


Introduction to Stochastic Processes

keywords:
Mathematics
Probability and Statistics

uk: Математика, природничі науки

description: This course is an introduction to Markov chains, random walks, martingales, and Galton-Watsom tree. The course requires basic knowledge in probability theory and linear algebra including conditional expectation and matrix.

uk: вхід без авторизації


uk: Математика, природничі науки

description:
This graduate-level course focuses on one-dimensional nonparametric statistics developed mainly from around 1945 and deals with order statistics and ranks, allowing very general distributions.

For multidimensional nonparametric statistics, an early approach was to choose a fixed coordinate system and work with order statistics and ranks in each coordinate. A more modern method, to be followed in this course, is to look for rotationally or affine invariant procedures. These can be based on empirical processes as in computer learning theory.

Robustness, which developed mainly from around 1964, provides methods that are resistant to errors or outliers in the data, which can be arbitrarily large. Nonparametric methods tend to be robust.

uk: вхід без авторизації

name: Topics in Statistics: Nonparametrics and Robustness


keywords:
Engineering
Science
Computer Science
Artificial Intelligence
Mathematics
Probability and Statistics
Cognitive Science
Algorithms and Data Structures

uk: Комп'ютерні науки

de: Psychologie

uk: Психологія

en: Psychology

uk: Математика, природничі науки

de: Rechts-, Wirtschafts- und Sozialwissenschaften

uk: Право, економіка та суспільні науки

en: Law, Economics and Social Sciences

description: The main goal of this course is to study the generalization ability of a number of popular machine learning algorithms such as boosting, support vector machines and neural networks. Topics include Vapnik-Chervonenkis theory, concentration inequalities in product spaces, and other elements of empirical process theory.

uk: вхід без авторизації

name: Topics in Statistics: Statistical Learning Theory


Probability and Random Variables

name: Spring 2014 18.440 Midterm Exam 1 Solutions

name: Spring 2016 18.600 Midterm Exam 1 Solutions

name: Spring 2017 18.600 Midterm Exam 1 Solutions

name: Spring 2018 18.600 Midterm Exam 1 Solutions

name: Spring 2019 18.600 Midterm Exam 1 Solutions

name: Fall 2012 18.440 Midterm Exam 1 Solutions

name: Fall 2011 18.440 Midterm Exam 1 Solutions

name: Spring 2011 18.440 Midterm Exam 1 Solutions

name: Spring 2014 18.440 Midterm Exam 2 Solutions

name: Spring 2016 18.600 Midterm Exam 2 Solutions

name: Spring 2017 18.600 Midterm Exam 2 Solutions

name: Spring 2018 18.600 Midterm Exam 2 Solutions

name: Spring 2019 18.600 Midterm Exam 2 Solutions

name: Fall 2012 18.440 Midterm Exam 2 Solutions

name: Fall 2011 18.440 Midterm Exam 2 with Solutions

name: Spring 2011 18.440 Midterm Exam 2 Solutions

name: Fall 2019 18.600 Midterm Exam 1 Solutions

name: Fall 2019 18.600 Midterm Exam 2 Solutions

name: 18.600 Practice Final Exam Partial Solutions

uk: Математика, природничі науки

description: This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

uk: вхід без авторизації


Spring 2011 18.440 Final Exam

uk: Математика, природничі науки

uk: вхід без авторизації


Spring 2011 18.440 Final Exam Solutions

uk: Математика, природничі науки

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Fall 2012 18.440 Final Exam

uk: Математика, природничі науки

uk: вхід без авторизації


Fall 2012 18.440 Final Exam Solutions

uk: Математика, природничі науки

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Spring 2014 18.440 Final Exam

uk: Математика, природничі науки

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Spring 2014 18.440 Final Exam Solutions

uk: Математика, природничі науки

uk: вхід без авторизації


Spring 2016 18.600 Final Exam

uk: Математика, природничі науки

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Spring 2016 18.600 Final Exam Solutions

uk: Математика, природничі науки

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Spring 2017 18.600 Final Exam

uk: Математика, природничі науки

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Spring 2017 18.600 Final Exam Solutions

uk: Математика, природничі науки

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Spring 2018 18.600 Final Exam

uk: Математика, природничі науки

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Spring 2018 18.600 Final Exam Solutions

uk: Математика, природничі науки

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Spring 2019 18.600 Final Exam

uk: Математика, природничі науки

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Spring 2019 18.600 Final Exam Solutions

uk: Математика, природничі науки

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Fall 2019 18.600 Final Exam

uk: Математика, природничі науки

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Fall 2019 18.600 Final Exam Solutions

uk: Математика, природничі науки

uk: вхід без авторизації


Fall 2012 18.440 Midterm Exam 1

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

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Spring 2014 18.440 Midterm Exam 1

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Spring 2014 18.440 Midterm Exam 1 Solutions


Spring 2016 18.600 Midterm Exam 1

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Spring 2016 18.600 Midterm Exam 1 Solutions


Spring 2017 18.600 Midterm Exam 1

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Spring 2017 18.600 Midterm Exam 1 Solutions


Spring 2018 18.600 Midterm Exam 1

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Spring 2018 18.600 Midterm Exam 1 Solutions


Spring 2019 18.600 Midterm Exam 1

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Spring 2019 18.600 Midterm Exam 1 Solutions


Fall 2011 18.440 Midterm Exam 1

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Fall 2011 18.440 Midterm Exam 1 Solutions


Spring 2011 18.440 Midterm Exam 1

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Spring 2011 18.440 Midterm Exam 1 Solutions


Fall 2012 18.440 Midterm Exam 2

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

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Spring 2014 18.440 Midterm Exam 2

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Spring 2014 18.440 Midterm Exam 2 Solutions


Spring 2016 18.600 Midterm Exam 2

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Spring 2016 18.600 Midterm Exam 2 Solutions


Spring 2017 18.600 Midterm Exam 2

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Spring 2017 18.600 Midterm Exam 2 Solutions


Spring 2018 18.600 Midterm Exam 2

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

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name: Spring 2018 18.600 Midterm Exam 2 Solutions


Spring 2019 18.600 Midterm Exam 2

uk: Математика, природничі науки

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uk: Математика, природничі науки

uk: вхід без авторизації

name: Spring 2019 18.600 Midterm Exam 2 Solutions


uk: Математика, природничі науки

uk: вхід без авторизації

name: Fall 2011 18.440 Midterm Exam 2 with Solutions


Spring 2011 18.440 Midterm Exam 2

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Spring 2011 18.440 Midterm Exam 2 Solutions


