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2000 Midterm I + Solutions
Read the Fine Print
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Midterm examination for a class at MIT covering game theory and its applications to economics. The one-hour-and-twenty-minute open book examination asks open ended theoretical questions. The exam contains questions and solutions.

Subject:
Economics
Mathematics
Social Science
Material Type:
Assessment
Provider:
TeachingWithData.org
Provider Set:
TeachingWithData.org
Author:
Massachusetts Institute of Technology
Muhamet Yildiz
Date Added:
11/07/2014
5 Pythagorean Solids
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CC BY-NC-SA
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This OER explores the basic organization of the Pythagorean Solids. It contains both an activity as well as resources for further exploration. It is a product of the OU Academy of the Lynx, developed in conjunction with the Galileo's World Exhibition at the University of Oklahoma.

Subject:
Arts and Humanities
History
Mathematics
Material Type:
Activity/Lab
Diagram/Illustration
Homework/Assignment
Lecture Notes
Primary Source
Student Guide
Date Added:
10/09/2015
Abrupt climate change, greenhouse gases, and the bipolar see-saw
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CC BY-NC-SA
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In this activity, students work with paleoclimate proxy data (d18O, CH4, CO2)from the Byrd and GISP2 ice cores to investigate millennial-scale climate changes during the Last Glacial/Deglacial time periods. Students must prepare a publication quality plot of the data and answer several questions about the similarities and differences between the time-series (north-south phasing, amplitude, symmetry) and use this information to assess the bipolar see-saw mechanism for abrupt climate changes. Students are encouraged to read two journal articles for more information and to synthesize their results with other information from lectures and earlier readings.

(Note: this resource was added to OER Commons as part of a batch upload of over 2,200 records. If you notice an issue with the quality of the metadata, please let us know by using the 'report' button and we will flag it for consideration.)

Subject:
Applied Science
Biology
Environmental Science
Life Science
Mathematics
Measurement and Data
Material Type:
Activity/Lab
Homework/Assignment
Provider:
Science Education Resource Center (SERC) at Carleton College
Provider Set:
Teach the Earth
Author:
Kathleen Johnson
Date Added:
08/28/2019
Ace Maths: Solutions Unit 2 - Developing Understanding in Mathematics
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CC BY-NC-SA
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The solutions unit consists of the following: General points for discussion relating to the teaching of the mathematical content in the activities. Step-by-step mathematical solutions to the activities. Annotations to the solutions to assist teachers in their understanding the maths as well as teaching issues relating to the mathematical content represented in the activities. Suggestions of links to alternative activities for the teaching of the mathematical content represented in the activities.

Subject:
Mathematics
Material Type:
Lecture Notes
Reading
Unit of Study
Provider:
OER Africa
Date Added:
02/27/2012
Ace Maths Unit 2: Developing Understanding in Mathematics
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CC BY-NC-SA
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The solutions unit consists of the following: General points for discussion relating to the teaching of the mathematical content in the activities. Step-by-step mathematical solutions to the activities. Annotations to the solutions to assist teachers in their understanding the maths as well as teaching issues relating to the mathematical content represented in the activities. Suggestions of links to alternative activities for the teaching of the mathematical content represented in the activities

Subject:
Mathematics
Material Type:
Lecture Notes
Reading
Unit of Study
Provider:
OER Africa
Date Added:
02/27/2012
Adopt a Blob
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CC BY-NC-SA
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At the beginning of the course, each student is assigned a unique blob - or a piece of material of a particular shape with specific material properties (density, bulk modulus, composition, viscosity, volatile content, etc) that is residing within the mantle at a specific environment (depth, pressure, temperature). Then as the semester continues as a topic is covered the student must assess (either quantitatively or qualitatively) what observable would be associated with their blob (for example, gravity anomalies, geoid anomalies, surface expressions, seismic tomography, phase transition topography). The student then develops a portfolio of their blob and its observables to then present at the end of the course with an explanation/interpretation for the source of the blob culiminating at building a geo-story around their anomaly.

Some blobs could be amorphous anomalies whereas other could have physical significance (though best not to tell the students ahead of time so they can make their own discovery as to what the blob is or isn't) such as subducted slabs at the CMB (or 660 km), plumes, lithospheric drip, lithospheric root, or a boring typical piece of the mantle.

(Note: this resource was added to OER Commons as part of a batch upload of over 2,200 records. If you notice an issue with the quality of the metadata, please let us know by using the 'report' button and we will flag it for consideration.)

