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2000 Midterm I + Solutions
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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:
Mathematics
Economics
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
Conditions of Use:
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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
Author:
Brent Purkaple
Kerry Magruder
Date Added:
01/28/2016
APEX Calculus
Conditions of Use:
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APEX Calculus is a calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now (Stewart, Thomas & Finney, etc.). The explanations of new concepts is clear, written for someone who does not yet know calculus. Each section ends with an exercise set with ample problems to practice & test skills (odd answers are in the back).

Subject:
Calculus
Material Type:
Textbook
Provider:
APEX: Affordable Print and Electronic TeXtbooks
Author:
Brian Heinold
Dimplekumar Chalishajar
Gregory Hartman
Troy Siemers
Date Added:
01/01/2014
Abstract Algebra
Conditions of Use:
No Strings Attached
Rating

This module aims to acquaint you with the mathematical aspects of rings and groups and the underlying algebraic structures and when they are looked at as non-empty sets, how their elements are combined by binary operations as well as how those elements behave under transformations such finding inverses. Some non-empty sets, under the operation of addition or multiplication do not include the inverses of their elements as members of the set and they are called semi-groups. The non-empty sets that include the inverses of their elements are full fledged groups. This module fills the gap arising from basic mathematics.

Subject:
Algebra
Material Type:
Module
Provider:
African Virtual University
Provider Set:
OER@AVU
Author:
Othow Onak Giel
Date Added:
03/10/2018
Abstract Algebra
Conditions of Use:
Read the Fine Print
Rating

Algebra is the language of modern mathematics. This course introduces students to that language through a study of groups, group actions, vector spaces, linear algebra, and the theory of fields.

Subject:
Algebra
Material Type:
Lecture
Provider:
Harvard University
Provider Set:
Harvard Extension School
Author:
Benedict Gross
Date Added:
01/09/2013
Abstract Algebra: Theory and Applications
Conditions of Use:
Read the Fine Print
Rating

This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly.

Subject:
Algebra
Material Type:
Textbook
Provider:
University of Puget Sound
Author:
Thomas Judson
Date Added:
01/01/2016
Active Calculus
Conditions of Use:
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Active Calculus is different from most existing calculus texts in at least the following ways: the text is free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the text is open source, and interested instructors can gain access to the original source files upon request; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; the exercises are few in number and challenging in nature.

Subject:
Mathematics
Calculus
Material Type:
Textbook
Provider:
Grand Valley State University
Author:
David Austin
Matt Boelkins
Steve Schlicker
Date Added:
02/19/2015
Active Calculus Multivariable
Conditions of Use:
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Active Calculus Multivariable is the continuation of Active Calculus to multivariable functions. The Active Calculus texts are different from most existing calculus texts in at least the following ways: the texts are free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the texts are open source, and interested instructors can gain access to the original source files upon request; the style of the texts requires students to be active learners — there are very few worked examples in the texts, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; the exercises are few in number and challenging in nature.

Subject:
Calculus
Material Type:
Textbook
Provider:
Grand Valley State University
Author:
David Austin
Matthew Boelkins
Steven Schlicker
Date Added:
07/01/2018
Agent-Based Evolutionary Game Dynamics
Conditions of Use:
No Strings Attached
Rating

This book is a guide to implement simple agent-based evolutionary models using NetLogo.

Subject:
Mathematics
Material Type:
Textbook
Author:
Luis R. Izquierdo
Segismundo S. Izquierdo
William H. Sandholm
Date Added:
06/28/2019
Algebra
Conditions of Use:
Read the Fine Print
Rating

This course discusses how to use algebra for a variety of everyday tasks, such as calculate change without specifying how much money is to be spent on a purchase, analyzing relationships by graphing, and describing real-world situations in business, accounting, and science.

Subject:
Algebra
Material Type:
Full Course
Provider:
The Saylor Foundation
Date Added:
08/28/2013
Algebra
Conditions of Use:
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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:
Mathematics
Algebra
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
Algebra II, Spring 2011
Conditions of Use:
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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.

Subject:
Algebra
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Artin, Michael
Date Added:
01/01/2011
Algebra and Trigonometry
Conditions of Use:
No Strings Attached
Rating

Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensures that the book meets the needs of a variety of courses. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

Subject:
Algebra
Trigonometry
Material Type:
Textbook
Provider:
Rice University
Provider Set:
OpenStax College
Author:
David Lippman
Jay Abramson
Jean-Marie Magnier
Melonie Rasmussen
Nicholas Belloit
Rachael Gross
Rick Norwood
Valeree Falduto
Date Added:
01/29/2015
Algorithms
Conditions of Use:
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This book aims to be an accessible introduction into the design and analysis of efficient algorithms. Throughout the book we will introduce only the most basic techniques and describe the rigorous mathematical methods needed to analyze them.

The topics covered include:

The divide and conquer technique.
The use of randomization in algorithms.
The general, but typically inefficient, backtracking technique.
Dynamic programming as an efficient optimization for some backtracking algorithms.
Greedy algorithms as an optimization of other kinds of backtracking algorithms.
Hill-climbing techniques, including network flow.

The goal of the book is to show you how you can methodically apply different techniques to your own algorithms to make them more efficient. While this book mostly highlights general techniques, some well-known algorithms are also looked at in depth. This book is written so it can be read from "cover to cover" in the length of a semester, where sections marked with a * may be skipped.

Subject:
Mathematics
Material Type:
Textbook
Provider:
Wikibooks
Date Added:
07/27/2016
Analysis 1
Conditions of Use:
No Strings Attached
Rating

The rationale of teaching analysis is to set the minimum content of Pure Mathematics required at undergraduate level for student of mathematics. It is important to note that skill in proving mathematical statements is one aspect that learners of Mathematics should acquire. The ability to give a complete and clear proof of a theorem is essential for the learner so that he or she can finally get to full details and rigor of analyzing mathematical concepts. Indeed it is in Analysis that the learner is given the exposition of subject matter as well as the techniques of proof equally. We also note here that if a course like calculus with its wide applications in Mathematical sciences is an end in itself then Analysis is the means by which we get to that end.

Subject:
Mathematics
Material Type:
Module
Provider:
African Virtual University
Provider Set:
OER@AVU
Author:
Jairus M. Khalagai
Date Added:
03/15/2018
Analysis 2
Conditions of Use:
No Strings Attached
Rating

The rationale of teaching analysis is to set the minimum content of Pure Mathematics required at undergraduate level for student of mathematics. It is important to note that skill in proving mathematical statements is one aspect that learners of Mathematics should acquire. The ability to give a complete and clear proof of a theorem is essential for the learner so that he or she can finally get to full details and rigor of analyzing mathematical concepts. Indeed it is in Analysis that the learner is given the exposition of subject matter as well as the techniques of proof equally. We also note here that if a course like calculus with its wide applications in Mathematical sciences is an end in itself then Analysis is the means by which we get to that end.

Subject:
Mathematics
Material Type:
Module
Provider:
African Virtual University
Provider Set:
OER@AVU
Author:
Jairus M. Khalagai
Date Added:
03/10/2018
Analysis I, Fall 2010
Conditions of Use:
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Analysis I covers fundamentals of mathematical analysis: metric spaces, convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations.

Subject:
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Wehrheim, Katrin
Date Added:
01/01/2010