Fall 2019 18.600 Midterm Exam 1

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Fall 2019 18.600 Midterm Exam 1 Solutions


Fall 2019 18.600 Midterm Exam 2

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Fall 2019 18.600 Midterm Exam 2 Solutions


18.600 Practice Final Exam

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: 18.600 Practice Final Exam Partial Solutions


18.600 Fall 2019 story sheet

uk: Математика, природничі науки

uk: вхід без авторизації


Statistics for Applications

name: Lecture 4: Parametric Inference (cont.) and Maximum Likelihood Estimation

name: Lecture 5: Maximum Likelihood Estimation (cont.)

name: Lecture 6: Maximum Likelihood Estimation (cont.) and the Method of Moments

name: Lecture 7: Parametric Hypothesis Testing

name: Lecture 8: Parametric Hypothesis Testing (cont.)

name: Lecture 9: Parametric Hypothesis Testing (cont.)

name: Lecture 11: Parametric Hypothesis Testing (cont.) and Testing Goodness of Fit

name: Lecture 12: Testing Goodness of Fit (cont.)

name: Lecture 19: Principal Component Analysis

name: Lecture 2: Introduction to Statistics (cont.)

name: Lecture 20: Principal Component Analysis (cont.)

name: Lecture 22: Generalized Linear Models (cont.)

name: Lecture 23: Generalized Linear Models (cont.)

name: Lecture 24: Generalized Linear Models (cont.)

uk: Математика, природничі науки

description: This course offers an in-depth the theoretical foundations for statistical methods that are useful in many applications. The goal is to understand the role of mathematics in the research and development of efficient statistical methods.

uk: вхід без авторизації


Lecture 1: Introduction to Statistics

uk: Математика, природничі науки

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uk: Математика, природничі науки

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uk: Математика, природничі науки

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Lecture 13: Regression

uk: Математика, природничі науки

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Lecture 14: Regression (cont.)

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 15: Regression (cont.)

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 17: Bayesian Statistics

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 18: Bayesian Statistics (cont.)

uk: Математика, природничі науки

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uk: Математика, природничі науки

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uk: Математика, природничі науки

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uk: Математика, природничі науки

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Lecture 21: Generalized Linear Models

uk: Математика, природничі науки

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uk: Математика, природничі науки

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uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 3: Parametric Inference

uk: Математика, природничі науки

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uk: Математика, природничі науки

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uk: Математика, природничі науки

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uk: Математика, природничі науки

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uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації


Mathematical Statistics

keywords:
Mathematics
Probability and Statistics
Social Science
Game Theory

de: Sozialwissenschaften/Soziologie

uk: Суспільні науки та соціологія

en: Social Sciences/Sociology

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

description: This course provides students with decision theory, estimation, confidence intervals, and hypothesis testing. It introduces large sample theory, asymptotic efficiency of estimates, exponential families, and sequential analysis.

uk: вхід без авторизації


Mathematical Statistics Mid-term Exam 1

uk: Суспільні науки та соціологія

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

description: This resource contains information regarding mathematical statistics, mid-term exam 1.

uk: вхід без авторизації


Mathematical Statistics Mid-term Exam 2

uk: Суспільні науки та соціологія

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

description: This resource contains information regarding mathematical statistics, mid-term exam 2.

uk: вхід без авторизації


Mathematics of Machine Learning

keywords:
Engineering
Computer Science
Artificial Intelligence
Mathematics
Probability and Statistics
Applied Mathematics
Data Mining
Algorithms and Data Structures
Discrete Mathematics

uk: Комп'ютерні науки

uk: Математика, природничі науки

description:
Broadly speaking, Machine Learning refers to the automated identification of patterns in data. As such it has been a fertile ground for new statistical and algorithmic developments. The purpose of this course is to provide a mathematically rigorous introduction to these developments with emphasis on methods and their analysis.

You can read more about Prof. Rigollet's work and courses [on his website](http://www-math.mit.edu/~rigollet/).

uk: вхід без авторизації


Linear Algebra

keywords:
Mathematics
Linear Algebra

uk: Математика, природничі науки

description: 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_](/courses/18-06sc-linear-algebra-fall-2011/), more emphasis is placed on theory and proofs.

uk: вхід без авторизації


Algebra I

keywords:
Mathematics
Algebra and Number Theory
Linear Algebra

uk: Математика, природничі науки

description: This undergraduate level Algebra I course covers groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups.

uk: вхід без авторизації


Algebra II

uk: Математика, природничі науки

description: This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.

uk: вхід без авторизації


Modern Algebra

keywords:
Mathematics
Algebra and Number Theory

uk: Математика, природничі науки

description: This undergraduate course focuses on traditional algebra topics that have found greatest application in science and engineering as well as in mathematics.

uk: вхід без авторизації


18.703 Modern Algebra, Exam 1

uk: Математика, природничі науки

description: This resource contains information exam 1.

uk: вхід без авторизації


18.703 Modern Algebra, Exam 2

uk: Математика, природничі науки

description: This resource contains information exam 2.

uk: вхід без авторизації


18.703 Modern Algebra, Exam 3

uk: Математика, природничі науки

description: This resource contains information exam 3.

uk: вхід без авторизації


keywords:
Mathematics
Computation
Algebra and Number Theory
Topology and Geometry

uk: Математика, природничі науки

description: In this undergraduate level seminar series, topics vary from year to year. Students present and discuss the subject matter, and are provided with instruction and practice in written and oral communication. Some experience with proofs required. The topic for fall 2008: Computational algebra and algebraic geometry.

uk: вхід без авторизації

name: Seminar in Algebra and Number Theory: Computational Commutative Algebra and Algebraic Geometry


uk: Математика, природничі науки

description: This is a seminar for mathematics majors, where the students present the lectures. No prior experience giving lectures is necessary.

uk: вхід без авторизації

name: Seminar in Algebra and Number Theory: Rational Points on Elliptic Curves


Commutative Algebra

uk: Математика, природничі науки

description: In this course students will learn about Noetherian rings and modules, Hilbert basis theorem, Cayley-Hamilton theorem, integral dependence, Noether normalization, the Nullstellensatz, localization, primary decomposition, DVRs, filtrations, length, Artin rings, Hilbert polynomials, tensor products, and dimension theory.

