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18.304 Undergraduate Seminar in Discrete Mathematics (MIT) 18.304 Undergraduate Seminar in Discrete Mathematics (MIT)

Description

This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic. This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic.

Subjects

discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math | discrete math | discrete mathematics | discrete mathematics | discrete | discrete | math | math | mathematics | mathematics | seminar | seminar | presentations | presentations | student presentations | student presentations | oral | oral | communication | communication | stable marriage | stable marriage | dych | dych | emergency | emergency | response vehicles | response vehicles | ambulance | ambulance | game theory | game theory | congruences | congruences | color theorem | color theorem | four color | four color | cake cutting | cake cutting | algorithm | algorithm | RSA | RSA | encryption | encryption | numberical integration | numberical integration | sorting | sorting | post correspondence problem | post correspondence problem | PCP | PCP | ramsey | ramsey | van der waals | van der waals | fibonacci | fibonacci | recursion | recursion | domino | domino | tiling | tiling | towers | towers | hanoi | hanoi | pigeonhole | pigeonhole | principle | principle | matrix | matrix | hamming | hamming | code | code | hat game | hat game | juggling | juggling | zero-knowledge | zero-knowledge | proof | proof | repeated games | repeated games | lewis carroll | lewis carroll | determinants | determinants | infinitude of primes | infinitude of primes | bridges | bridges | konigsberg | konigsberg | koenigsberg | koenigsberg | time series analysis | time series analysis | GARCH | GARCH | rational | rational | recurrence | recurrence | relations | relations | digital | digital | image | image | compression | compression | quantum computing | quantum computing

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.304 Undergraduate Seminar in Discrete Mathematics (MIT) 18.304 Undergraduate Seminar in Discrete Mathematics (MIT)

Description

This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic. This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic.

Subjects

discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math | discrete math | discrete mathematics | discrete mathematics | discrete | discrete | math | math | mathematics | mathematics | seminar | seminar | presentations | presentations | student presentations | student presentations | oral | oral | communication | communication | stable marriage | stable marriage | dych | dych | emergency | emergency | response vehicles | response vehicles | ambulance | ambulance | game theory | game theory | congruences | congruences | color theorem | color theorem | four color | four color | cake cutting | cake cutting | algorithm | algorithm | RSA | RSA | encryption | encryption | numberical integration | numberical integration | sorting | sorting | post correspondence problem | post correspondence problem | PCP | PCP | ramsey | ramsey | van der waals | van der waals | fibonacci | fibonacci | recursion | recursion | domino | domino | tiling | tiling | towers | towers | hanoi | hanoi | pigeonhole | pigeonhole | principle | principle | matrix | matrix | hamming | hamming | code | code | hat game | hat game | juggling | juggling | zero-knowledge | zero-knowledge | proof | proof | repeated games | repeated games | lewis carroll | lewis carroll | determinants | determinants | infinitude of primes | infinitude of primes | bridges | bridges | konigsberg | konigsberg | koenigsberg | koenigsberg | time series analysis | time series analysis | GARCH | GARCH | rational | rational | recurrence | recurrence | relations | relations | digital | digital | image | image | compression | compression | quantum computing | quantum computing

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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Teaching secondary mathematics

Description

This free course will identify and explore some of the key issues around teaching mathematics in secondary schools. Through coming to understand these issues and debates

Subjects

Mathematics Education | Professional Development in Education | Teacher Training | EXM885_1 | mathematics | mathematics education | mathematics teacher | mathematics pedagogy

License

Except for third party materials and otherwise stated in the acknowledgement section (see our terms and conditions http://www.open.ac.uk/conditions) this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence. - http://creativecommons.org/licenses/by-nc-sa/4.0 Except for third party materials and otherwise stated in the acknowledgement section (see our terms and conditions http://www.open.ac.uk/conditions) this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence. - http://creativecommons.org/licenses/by-nc-sa/4.0

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Teaching secondary mathematics

Description

This free course, Teaching secondary mathematics, will identify and explore some of the key issues around teaching mathematics in secondary schools. Through coming to understand these issues and debates, you will reflect on and develop your practice as a mathematics teacher and develop a greater awareness of the wider context of mathematics education and how this affects mathematics in the secondary school curriculum. First published on Wed, 22 Jun 2016 as Teaching secondary mathematics. To find out more visit The Open University's Openlearn website. Creative-Commons 2016

Subjects

Education | Education Careers | EXM885_1 | mathematics | mathematics education | mathematics teacher | mathematics pedagogy

License

Licensed under a Creative Commons Attribution - NonCommercial-ShareAlike 2.0 Licence - see http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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18.304 Undergraduate Seminar in Discrete Mathematics (MIT)

Description

This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic.