Subject:
Biology
Business and Communication
Communication
Life Science
Mathematics
Measurement and Data
Material Type:
Activity/Lab
Provider:
Science Education Resource Center (SERC) at Carleton College
Provider Set:
Teach the Earth
Author:
Catherine Cooper
Date Added:
03/02/2020
Advanced Analytic Methods in Science and Engineering
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CC BY-NC-SA
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Advanced Analytic Methods in Science and Engineering is a comprehensive treatment of the advanced methods of applied mathematics. It was designed to strengthen the mathematical abilities of graduate students and train them to think on their own.

Subject:
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Cheng, Hung
Date Added:
09/01/2004
Advanced Calculus for Engineers
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CC BY-NC-SA
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This course analyzes the functions of a complex variable and the calculus of residues. It also covers subjects such as ordinary differential equations, partial differential equations, Bessel and Legendre functions, and the Sturm-Liouville theory.

Subject:
Calculus
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Bush, John
Margetis, Dionisios
Date Added:
09/01/2004
Advanced Complexity Theory
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CC BY-NC-SA
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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.

Subject:
Applied Science
Computer Science
Engineering
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Bavarian, Mohammad
Moshkovitz, Dana
Date Added:
02/01/2016
Advanced Engineering Mathematics and Analysis - Nils Tilton & Corey R. Randall
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CC BY-NC-SA
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An open-source textbook covering vector calculus, ordinary and partial differential equations, and Fourier series. The textbook is used in a first-year graduate level course in the Department of Mechanical Engineering at the Colorado School of Mines. It undergoes extensive revisions annually, but is relatively complete.

Subject:
Applied Science
Engineering
Mathematics
Material Type:
Textbook
Author:
Allyson Turner
Emily Bongiovanni
Nils Tilton
Seth Vuletich
Date Added:
08/19/2022
Advanced Partial Differential Equations with Applications
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CC BY-NC-SA
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The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc.

Subject:
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Rosales, Rodolfo
Date Added:
09/01/2009
Advanced Stochastic Processes
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CC BY-NC-SA
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This class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models.

Subject:
Mathematics
Statistics and Probability
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Gamarnik, David
Date Added:
09/01/2013
Algebra
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CC BY-SA
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In this video, we explore some concepts fundamental to algebra. To streamline the discussion of relationships between physical quantities, we introduce variables, functions, composition, and inverse. By thinking about the concept of an inverse function, we obtain our first glimpse of the imaginary root (i.e. square-root of -1) and the complex plane.

Subject:
Algebra
Mathematics
Material Type:
Lecture Notes
Provider:
Look At Physics
Provider Set:
A Mathematical Way to Think About Biology
Author:
David Liao
Date Added:
10/08/2011
Algebraic Geometry
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CC BY-NC-SA
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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.

Subject:
Algebra
Geometry
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Bezrukavnikov, Roman
Date Added:
09/01/2015
Algebraic Geometry
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CC BY-NC-SA
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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.

Subject:
Algebra
Geometry
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Olsson, Martin
Date Added:
09/01/2003
Algebraic Geometry
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CC BY-NC-SA
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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.

Subject:
Algebra
Geometry
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Kedlaya, Kiran
Date Added:
02/01/2009
Algebraic Techniques and Semidefinite Optimization
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CC BY-NC-SA
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This research-oriented course will focus on algebraic and computational techniques for optimization problems involving polynomial equations and inequalities with particular emphasis on the connections with semidefinite optimization. The course will develop in a parallel fashion several algebraic and numerical approaches to polynomial systems, with a view towards methods that simultaneously incorporate both elements. We will study both the complex and real cases, developing techniques of general applicability, and stressing convexity-based ideas, complexity results, and efficient implementations. Although we will use examples from several engineering areas, particular emphasis will be given to those arising from systems and control applications.

Subject:
Algebra
Applied Science
Engineering
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Parrilo, Pablo
Date Added:
02/01/2006
Algebraic Topology I
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CC BY-NC-SA
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This is a course on the singular homology of topological spaces. Topics include: Singular homology, CW complexes, Homological algebra, Cohomology, and Poincare duality.

Subject:
Geometry
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Miller, Haynes
Date Added:
09/01/2016
Algebraic Topology II
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CC BY-NC-SA
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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.

Subject:
Geometry
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Miller, Haynes
Date Added:
02/01/2020