uk: вхід без авторизації


Noncommutative Algebra

uk: Математика, природничі науки

description: Noncommutative algebra studies algebraic phenomena involving multiplication for which commutativity law fails, such as product of matrices in linear algebra; such phenomena arise in various disciplines ranging from quantum physics to number theory.

uk: вхід без авторизації


Introduction to Representation Theory

uk: Математика, природничі науки

description: The goal of this course is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.

uk: вхід без авторизації


Algebraic Geometry

keywords:
Mathematics
Algebra and Number Theory
Topology and Geometry

uk: Математика, природничі науки

description: 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.

uk: вхід без авторизації


uk: Математика, природничі науки

description: This is the first semester of a two-semester sequence on Algebraic Geometry. The goal of the course is to introduce the basic notions and techniques of modern algebraic geometry. It covers fundamental notions and results about algebraic varieties over an algebraically closed field; relations between complex algebraic varieties and complex analytic varieties; and examples with emphasis on algebraic curves and surfaces. This course is an introduction to the language of schemes and properties of morphisms.

uk: вхід без авторизації


uk: Математика, природничі науки

description: This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology. Together with 18.725 Algebraic Geometry, students gain an understanding of the basic notions and techniques of modern algebraic geometry.

uk: вхід без авторизації


uk: Математика, природничі науки

description: The main aims of this seminar will be to go over the classification of surfaces (Enriques-Castelnuovo for characteristic zero, Bombieri-Mumford for characteristic p), while working out plenty of examples, and treating their geometry and arithmetic as far as possible.

uk: вхід без авторизації

name: Topics in Algebraic Geometry: Algebraic Surfaces


uk: Математика, природничі науки

description: The topics for this course vary each semester. This semester, the course aims to introduce techniques for studying intersection theory on moduli spaces. In particular, it covers the geometry of homogeneous varieties, the Deligne-Mumford moduli spaces of stable curves and the Kontsevich moduli spaces of stable maps using intersection theory.

uk: вхід без авторизації

name: Topics in Algebraic Geometry: Intersection Theory on Moduli Spaces


keywords:
Mathematics
Algebra and Number Theory
Topology and Geometry
Linear Algebra

uk: Математика, природничі науки

description: Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems.

uk: вхід без авторизації

name: Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathematical Physics


Lie Groups and Lie Algebras I

uk: Математика, природничі науки

description: This course is the first half of the year-long introductory graduate sequence 18.745/18.755 on Lie groups and Lie algebras. Topics include foundations of the theory of Lie groups and Lie algebras; theorems of Engel and Lie; the universal enveloping algebra, the Poincare-Birkhoff-Witt theorem; free Lie algebras; the Campbell-Hausdorff formula; classification and structure of finite dimensional complex simple Lie algebras; their finite dimensional representations; and the Weyl character formula.

uk: вхід без авторизації


Introduction to Lie Groups

keywords:
Mathematics
Algebra and Number Theory
Topology and Geometry
Differential Equations

uk: Математика, природничі науки

description:
This course is devoted to the theory of Lie Groups with emphasis on its connections with Differential Geometry. The text for this class is [_Differential Geometry, Lie Groups and Symmetric Spaces_](http://www.ams.org/bookstore?fn=20&arg1=gsmseries&item=GSM-34) by Sigurdur Helgason (American Mathematical Society, 2001).

Much of the course material is based on Chapter I (first half) and Chapter II of the text. The text however develops basic Riemannian Geometry, Complex Manifolds, as well as a detailed theory of Semisimple Lie Groups and Symmetric Spaces.

uk: вхід без авторизації


Lie Groups and Lie Algebras II

uk: Математика, природничі науки

description: This course is the second half of the year-long introductory graduate sequence [*Lie Groups and Lie Algebras I*](https://ocw.mit.edu/courses/18-745-lie-groups-and-lie-algebras-i-fall-2020/) *& Lie Groups and Lie Algebras II*. Topics include classical groups, Haar measure on locally compact groups, the representation-theoretic understanding of the hydrogen atom, representations of compact (in particular, finite) groups, the Peter-Weyl theorem with proof, maximal tori, Cartan and Iwasawa decompositions, classification of real reductive Lie groups, topology of Lie groups, proof of the third fundamental theorem of Lie theory, Levi decomposition, Ado's theorem, Borel subgroups, and flag manifolds.

uk: вхід без авторизації


Representations of Lie Groups

uk: Математика, природничі науки

description: The goal of this course is to give an introduction to the representation theory of compact and non-compact Lie groups. It will rely on some material from [*18.745 Lie Groups and Lie Algebras I*](https://ocw.mit.edu/courses/18-745-lie-groups-and-lie-algebras-i-fall-2020/) and [*18.755 Lie Groups and Lie Algebras II*](https://ocw.mit.edu/courses/18-755-lie-groups-and-lie-algebras-ii-spring-2024/), but full familiarity with this material is not required. Topics include continuous representations; algebras of measures on a Lie group; K-finite, smooth, and analytic vectors; admissible representations; unitary representations; the Harish-Chandra admissibility and analyticity theorems; (g,K)-modules; infinitesimal equivalence and realizations; Harish-Chandra’s globalization theorem; representations of SL(2,R), the Chevalley restriction theorem; the Chevalley-Shepard-Todd theorem; Kostant’s theorem; Harish-Chandra isomorphism; Bernstein-Gelfand-Gelfand category O; projective functors; classification of irreducible Harish-Chandra bimodules; the nilpotent cone; the Duflo-Joseph theorem; Duflo’s primitive ideal theorem; the Borel-Weil theorem; Springer resolution; Beilinson-Bernstein localization; D-modules; and classification of representations of a semisimple real group in terms of the orbits of the complexified maximal compact subgroup on the flag variety.

uk: вхід без авторизації


Topics in Lie Theory: Tensor Categories

uk: Математика, природничі науки

description: This course will give a detailed introduction to the theory of tensor categories and review some of its connections to other subjects (with a focus on representation-theoretic applications). In particular, we will discuss categorifications of such notions from ring theory as: module, morphism of modules, Morita equivalence of rings, commutative ring, the center of a ring, the centralizer of a subring, the double centralizer property, graded ring, etc.

uk: вхід без авторизації


Theory of Numbers

name: Theory of Numbers,  Exam Final Guidelines

name: Theory of Numbers, Exam 1 Practice Solutions

name: Theory of Numbers, Exam Final Practice Solutions

name: Theory of Numbers, Exam 2 Practice Solutions

uk: Математика, природничі науки

description: This course is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions.