Subjects

discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math | discrete mathematics | discrete | math | mathematics | seminar | presentations | student presentations | oral | communication | stable marriage | dych | emergency | response vehicles | ambulance | game theory | congruences | color theorem | four color | cake cutting | algorithm | RSA | encryption | numberical integration | sorting | post correspondence problem | PCP | ramsey | van der waals | fibonacci | recursion | domino | tiling | towers | hanoi | pigeonhole | principle | matrix | hamming | code | hat game | juggling | zero-knowledge | proof | repeated games | lewis carroll | determinants | infinitude of primes | bridges | konigsberg | koenigsberg | time series analysis | GARCH | rational | recurrence | relations | digital | image | compression | quantum computing

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.091 Mathematical Exposition (MIT) 18.091 Mathematical Exposition (MIT)

Description

This course provides techniques of effective presentation of mathematical material. Each section of this course is associated with a regular mathematics subject, and uses the material of that subject as a basis for written and oral presentations. The section presented here is on chaotic dynamical systems. This course provides techniques of effective presentation of mathematical material. Each section of this course is associated with a regular mathematics subject, and uses the material of that subject as a basis for written and oral presentations. The section presented here is on chaotic dynamical systems.

Subjects

oral presentation | oral presentation | mathematics writing | mathematics writing | mathematics presentation | mathematics presentation | 17.881 | 17.881 | 17.882 | 17.882

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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Teaching secondary mathematics

Description

This free course will identify and explore some of the key issues around teaching mathematics in secondary schools. Through coming to understand these issues and debates you will reflect on and develop your practice as a mathematics teacher and develop a greater awareness of the wider context of mathematics education and how this affects mathematics in the secondary school curriculum.

Subjects

Education | Education Careers | EXM885_1 | mathematics | mathematics education | mathematics teacher | mathematics pedagogy

License

Except for third party materials and otherwise stated in the acknowledgement section (see our terms and conditions http://www.open.ac.uk/conditions) this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence. - http://creativecommons.org/licenses/by-nc-sa/4.0 Except for third party materials and otherwise stated in the acknowledgement section (see our terms and conditions http://www.open.ac.uk/conditions) this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence. - http://creativecommons.org/licenses/by-nc-sa/4.0

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22.00J Introduction to Modeling and Simulation (MIT) 22.00J Introduction to Modeling and Simulation (MIT)

Description

This course surveys the basic concepts of computer modeling in science and engineering using discrete particle systems and continuum fields. It covers techniques and software for statistical sampling, simulation, data analysis and visualization, and uses statistical, quantum chemical, molecular dynamics, Monte Carlo, mesoscale and continuum methods to study fundamental physical phenomena encountered in the fields of computational physics, chemistry, mechanics, materials science, biology, and applied mathematics. Applications are drawn from a range of disciplines to build a broad-based understanding of complex structures and interactions in problems where simulation is on equal footing with theory and experiment. A term project allows development of individual interests. Students are mentor This course surveys the basic concepts of computer modeling in science and engineering using discrete particle systems and continuum fields. It covers techniques and software for statistical sampling, simulation, data analysis and visualization, and uses statistical, quantum chemical, molecular dynamics, Monte Carlo, mesoscale and continuum methods to study fundamental physical phenomena encountered in the fields of computational physics, chemistry, mechanics, materials science, biology, and applied mathematics. Applications are drawn from a range of disciplines to build a broad-based understanding of complex structures and interactions in problems where simulation is on equal footing with theory and experiment. A term project allows development of individual interests. Students are mentor

