6.045J Automata, Computability, and Complexity (MIT)

This course is offered to undergraduates and introduces basic mathematical models of computation and the finite representation of infinite objects. The course is slower paced than 6.840J/18.404J. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems.

Numerical Methods Applied to Chemical Engineering, Fall 2001

Numerical methods for solving problems arising in heat and mass transfer, fluid mechanics, chemical reaction engineering, and molecular simulation. Topics: numerical linear algebra, solution of nonlinear algebraic equations and ordinary differential equations, solution of partial differential equations (e.g. Navier-Stokes), numerical methods in molecular simulation (dynamics, geometry optimization). All methods are presented within the context of chemical engineering problems. Familiarity with s

Patricia Johnston Sings "I See the Sun"

This beautifully done video sings about the sun, moon, stars, ...Some of the lyrics include "I see the sun-a big round sun. I see the moon-a big round moon. I see the stars-the little, little stars---smiling just for me". These videos by Patricia Johnston were designed for young French children to begin to learn English. This is a great teaching resource for early childhood learners and/or special education students and would work well in conjunction with a unit on Earth and to help build backgr

Mathematical Modeling Using Real Radioactivity Data

In this lab, you can explore how radioactive radiation changes as a function of distance. This curriculum sets the Radioactivity iLab in the context of mathematics curriculum, asking you to consider:
What type of mathematical function governs the intensity of radiation over distance?

Policy Analysis of Multi-Actor Systems

This course is about solving complex problems. Our favorite problems are not just technically complex but also characterized by the presence of many different social actors that hold conflicting interests, objectives, and perceptions and act strategically to get the best out of a problem situation. This course offers guidance for policy analysts who want to assess if and how their analysis could be of help, based on the premise that problem formulation is the cornerstone in addressing complex pr

What is the Right Answer

The purpose of this resource is to introduce students to the concept that sometimes there is no one "right" answer to a question or measurement. Students learn to be careful when searching for a right answer to questions such as 'What time is it?' by comparing multiple measurements of the time of day. Students gain an intuitive understanding of the characteristics of imperfect measurements. Using different clocks, students simultaneously record the displayed times. The resulting time measurement

15 year old from Malawi builds windmill using spare parts

William Kamkwamba, a school drop-out (his family couldn't afford the fees) who lives in a remote village with no electricity, built his family a windmill using bicycle parts and scrap materials. The young inventor only had a photograph in a primary school textbook on energy to guide him.

ICT use in school: vision and performance measures

The implementation of ICT in schools requires a vision on ICT use in school, the formulation of clear strategic goals, and the planning and organisation of the use of ICT in school.
The pursued goals are those points we want to reach for the learner by setting up ICT use in school. At the same time the pursued goals are the results of using ICT as expected by the stakeholders, being the learner, the teacher, the ICT coordinator, and on an indirect way the parents, the environment and the funding

Changes in education: implications for teacher education.

This communication present the implication of the introducing of ICT in teacher training education, at the IUFM of Grenoble.

Introduction to Vectors and Tensors, Vol. 2, Vector and Tensor Analysis

Introduction to Vectors and Tensors, Vol. 2, Vector and Tensor Analysis is a typed revision of the book originally published by Plenum Press in 1976 as Volume 2 in their series on Mathematical Concepts and Methods in Science and Engineering, edited by Angelo Miele. PDF File.

Introduction to Vectors and Tensors, Vol. 1, Linear and Multilinear Algebra

Introduction to Vectors and Tensors, Vol. 1, Linear and Multilinear Algebra is a typed revision that was originally published by Plenum Press in 1976 as Volume 1 in a series on Mathematical Concepts and Methods in Science and Engineering, edited by Angelo Miele. PDF File.

A Logo-based Task for Arithmetical Activity

Young children attend to answer-getting readings of arithmetical notation. This is evidenced by many childrens exclusive acceptance of a + b = c syntaxes that lend themselves to computational readings (e.g. Behr et al., 1976; Carpenter & Levi, 2000; Knuth, Stephens, McNeil & Alibali 2006). Even those children who do accept a wider variety of syntaxes, such as a + b = b + a and c = a + b , adhere to a computational view involving getting answers to both sides of the equals sign and checking the

Introduction to Economic Analysis

This book presents introductory economics ("principles") material using standard mathematical tools, including calculus. It is designed for a relatively sophisticated undergraduate who has not taken a basic university course in economics. It also contains the standard intermediate microeconomics material. 328 page pdf.

Energy Balance Climate Model

Students explore a Global Energy Balance Climate Model Using Stella II. This Stella model focuses on global energy balance and creating a useful climate model. Students can explore how the model planetary surface and atmospheric temperatures respond to variations in solar input, atmospheric and surface albedo, atmospheric water vapor and carbon dioxide, volcanic eruptions, and mixed layer ocean depth. Climate feedbacks such as water vapor or ice-albedo can be turned on or off. The activity provi

Daisy World Model

The Daisy World model is intended to illustrate a mechanism through which biota might optimize their environment by means of negative feedback. The model offers a very simplified approach to a feedback system and can provide an introductory lesson in how models work. The aim of the model is to implement and test a mathematical model describing possible influence of biota on an abiotic (climatic) system using GAWK and GNUPLOT. The model tests the hypothesis that biota can influence the planetary

Crossroads in Mathematics: Standards for introductory college mathematics before calculus.

Crossroads in Mathematics: Standards for Introductory College Mathematics Before Calculus has two major goals: to improve mathematics education at two-year colleges and at the lower division of four-year colleges and universities and to encourage more students to study mathematics. The document presents standards that are intended to revitalize the mathematics curriculum preceding calculus and to stimulate changes in instructional methods so that students will be engaged as active learners in wo

Can you draw a picture of the stars on an American flag?

This online activity offers students a chance to analyze possible patterns for the 50 stars on the US flag. Students determine the possible patterns using the clue that each row contains either one more or one less star than the row next to it. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. The activity features a solution hint and a solution that suggests two ways to think about the problem and shows

Middle School Portal: Math and Science Pathways (MSP2)

This online challenge activity introduces a gift-counting problem that requires students to organize information in a table and then to draw conclusions. The importance of organizing information for decision making is noted for census takers, librarians, and demographers. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. The solution hint suggests how to organize a useful table. Related questions ask stud

Morphing : can you turn a frown into a smile?

This online challenge activity offers students a look into the world of computer animation. It features a simplified explanation of how one image can be transformed into another image using digitization and explains the mathematics concept of the average. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. Related questions ask students to consider other situations that require the use of percentages to mea