uk: вхід без авторизації


Theory of Numbers, Exam 1 Guidelines

uk: Математика, природничі науки

description: This file contains information regarding Guidelines for Midterm1.

uk: вхід без авторизації


Theory of Numbers,  Exam 2 Guidelines

uk: Математика, природничі науки

description: This file contains information regarding Guidelines for Midterm 2.

uk: вхід без авторизації


uk: Математика, природничі науки

description: This file contains information regarding Guidelines for Final exam .

uk: вхід без авторизації


uk: Математика, природничі науки

description: This file contains information regarding Solutions to practice problems for Midterm 1.

uk: вхід без авторизації


uk: Математика, природничі науки

description: This file contains information regarding Solution to Practice Questions for Final Exam.

uk: вхід без авторизації


Theory of Numbers, Exam 1 Practice

uk: Математика, природничі науки

description: This file contains information regarding Practice problems for Midterm1.

uk: вхід без авторизації


uk: Математика, природничі науки

description: This file contains information regarding Practice Questions for Midterm 2.

uk: вхід без авторизації


Theory of Numbers, Exam Final Practice

uk: Математика, природничі науки

description: This file contains information regarding Practice Questions for Final Exam.

uk: вхід без авторизації


Theory of Numbers, Exam 2 Practice

uk: Математика, природничі науки

uk: вхід без авторизації


Introduction to Arithmetic Geometry

uk: Математика, природничі науки

description: This course is an introduction to arithmetic geometry, a subject that lies at the intersection of algebraic geometry and number theory. Its primary motivation is the study of classical [Diophantine problems](http://en.wikipedia.org/wiki/Diophantine_equation) from the modern perspective of algebraic geometry.

uk: вхід без авторизації


Elliptic Curves

keywords:
Engineering
Computer Science
Mathematics
Computation
Algebra and Number Theory

uk: Комп'ютерні науки

uk: Математика, природничі науки

description: This course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography. While this is an introductory course, we will (gently) work our way up to some fairly advanced material, including an overview of the proof of Fermat's last theorem.

uk: вхід без авторизації


Number Theory I

uk: Математика, природничі науки

description: This is the first semester of a one-year graduate course in number theory covering standard topics in algebraic and analytic number theory. At various points in the course, we will make reference to material from other branches of mathematics, including topology, complex analysis, representation theory, and algebraic geometry.

uk: вхід без авторизації


Number Theory II: Class Field Theory

uk: Математика, природничі науки

description: This course is the continuation of [_18.785 Number Theory I_](/courses/18-785-number-theory-i-fall-2019/). It begins with an analysis of the quadratic case of Class Field Theory via Hilbert symbols, in order to give a more hands-on introduction to the ideas of Class Field Theory. More advanced topics in number theory are discussed in this course, such as Galois cohomology, proofs of class field theory, modular forms and automorphic forms, Galois representations, and quadratic forms.

uk: вхід без авторизації


Topics in Algebraic Number Theory

uk: Математика, природничі науки

description: This course is a first course in algebraic number theory. Topics to be covered include number fields, class numbers, Dirichlet's units theorem, cyclotomic fields, local fields, valuations, decomposition and inertia groups, ramification, basic analytic methods, and basic class field theory. An additional theme running throughout the course will be the use of computer algebra to investigate number-theoretic questions; this theme will appear primarily in the problem sets.

uk: вхід без авторизації


finalexam.pdf

uk: Математика, природничі науки

description: This file contains the questions asked in the final exam.

uk: вхід без авторизації


midterm.pdf

uk: Математика, природничі науки

description: This file contains the questions asked in the midterm exam.

uk: вхід без авторизації


Topics in Algebraic Number Theory

uk: Математика, природничі науки

description: This course provides an introduction to algebraic number theory. Topics covered include dedekind domains, unique factorization of prime ideals, number fields, splitting of primes, class group, lattice methods, finiteness of the class number, Dirichlet's units theorem, local fields, ramification, discriminants.

uk: вхід без авторизації


Project Laboratory in Mathematics

uk: Математика, природничі науки

description:
_Project Laboratory in Mathematics_ is a course designed to give students a sense of what it's like to do mathematical research. In teams, students explore puzzling and complex mathematical situations, search for regularities, and attempt to explain them mathematically. Students share their results through professional-style papers and presentations.

This course site was created specifically for educators interested in offering students a taste of mathematical research. This site features extensive description and commentary from the instructors about why the course was created and how it operates.

uk: вхід без авторизації


Geometry and Topology in the Plane

keywords:
Mathematics
Topology and Geometry

uk: Математика, природничі науки

description: This course introduces students to selected aspects of geometry and topology, using concepts that can be visualized easily. We mix geometric topics (such as hyperbolic geometry or billiards) and more topological ones (such as loops in the plane). The course is suitable for students with no prior exposure to differential geometry or topology. Think of it as a moderate hike, overlooking various parts of the geometry and topology landscape. Bits are flat, bits are uphill, there are occasional rocky parts (may be different for everyone), but none that are designed to be cliff faces. The class moves from one topic to the next quickly, so it’s important to learn continuously.

uk: вхід без авторизації


Introduction to Topology

uk: Математика, природничі науки

description: This course introduces topology, covering topics fundamental to modern analysis and geometry. It also deals with subjects like topological spaces and continuous functions, connectedness, compactness, separation axioms, and selected further topics such as function spaces, metrization theorems, embedding theorems and the fundamental group.

uk: вхід без авторизації


Seminar in Topology

uk: Математика, природничі науки

description: This course is a seminar in topology. The main mathematical goal is to learn about the fundamental group, homology and cohomology. The main non-mathematical goal is to obtain experience giving math talks.

uk: вхід без авторизації


Algebraic Topology I

uk: Математика, природничі науки

description: This is a course on the singular homology of topological spaces. Topics include: Singular homology, CW complexes, Homological algebra, Cohomology, and Poincare duality.

uk: вхід без авторизації


Algebraic Topology II

uk: Математика, природничі науки

description: This is the second part of the two-course series on algebraic topology. Topics include basic homotopy theory, obstruction theory, classifying spaces, spectral sequences, characteristic classes, and Steenrod operations.

uk: вхід без авторизації


Graduate Topology Seminar: Kan Seminar

uk: Математика, природничі науки

description: This is a literature seminar with a focus on classic papers in Algebraic Topology. It is named after the late MIT professor [Daniel Kan](http://math.mit.edu/about/history/obituaries/kan.php). Each student gives one or two talks on each of three papers, chosen in consultation with the instructor, reads all the papers presented by other students, and writes reactions to the papers. This course is useful not only to students pursuing algebraic topology as a field of study, but also to those interested in symplectic geometry, representation theory, and combinatorics.