Subjects

computer modeling | computer modeling | discrete particle system | discrete particle system | continuum | continuum | continuum field | continuum field | statistical sampling | statistical sampling | data analysis | data analysis | visualization | visualization | quantum | quantum | quantum method | quantum method | chemical | chemical | molecular dynamics | molecular dynamics | Monte Carlo | Monte Carlo | mesoscale | mesoscale | continuum method | continuum method | computational physics | computational physics | chemistry | chemistry | mechanics | mechanics | materials science | materials science | biology; applied mathematics | biology; applied mathematics | fluid dynamics | fluid dynamics | heat | heat | fractal | fractal | evolution | evolution | melting | melting | gas | gas | structural mechanics | structural mechanics | FEM | FEM | finite element | finite element | biology | biology | applied mathematics | applied mathematics | 1.021 | 1.021 | 2.030 | 2.030 | 3.021 | 3.021 | 10.333 | 10.333 | 18.361 | 18.361 | HST.588 | HST.588 | 22.00 | 22.00

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.304 Undergraduate Seminar in Discrete Mathematics (MIT) 18.304 Undergraduate Seminar in Discrete Mathematics (MIT)

Description

This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic. This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic.

Subjects

discrete math | discrete math | discrete mathematics | discrete mathematics | presentations | presentations | student presentations | student presentations | oral communication | oral communication | combinatorics | combinatorics | graph theory | graph theory | Proofs from the Book | Proofs from the Book | mathematics communication | mathematics communication

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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6.231 Dynamic Programming and Stochastic Control (MIT) 6.231 Dynamic Programming and Stochastic Control (MIT)

Description

This course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). Approximation methods for problems involving large state spaces are also presented and discussed. This course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). Approximation methods for problems involving large state spaces are also presented and discussed.

Subjects

dynamic programming | dynamic programming | | stochastic control | | stochastic control | | mathematics | optimization | | | mathematics | optimization | | algorithms | | algorithms | | probability | | probability | | Markov chains | | Markov chains | | optimal control | optimal control | stochastic control | stochastic control | mathematics | mathematics | optimization | optimization | algorithms | algorithms | probability | probability | Markov chains | Markov chains

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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Experiences of learning mathematics

Description

This unit is aimed at teachers who wish to review how they go about the practice of teaching maths, those who are considering becoming maths teachers, or those who are studying maths courses and would like to understand more about the teaching process.

Subjects

mathematics and statistics | mathematics | teaching | teaching_maths | teaching_techniques | Education | X000

License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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SP.341 History and Philosophy of Mechanics: Newton's Principia Mathematica (MIT) SP.341 History and Philosophy of Mechanics: Newton's Principia Mathematica (MIT)

Description

This course focuses on an in-depth reading of Principia Mathematica Philosophiae Naturalis by Isaac Newton, as well as several related commentaries and historical philosophical texts. This course focuses on an in-depth reading of Principia Mathematica Philosophiae Naturalis by Isaac Newton, as well as several related commentaries and historical philosophical texts.

Subjects

intellectual history | intellectual history | history of mathematics | history of mathematics | history of science and technology | history of science and technology | Isaac Newton | Isaac Newton | calculus | calculus | laws of motion | laws of motion

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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Working on your own mathematics

Description

This unit focuses on your initial encounters with research. It invites you to think about how perceptions of mathematics have influenced you in your prior learning, your teaching and the attitudes of learners.

Subjects

mathematics and statistics | mathematics | teaching | teaching_maths | teaching_techniques | Education | X000

License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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Modelling displacements and velocities

Description

In this unit you will see first how to convert vectors from geometric form, in terms of a magnitude and direction, to component form, and then how conversion in the opposite sense is accomplished. The ability to convert between these different forms of a vector is useful in certain problems involving displacement and velocity, as shown in Section 2, in which you will also work with bearings.

Subjects

mathematics and statistics | mathematics | maths_modelling | modelling | vectors | Education | X000

License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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6.251J Introduction to Mathematical Programming (MIT) 6.251J Introduction to Mathematical Programming (MIT)

Description

This course offers an introduction to optimization problems, algorithms, and their complexity, emphasizing basic methodologies and the underlying mathematical structures. The main topics covered include: Theory and algorithms for linear programming Network flow problems and algorithms Introduction to integer programming and combinatorial problems This course offers an introduction to optimization problems, algorithms, and their complexity, emphasizing basic methodologies and the underlying mathematical structures. The main topics covered include: Theory and algorithms for linear programming Network flow problems and algorithms Introduction to integer programming and combinatorial problems

Subjects

optimization | optimization | algorithms | algorithms | linear programming | linear programming | network flow problems | network flow problems | integer programming | integer programming | combinatorial problems | combinatorial problems | mathematics | mathematics | mathematical programming | mathematical programming | 6.251 | 6.251 | 15.081 | 15.081