uk: вхід без авторизації


uk: Математика, природничі науки

description: The goal of this course is to describe some of the tools which enter into the proof of Sullivan's conjecture.

uk: вхід без авторизації

name: Topics in Algebraic Topology: The Sullivan Conjecture


Differential Geometry

uk: Математика, природничі науки

description: This course is an introduction to differential geometry. The course itself is mathematically rigorous, but still emphasizes concrete aspects of geometry, centered on the notion of curvature.

uk: вхід без авторизації


Geometry of Manifolds

keywords:
Mathematics
Topology and Geometry
Linear Algebra
Differential Equations

uk: Математика, природничі науки

description: Geometry of Manifolds analyzes topics such as the differentiable manifolds and vector fields and forms. It also makes an introduction to Lie groups, the de Rham theorem, and Riemannian manifolds.

uk: вхід без авторизації


uk: Математика, природничі науки

description: This is a second-semester graduate course on the geometry of manifolds. The main emphasis is on the geometry of symplectic manifolds, but the material also includes long digressions into complex geometry and the geometry of 4-manifolds, with special emphasis on topological considerations.

uk: вхід без авторизації


Topics in Geometry: Dirac Geometry

keywords:
Mathematics
Topology and Geometry
Linear Algebra

uk: Математика, природничі науки

description: This is an introductory (i.e. first year graduate students are welcome and expected) course in generalized geometry, with a special emphasis on Dirac geometry, as developed by Courant, Weinstein, and Severa, as well as generalized complex geometry, as introduced by Hitchin. Dirac geometry is based on the idea of unifying the geometry of a Poisson structure with that of a closed 2-form, whereas generalized complex geometry unifies complex and symplectic geometry. For this reason, the latter is intimately related to the ideas of mirror symmetry.

uk: вхід без авторизації


Topics in Geometry: Mirror Symmetry

keywords:
Science
Physics
Mathematics
Particle Physics
Topology and Geometry
Linear Algebra

uk: Математика, природничі науки

uk: Фізика, Астрономія

description: This course will focus on various aspects of mirror symmetry. It is aimed at students who already have some basic knowledge in symplectic and complex geometry (18.966, or equivalent). The geometric concepts needed to formulate various mathematical versions of mirror symmetry will be introduced along the way, in variable levels of detail and rigor.

uk: вхід без авторизації


Seminar in Geometry

keywords:
Mathematics
Topology and Geometry
Linear Algebra
Differential Equations
Calculus
Mathematical Analysis

uk: Математика, природничі науки

description: In this course, students take turns in giving lectures. For the most part, the lectures are based on Robert Osserman's classic book _A Survey of Minimal Surfaces_, Dover Phoenix Editions. New York: Dover Publications, May 1, 2002. ISBN: 0486495140.

uk: вхід без авторизації


keywords:
Mathematics
Probability and Statistics
Applied Mathematics
Linear Algebra
Calculus
Mathematical Analysis

uk: Математика, природничі науки

description: This course is an introduction to the basics of random matrix theory, motivated by engineering and scientific applications.

uk: вхід без авторизації

name: Random Matrix Theory and Its Applications


keywords:
Engineering
Computer Science
Electrical Engineering
Algorithms and Data Structures
Theory of Computation
Telecommunications
Computer Networks

uk: Комп'ютерні науки

de: Elektrotechnik und Informationstechnik

uk: Електротехніка та інформаційні технології

en: Electrical Engineering and Information Engineering

description:
We will discuss numerous research problems that are related to the internet. Sample topics include: routing algorithms such as BGP, communication protocols such as TCP, algorithms for intelligently selecting a resource in the face of uncertainty, bandwidth sensing tools, load balancing algorithms, streaming protocols, determining the structure of the internet, cost optimization, DNS-related problems, visualization, and large-scale data processing. The seminar is intended for students who are ready to work on challenging research problems. Each lecture will discuss:

*   methods used today
*   issues and problems
*   formulation of concrete problems
*   potential new lines of research

A modest amount of background information will be provided so that the importance and context of the problems can be understood. No previous study of the internet is required, but experience with algorithms and/or theoretical computer science at the graduate/research level is needed.

uk: вхід без авторизації

name: Topics in Theoretical Computer Science : Internet Research Problems


Simplicity Theory

keywords:
Mathematics
Algebra and Number Theory
Mathematical Logic

en: Mathematics

uk: Математика, природничі науки

description: This is an advanced topics course in model theory whose main theme is simple theories. We treat simple theories in the framework of compact abstract theories, which is more general than that of first order theories. We cover the basic properties of independence (i.e., non-dividing) in simple theories, the characterization of simple theories by the existence of a notion of independence, and hyperimaginary canonical bases.

uk: вхід без авторизації


Topics in Combinatorial Optimization

keywords:
Engineering
Computer Science
Mathematics
Systems Engineering
Applied Mathematics
Computation
Theory of Computation
Systems Optimization

uk: Комп'ютерні науки

en: Engineering Sciences

uk: Математика, природничі науки

description: In this graduate-level course, we will be covering advanced topics in combinatorial optimization. We will start with non-bipartite matchings and cover many results extending the fundamental results of matchings, flows and matroids. The emphasis is on the derivation of purely combinatorial results, including min-max relations, and not so much on the corresponding algorithmic questions of how to find such objects. The intended audience consists of Ph.D. students interested in optimization, combinatorics, or combinatorial algorithms.

uk: вхід без авторизації


uk: Математика, природничі науки

description: This course is a seminar intended for undergraduate students who enjoy solving challenging mathematical problems, and to prepare them for the Putnam Competition. All students officially registered in the class are required to participate in the [William Lowell Putnam Mathematical Competition](https://en.wikipedia.org/wiki/William_Lowell_Putnam_Mathematical_Competition).