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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SP.268 The Mathematics in Toys and Games (MIT) SP.268 The Mathematics in Toys and Games (MIT)

Description

We will explore the mathematical strategies behind popular games, toys, and puzzles. Topics covered will combine basic fundamentals of game theory, probability, group theory, and elementary programming concepts. Each week will consist of a lecture and discussion followed by game play to implement the concepts learned in class. We will explore the mathematical strategies behind popular games, toys, and puzzles. Topics covered will combine basic fundamentals of game theory, probability, group theory, and elementary programming concepts. Each week will consist of a lecture and discussion followed by game play to implement the concepts learned in class.

Subjects

toys | toys | games | games | mathematics | mathematics | game theory | game theory | probability | probability | group theory | group theory | programming | programming | combinatorial game theory | combinatorial game theory

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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Modelling with Fourier series

Description

This unit shows how partial differential equations can be used to model phenomena such as waves and heat transfer. The prerequisite requirements to gain full advantage from this unit are an understanding of ordinary differential equations and basic familiarity with partial differential equations.

Subjects

mathematics and statistics | differential | equations | fourier | mathematics | maths_modelling | modelling | Education | X000

License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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Statistics 250 - Introduction to Statistics and Data Analysis Statistics 250 - Introduction to Statistics and Data Analysis

Description

Content Type:  Course Short Title/Course Code:  statistics250 Attention students enrolled in the Winter 2015 course: You can download full-text versions of the Workbook and Interactive Lecture Notes from the "Materials" tab of this course. You may also purchase copies from Amazon.com: (Interactive Lecture Notes), and (Workbook) Statistics is the science that turns data into information and information into knowledge. This class covers applied statistical methodology from an analysis-of-data viewpoint. Topics covered include frequency distributions; measures of location; mean, median, mode; measures of dispersion; variance; graphic presentati Content Type:  Course Short Title/Course Code:  statistics250 Attention students enrolled in the Winter 2015 course: You can download full-text versions of the Workbook and Interactive Lecture Notes from the "Materials" tab of this course. You may also purchase copies from Amazon.com: (Interactive Lecture Notes), and (Workbook) Statistics is the science that turns data into information and information into knowledge. This class covers applied statistical methodology from an analysis-of-data viewpoint. Topics covered include frequency distributions; measures of location; mean, median, mode; measures of dispersion; variance; graphic presentati

Subjects

mathematics | mathematics | open textbooks | open textbooks | quantitative analysis | quantitative analysis | SPSS | SPSS | statistics | statistics

License

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First-order differential equations

Description

This unit introduces the topic of differential equations. The subject is developed without assuming that you have come across it before, but it is taken for granted that you have a basic grounding in calculus. In particular, you will need to have a good grasp of the basic rules for differentiation and integration.

Subjects

mathematics and statistics | calculus | differential | equations | mathematics | maths_modelling | Education | X000

License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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12.540 Principles of the Global Positioning System (MIT) 12.540 Principles of the Global Positioning System (MIT)

Description

The aim of this course is to introduce the principles of the Global Positioning System and to demonstrate its application to various aspects of Earth Sciences. The specific content of the course depends each year on the interests of the students in the class. In some cases, the class interests are towards the geophysical applications of GPS and we concentrate on high precision(millimeter level) positioning on regional and global scales. In other cases, the interests have been more toward engineering applications of kinematic positioning with GPS in which case the concentration is on positioning with slightly less accuracy but being able to do so for a moving object. In all cases, we concentrate on the fundamen The aim of this course is to introduce the principles of the Global Positioning System and to demonstrate its application to various aspects of Earth Sciences. The specific content of the course depends each year on the interests of the students in the class. In some cases, the class interests are towards the geophysical applications of GPS and we concentrate on high precision(millimeter level) positioning on regional and global scales. In other cases, the interests have been more toward engineering applications of kinematic positioning with GPS in which case the concentration is on positioning with slightly less accuracy but being able to do so for a moving object. In all cases, we concentrate on the fundamen