uk: вхід без авторизації

name: Mathematical Problem Solving (Putnam Seminar)


keywords:
Mathematics
Applied Mathematics
Linear Algebra
Calculus

name: Lecture 4 Part 1: Gradients and Inner Products in Other Vector Spaces

name: Lecture 4 Part 2: Nonlinear Root Finding, Optimization, and Adjoint Gradient Methods

name: Lecture 5 Part 1: Derivative of Matrix Determinant and Inverse

name: Lecture 5 Part 2: Forward Automatic Differentiation via Dual Numbers

name: Lecture 5 Part 3: Differentiation on Computational Graphs

name: Lecture 6 Part 1: Adjoint Differentiation of ODE Solutions

name: Lecture 6 Part 2: Calculus of Variations and Gradients of Functionals

name: Lecture 7 Part 1: Derivatives of Random Functions

name: Lecture 7 Part 2: Second Derivatives, Bilinear Forms, and Hessian Matrices

name: Lecture 8 Part 1: Derivatives of Eigenproblems

name: Lecture 8 Part 2: Automatic Differentiation on Computational Graphs

name: Lecture 1 Part 2: Derivatives as Linear Operators

name: Lecture 1 Part 1: Introduction and Motivation

name: Lecture 2 Part 1: Derivatives in Higher Dimensions: Jacobians and Matrix Functions

name: Lecture 2 Part 2: Vectorization of Matrix Functions

name: Lecture 3 Part 1: Kronecker Products and Jacobians

name: Lecture 3 Part 2: Finite-Difference Approximations

uk: Математика, природничі науки

description:
We all know that calculus courses such as [*18.01 Single Variable Calculus*](https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/) and [*18.02 Multivariable Calculus*](https://ocw.mit.edu/courses/18-02sc-multivariable-calculus-fall-2010/) cover univariate and vector calculus, respectively. Modern applications such as machine learning and large-scale optimization require the next big step, "matrix calculus" and calculus on arbitrary vector spaces.

This class covers a coherent approach to matrix calculus showing techniques that allow you to think of a matrix holistically (not just as an array of scalars), generalize and compute derivatives of important matrix factorizations and many other complicated-looking operations, and understand how differentiation formulas must be reimagined in large-scale computing.

uk: вхід без авторизації

name: Matrix Calculus for Machine Learning and Beyond


uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Lecture 4 Part 1: Gradients and Inner Products in Other Vector Spaces


uk: Математика, природничі науки

uk: вхід без авторизації

name: Lecture 4 Part 2: Nonlinear Root Finding, Optimization, and Adjoint Gradient Methods


uk: Математика, природничі науки

uk: вхід без авторизації

name: Lecture 5 Part 1: Derivative of Matrix Determinant and Inverse


uk: Математика, природничі науки

uk: вхід без авторизації

name: Lecture 5 Part 2: Forward Automatic Differentiation via Dual Numbers


uk: Математика, природничі науки

uk: вхід без авторизації

name: Lecture 5 Part 3: Differentiation on Computational Graphs


uk: Математика, природничі науки

uk: вхід без авторизації

name: Lecture 6 Part 1: Adjoint Differentiation of ODE Solutions


uk: Математика, природничі науки

uk: вхід без авторизації

name: Lecture 6 Part 2: Calculus of Variations and Gradients of Functionals


uk: Математика, природничі науки

uk: вхід без авторизації

name: Lecture 7 Part 1: Derivatives of Random Functions


uk: Математика, природничі науки

uk: вхід без авторизації

name: Lecture 7 Part 2: Second Derivatives, Bilinear Forms, and Hessian Matrices


uk: Математика, природничі науки

uk: вхід без авторизації

name: Lecture 8 Part 1: Derivatives of Eigenproblems


uk: Математика, природничі науки

uk: вхід без авторизації

name: Lecture 8 Part 2: Automatic Differentiation on Computational Graphs


Topics in Mathematics of Data Science

keywords:
Engineering
Computer Science
Mathematics
Probability and Statistics
Applied Mathematics
Data Mining

uk: Комп'ютерні науки

uk: Математика, природничі науки

description: This is a mostly self-contained research-oriented course designed for undergraduate students (but also extremely welcoming to graduate students) with an interest in doing research in theoretical aspects of algorithms that aim to extract information from data. These often lie in overlaps of two or more of the following: Mathematics, Applied Mathematics, Computer Science, Electrical Engineering, Statistics, and / or Operations Research.

uk: вхід без авторизації


keywords:
Mathematics
Probability and Statistics
Business
Finance
Applied Mathematics

name: Lecture 1: Introduction, Financial Terms and Concepts

name: Lecture 10: Regularized Pricing and Risk Models

name: Lecture  19: Black-Scholes Formula, Risk-neutral Valuation

name: Lecture 20: Option Price and Probability Duality

name: Lecture 21: Stochastic Differential Equations

name: Lecture 24: HJM Model for Interest Rates and Credit

name: Lecture 26: Introduction to Counterparty Credit Risk

de: Betriebswirtschaftslehre

uk: Бізнес-адміністрування

en: Business Administration

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

de: Wirtschaftswissenschaften

uk: Бізнес та економіка

en: Business and Economics

description: The purpose of the class is to expose undergraduate and graduate students to the mathematical concepts and techniques used in the financial industry. Mathematics lectures are mixed with lectures illustrating the corresponding application in the financial industry. MIT mathematicians teach the mathematics part while industry professionals give the lectures on applications in finance.

uk: вхід без авторизації

name: Topics in Mathematics with Applications in Finance


uk: Бізнес-адміністрування

de: Mathematik

uk: Математика, природничі науки

en: Mathematics, Natural Sciences

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації

en: no login required


uk: Бізнес-адміністрування

de: Mathematik, Naturwissenschaften

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


Lecture 11: Time Series Analysis II

uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

de: keine Anmeldung erforderlich

uk: вхід без авторизації


Lecture 12: Time Series Analysis III

uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


Lecture 13: Commodity Models

uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


Lecture 14: Portfolio Theory

uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


Lecture 15: Factor Modeling

uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


Lecture 16: Portfolio Management

uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


Lecture 17: Stochastic Processes II

uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


Lecture 18: Itō Calculus

uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


Lecture 2: Linear Algebra

uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


Lecture 23: Quanto Credit Hedging

uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


Lecture 25: Ross Recovery Theorem

uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


Lecture 3: Probability Theory

uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


Lecture 5: Stochastic Processes I

uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


Lecture 6: Regression Analysis

uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


Lecture 7: Value At Risk (VAR) Models

uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


Lecture 8: Time Series Analysis I

uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


Lecture 9: Volatility Modeling

uk: Бізнес-адміністрування

uk: Математика, природничі науки

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

uk: вхід без авторизації


Applied Category Theory

keywords:
Mathematics
Applied Mathematics
Topology and Geometry

uk: Математика, природничі науки

description: Category theory is a relatively new branch of mathematics that has transformed much of pure math research. The technical advance is that category theory provides a framework in which to organize formal systems and by which to translate between them, allowing one to transfer knowledge from one field to another. But this same organizational framework also has many compelling examples outside of pure math. In this course, we will give seven sketches on real-world applications of category theory.

uk: вхід без авторизації

de: Kurs

en: Course


keywords:
Engineering
Computer Science
Mathematics
Applied Mathematics
Computation
Algorithms and Data Structures
Computer Networks
Computer Design and Engineering

uk: Комп'ютерні науки

de: Ingenieurwissenschaften

uk: Математика, природничі науки

description:
This half-semester course introduces computational thinking through applications of data science, artificial intelligence, and mathematical models using the Julia programming language. This Spring 2020 version is a fast-tracked curriculum adaptation to focus on applications to COVID-19 responses.

See the MIT News article [Computational Thinking Class Enables Students to Engage in Covid-19 Response](https://news.mit.edu/2020/computational-thinking-class-enables-students-engage-covid-19-response-0407)

uk: вхід без авторизації

name: Introduction to Computational Thinking with Julia, with Applications to Modeling the COVID-19 Pandemic


Introduction to Metric Spaces

keywords:
Mathematics
Mathematical Analysis

name: Lecture 1: Motivation, Intuition, and Examples

uk: Математика, природничі науки

description: This course provides a basic introduction to metric spaces. It covers metrics, open and closed sets, continuous functions (in the topological sense), function spaces, completeness, and compactness.

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 2: General Theory

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 3: Compact Sets in Rⁿ

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 4: Compact Metric Spaces

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 5: Complete Metric Spaces

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 6: Where We Go from Here

uk: Математика, природничі науки

uk: вхід без авторизації


Introduction to Computational Thinking

keywords:
Engineering
Computer Science
Mathematics
Energy
Applied Mathematics
Computation
Algorithms and Data Structures
Computer Networks
Computer Design and Engineering
Climate

uk: Комп'ютерні науки

uk: Математика, природничі науки

description: This is an introductory course on computational thinking. We use the Julia programming language to approach real-world problems in varied areas, applying data analysis and computational and mathematical modeling. In this class you will learn computer science, software, algorithms, applications, and mathematics as an integrated whole. Topics include image analysis, particle dynamics and ray tracing, epidemic propagation, and climate modeling.

uk: вхід без авторизації


uk: Комп'ютерні науки

uk: Математика, природничі науки

description:
This class uses revolutionary programmable interactivity to combine material from three fields -- Computer Science + Mathematics + Applications -- creating an engaging, efficient learning solution to prepare students to be sophisticated and intuitive thinkers, programmers, and solution providers for the modern interconnected online world.

Upon completion, students are well trained to be scientific “trilinguals,” seeing and experimenting with mathematics interactively as math is meant to be seen, and ready to participate and contribute to open source development of large projects and ecosystems.

uk: вхід без авторизації


The Art of Counting

keywords:
Mathematics
Algebra and Number Theory

uk: Математика, природничі науки

description: 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 _2{{< sup "n-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.

uk: вхід без авторизації


Category Theory for Scientists

keywords:
Science
Mathematics
Discrete Mathematics
Mathematical Logic

uk: Математика, природничі науки

description: The goal of this class is to prove that category theory is a powerful language for understanding and formalizing common scientific models. The power of the language will be tested by its ability to penetrate into taken-for-granted ideas, either by exposing existing weaknesses or flaws in our understanding, or by highlighting hidden commonalities across scientific fields.

uk: вхід без авторизації


High-Dimensional Statistics

keywords:
Mathematics
Probability and Statistics
Discrete Mathematics

uk: Математика, природничі науки

description:
This course offers an introduction to the finite sample analysis of high- dimensional statistical methods. The goal is to present various proof techniques for state-of-the-art methods in regression, matrix estimation and principal component analysis (PCA) as well as optimality guarantees. The course ends with research questions that are currently open.

You can read more about Prof. Rigollet's work and courses [on his website](http://www-math.mit.edu/~rigollet/)

uk: вхід без авторизації


Introduction To MATLAB Programming

keywords:
Engineering
Computer Science
Mathematics
Systems Engineering
Applied Mathematics
Programming Languages
Computational Modeling and Simulation

name: Lecture 1: Using MATLAB for the First Time

uk: Комп'ютерні науки

uk: Математика, природничі науки

description: This course is intended to assist undergraduates with learning the basics of programming in general and programming MATLAB® in particular.

uk: вхід без авторизації


uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 2: The Command Prompt

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 3: Using Files

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 4: Plotting

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 5: Scripts and Functions

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


Lecture 6: Debugging

uk: Комп'ютерні науки

uk: Математика, природничі науки

uk: вхід без авторизації


The Polynomial Method

keywords:
Mathematics
Algebra and Number Theory
Discrete Mathematics

uk: Математика, природничі науки

description: This course offers an introduction to the polynomial method as applied to solving problems in combinatorics in the last decade. The course also explores the connections between the polynomial method as used in these problems to the polynomial method in other fields, including computer science, number theory, and analysis.

uk: вхід без авторизації


How and Why Machines Work

keywords:
Engineering
Mechanical Engineering
Mechanical Design

de: Maschinenbau/Verfahrenstechnik

uk: Машинобудування/Технологія

en: Mechanical Engineering / Process Engineering

description: Subject studies how and why machines work, how they are conceived, how they are developed (drawn), and how they are utilized. Students learn from the hands-on experiences of taking things apart mentally and physically, drawing (sketching, 3D CAD) what they envision and observe, taking occasional field trips, and completing an individual term project (concept, creation, and presentation). Emphasis on understanding the physics and history of machines.

uk: вхід без авторизації


Mechanics & Materials I

keywords:
Engineering
Mechanical Engineering
Materials Science and Engineering
Solid Mechanics

uk: Машинобудування/Технологія

description: This course provides an introduction to the mechanics of solids with applications to science and engineering. We emphasize the three essential features of all mechanics analyses, namely: (a) the geometry of the motion and/or deformation of the structure, and conditions of geometric fit, (b) the forces on and within structures and assemblages; and (c) the physical aspects of the structural system (including material properties) which quantify relations between the forces and motions/deformation.