Subjects

Global Positioning System | Global Positioning System | Earth Sciences | Earth Sciences | geophysical applications | geophysical applications | GPS | GPS | engineering applications | engineering applications | kinematic positioning | kinematic positioning | precision | precision | accuracy | accuracy | moving objects | moving objects | coordinate | coordinate | time | time | systems | systems | satellite | satellite | geodetic | geodetic | orbital | orbital | motions | motions | pseudo ranges | pseudo ranges | carrier phases | carrier phases | stochastic | stochastic | mathematics | mathematics | models | models | data | data | analysis | analysis | estimation | estimation

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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22.00J Introduction to Modeling and Simulation (MIT)

Description

This course surveys the basic concepts of computer modeling in science and engineering using discrete particle systems and continuum fields. It covers techniques and software for statistical sampling, simulation, data analysis and visualization, and uses statistical, quantum chemical, molecular dynamics, Monte Carlo, mesoscale and continuum methods to study fundamental physical phenomena encountered in the fields of computational physics, chemistry, mechanics, materials science, biology, and applied mathematics. Applications are drawn from a range of disciplines to build a broad-based understanding of complex structures and interactions in problems where simulation is on equal footing with theory and experiment. A term project allows development of individual interests. Students are mentor

Subjects

computer modeling | discrete particle system | continuum | continuum field | statistical sampling | data analysis | visualization | quantum | quantum method | chemical | molecular dynamics | Monte Carlo | mesoscale | continuum method | computational physics | chemistry | mechanics | materials science | biology; applied mathematics | fluid dynamics | heat | fractal | evolution | melting | gas | structural mechanics | FEM | finite element | biology | applied mathematics | 1.021 | 2.030 | 3.021 | 10.333 | 18.361 | HST.588 | 22.00

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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Differential equations

Description

This unit extends the ideas introduced in the unit on first-order differential equations to a particular type of second-order differential equations which has a variety of applications. The unit assumes that you have previously had a basic grounding in calculus, know something about first-order differential equations and some familiarity with complex numbers.

Subjects

mathematics and statistics | calculus | complex_numbers | differential | equations | mathematics | maths_modelling | Education | X000

License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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Using vectors to model

Description

This unit introduces the topic of vectors. The subject is developed without assuming you have come across it before, but the unit assumes that you have previously had a basic grounding in algebra and trigonometry, and how to use Cartesian coordinates for specifying a point in a plane.

Subjects

mathematics and statistics | mathematics | maths_modelling | model | vectors | Education | X000

License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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Modelling static problems

Description

This unit lays the foundation of the subject of mechanics. Mechanics is concerned with how and why objects stay put, and how and why they move. In particular, this unit - Modelling Static Problems - considers why objects stay put. And it assumes that you have a good working knowledge of vectors.

Subjects

mathematics and statistics | mathematics | maths_modelling | modelling | vectors | Education | X000

License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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16.00 Introduction to Aerospace Engineering and Design (MIT) 16.00 Introduction to Aerospace Engineering and Design (MIT)

Description

The fundamental concepts, and approaches of aerospace engineering, are highlighted through lectures on aeronautics, astronautics, and design. Active learning aerospace modules make use of information technology. Student teams are immersed in a hands-on, lighter-than-air (LTA) vehicle design project, where they design, build, and fly radio-controlled LTA vehicles. The connections between theory and practice are realized in the design exercises. Required design reviews precede the LTA race competition. The performance, weight, and principal characteristics of the LTA vehicles are estimated and illustrated using physics, mathematics, and chemistry known to freshmen, the emphasis being on the application of this knowledge to aerospace engineering and design rather than on exposure to new scien The fundamental concepts, and approaches of aerospace engineering, are highlighted through lectures on aeronautics, astronautics, and design. Active learning aerospace modules make use of information technology. Student teams are immersed in a hands-on, lighter-than-air (LTA) vehicle design project, where they design, build, and fly radio-controlled LTA vehicles. The connections between theory and practice are realized in the design exercises. Required design reviews precede the LTA race competition. The performance, weight, and principal characteristics of the LTA vehicles are estimated and illustrated using physics, mathematics, and chemistry known to freshmen, the emphasis being on the application of this knowledge to aerospace engineering and design rather than on exposure to new scien

Subjects

aerospace engineering | | aerospace engineering | | aerospace design | | aerospace design | | aeronautics | | aeronautics | | astronautics | | astronautics | | lighter-than-air (LTA) vehicle design | | lighter-than-air (LTA) vehicle design | | physics | | physics | | mathematics | | mathematics | | chemistry | chemistry | journey to mars | journey to mars | challenger | challenger

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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