uk: вхід без авторизації


Mechanics and Materials II

uk: Машинобудування/Технологія

description: This course provides Mechanical Engineering students with an awareness of various responses exhibited by solid engineering materials when subjected to mechanical and thermal loadings; an introduction to the physical mechanisms associated with design-limiting behavior of engineering materials, especially stiffness, strength, toughness, and durability; an understanding of basic mechanical properties of engineering materials, testing procedures used to quantify these properties, and ways in which these properties characterize material response; quantitative skills to deal with materials-limiting problems in engineering design; and a basis for materials selection in mechanical design.

uk: вхід без авторизації


uk: Машинобудування/Технологія

description: Practice quiz solution.

uk: вхід без авторизації

de: Übung

en: Drill and Practice


uk: Машинобудування/Технологія

description: Practice quiz.

uk: вхід без авторизації


Modeling Dynamics and Control I

keywords:
Engineering
Mathematics
Mechanical Engineering
Systems Engineering
Applied Mathematics
Computational Modeling and Simulation
Dynamics and Control

uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This course is the first of a two term sequence in modeling, analysis and control of dynamic systems. The various topics covered are as follows: mechanical translation, uniaxial rotation, electrical circuits and their coupling via levers, gears and electro-mechanical devices, analytical and computational solution of linear differential equations, state-determined systems, Laplace transforms, transfer functions, frequency response, Bode plots, vibrations, modal analysis, open- and closed-loop control, instability, time-domain controller design, and introduction to frequency-domain control design techniques. Case studies of engineering applications are also covered.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This resource contains additional materials for problem set 2's solution.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This resource contains soluions for problems related to initial and final value theorems.

uk: вхід без авторизації


firstorderbode.pdf

uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This resource contains graphs plotted on Bode Plot of First Order System.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This quiz has three problems. The numerical weighting of each problem is identical. The quiz is closed-book. The problems concerns the second-order response.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This resource contains the problems on writing differential equation when the force of the wind and viscous drag of the water effects the sails of ship.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This resource contains problems on differential equation for the deflection of the springs, damping ratio of the mass-spring-damper system when the fender is in contact with the barrier etc.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This resource contains the review for quiz 3 on circuits and the impedance method, Mechanically equivalent circuits, method to make (or analyze) a Bode plot and associated circuit diagrams.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This resource contains problems on Mass Spring system with no damper, Transfer function from Bode plot, Input and Output waveform and its graph.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This resource contains solutions for 4 problems on RLC circuit analysis, transfer function.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This resource contains three problems on Bode plot and step response and circuit diagrams for the same.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This resource contains problems on transfer functions, Bode plot of a certain system (for a chosen input and output)and associated diagrams.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This resource contains problems on RLC circuit analysis, transfer function, Block Diagram, Step response.

uk: вхід без авторизації


secondorderbode.pdf

uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This resource contains the graph on Bode plot of Underdamped Second Order System

uk: вхід без авторизації


Dynamics and Control I

keywords:
Engineering
Mathematics
Mechanical Engineering
Applied Mathematics
Dynamics and Control

uk: Машинобудування/Технологія

uk: Математика, природничі науки

description:
This class is an introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Topics include kinematics; force-momentum formulation for systems of particles and rigid bodies in planar motion; work-energy concepts; virtual displacements and virtual work; Lagrange's equations for systems of particles and rigid bodies in planar motion; linearization of equations of motion; linear stability analysis of mechanical systems; free and forced vibration of linear multi-degree of freedom models of mechanical systems; and matrix eigenvalue problems. The class includes an introduction to numerical methods and using MATLAB® to solve dynamics and vibrations problems.

This version of the class stresses kinematics and builds around a strict but powerful approach to kinematic formulation which is different from the approach presented in Spring 2007. Our notation was adapted from that of Professor Kane of Stanford University.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: Exam with problems on a robotic arm, wheels of a railway engine, and wheels with a spring.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: Exam with problems on a space shuttle orbiter and an astronaut, L-shape, and system of pulleys.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: Exam with problems on sliding masses, cam follower and, ski-board on an incline.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: Exam with problems on dynamics and control.

uk: вхід без авторизації


final.pdf

uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: Final exam on dynamics and control.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: Final exam with problems on a non-uniform disc, equilibria and stability, and a rolling disc between parallel rods.

uk: вхід без авторизації


survey.pdf

uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: Practice quiz with a prerequisites check and sample future problems.

uk: вхід без авторизації


Dynamics and Control I

uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: Introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Kinematics. Force-momentum formulation for systems of particles and rigid bodies in planar motion. Work-energy concepts. Virtual displacements and virtual work. Lagrange's equations for systems of particles and rigid bodies in planar motion. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear multi-degree of freedom models of mechanical systems; matrix eigenvalue problems. Introduction to numerical methods and MATLAB® to solve dynamics and vibrations problems.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This resource contains an exam with questions: Conical pendulum, Rod pendulum with moving pivot, and Rolling wheel.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This resource contains a practice exam with three problems.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This resource contains an exam with three questions.

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

description: This resource contains the practice final exam with five problems.

uk: вхід без авторизації


Dynamics and Vibration (13.013J)

keywords:
Engineering
Science
Physics
Mechanical Engineering
Solid Mechanics
Ocean Structures
Classical Mechanics
Ocean Engineering
Dynamics and Control

de: Physik

en: Physics

uk: Машинобудування/Технологія

uk: Математика, природничі науки

de: Physik, Astronomie

uk: Фізика, Астрономія

en: Physics, Astronomy

description:
Introduction to dynamics and vibration of lumped-parameter models of mechanical systems. Three-dimensional particle kinematics. Force-momentum formulation for systems of particles and for rigid bodies (direct method). Newton-Euler equations. Work-energy (variational) formulation for systems particles and for rigid bodies (indirect method). Virtual displacements and work. Lagrange's equations for systems of particles and for rigid bodies. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear damped lumped parameter multi-degree of freedom models of mechanical systems. Application to the design of ocean and civil engineering structures such as tension leg platforms.

This subject was originally offered in Course 13 (Department of Ocean Engineering) as 13.013J. In 2005, ocean engineering became part of Course 2 (Department of Mechanical Engineering), and this subject merged with 2.003.

uk: вхід без авторизації


final.pdf

uk: Машинобудування/Технологія

uk: Математика, природничі науки

uk: Фізика, Астрономія

description: Dynamics Quiz 3

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

uk: Фізика, Астрономія

description: Quiz 1

uk: вхід без авторизації


uk: Машинобудування/Технологія

uk: Математика, природничі науки

uk: Фізика, Астрономія

description: Quiz II

uk: вхід без авторизації