Egyptian mathematics
The Egyptians are known for being ahead of their time in comparison to some civilisations that came after them. This unit looks at how the Egyptians solved mathematical problems in everyday life and the technology they used. An understanding of this area has only been possible following the translation of the Rosetta Stone.
Author(s): The Open University

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Global Eradication of Infectious Diseases: Can 'Not Very Much' undermine the goal of 'None at All'?
Despite the well-publicised success of global smallpox eradication, 'zero' remains an elusive goal for the majority of vaccine-preventable diseases, making reduced pathogen circulation, or direct protection of the vulnerable more achievable strategies. We will consider potential deleterious consequences of reduced infection transmission, in the context of diseases such as influenza and pertussis, where immunity following natural exposure may be superior to that following immunisation. Implicati
Author(s): Jodie McVernon

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Stability and Complexity in Model Banking Systems
The recent banking crises have made it clear that increasingly complex strategies for managing risk in individual banks and investment funds (pension funds, etc) has not been matched by corresponding attention to overall systemic risks. Simple mathematical caricatures of 'banking ecosystems', which capture some of the essential dynamics and which have some parallels (along with significant differences) with earlier work on stability and complexity in ecological food webs, have interesting implic
Author(s): Robert May

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Learning to Think Mathematically
Concerned that most students leave college thinking of mathematics as a fixed body of knowledge to be memorized, Cooperstein designed a new course to help students learn to think mathematically for themselves. This website serves as a course portfolio that documents the new class, Introduction to Mathematical Problem Solving. The principal activity in the class involved students working on and discussing novel problems which required them to formulate experiments, work out cases, look for patter
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DNA Microarrays: Background, Interactive Databases, and Hands-on Data Analysis
DNA microarrays are influencing many areas of biology. DNA microarrays allow investigators to measure simultaneously the activity of every gene in a genome. This paper provides the reader with background information, a set of interactive questions, and most importantly, free software (MAGIC Tool) for use in the undergraduate curriculum. MAGIC Tool (www.bio.davidson.edu/MAGIC) resources allow the user to understand how DNA microarray data are analyzed by providing raw data, instructions, mathemat
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Classroom Innovations through Lesson Study
Classroom Innovations through Lesson Study is an APEC EDNET Project that aims to improve the quality of education in the area of Mathematics. This project is sponsored by APEC Members Japan and Thailand. The APEC-Tsukuba International Conference III was broadcast live from Tokyo, December 9-10, 2007. The project has produced useful papers describing mathematical thinking, lesson videos of classroom instruction. This project focuses on Lesson Study with the goal of improving the quality of educat
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Introduction to Nanoscale Science: Surface Area to Volume Ratio Module
Many intriguing phenomena observed in the "nanoworld" can be attributed to the increase in the surface to volume ratio ( SVR ) at the nanoscale. Understanding the surface area effects to volume changes is thus crucial to the understanding of nanoscale phenomena and nanotechnology applications. As an introduction to the nanoworld, the major goals of this module are to (1) give students a feel for just how small the nanoscale is, (2) give students practice in mathematically communicating nanoscale
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Private Universe Project in Mathematics: Workshop 2. Are You Convinced?
Proof making is one of the key ideas in mathematics. Looking at teachers and students grappling with the same probability problem, we see how two kinds of proof—proof by cases and proof by induction—naturally grow out of the need to justify and convince others.,Englewood, New Jersey—Teachers Workshop Englewood, a town with unsatisfactory student test scores, is implementing a long-term project to improve math achievement. As part of a professional development workshop designed in part to give
Author(s): Harvard-Smithsonian Center for Astrophysics

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Smithsonian Institution-Astrophysical Observatory "All Rights Reserved"

The Great Magnet, the Earth
This site provides a non-mathematical introduction to the magnetism of the Earth, the Sun, the planets and their environments, following a historical thread. In 1600, four hundred years ago William Gilbert, later physician to Queen Elizabeth I of England, published his great study of magnetism, "De Magnete"--"On the Magnet". It gave the first rational explanation to the mysterious ability of the compass needle to point north-south: the Earth itself was magnetic. "De Magnete" opened the era of mo
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How to use Microsoft Excel in the Classroom

I am finding my students are increasingly using spreadsheets to solve mathematical problems in class and represent their data and findings in meaningful ways.  Th
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15.075 Applied Statistics (MIT)
This course is an introduction to applied statistics and data analysis. Topics include collecting and exploring data, basic inference, simple and multiple linear regression, analysis of variance, nonparametric methods, and statistical computing. It is not a course in mathematical statistics, but provides a balance between statistical theory and application. Prerequisites are calculus, probability, and linear algebra. We would like to acknowledge the contributions that Prof. Roy Welsch (MIT), Pro
Author(s): Newton, Elizabeth

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14.12 Economic Applications of Game Theory (MIT)
Game Theory is a misnomer for Multiperson Decision Theory, the analysis of situations in which payoffs to agents depend on the behavior of other agents. It involves the analysis of conflict, cooperation, and (tacit) communication. Game theory has applications in several fields, such as economics, politics, law, biology, and computer science. In this course, I will introduce the basic tools of game theoretic analysis. In the process, I will outline some of the many applications of game theory, pr
Author(s): Yildiz, Muhamet

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Materials Genome Initiative: Three Years of Progress
By: nsf Advanced materials are essential to human well-being and are the cornerstone for emerging industries. Yet today, it can take ten to twenty years or more from initial research on a new material to first use. That's why in June 2011 President Obama launched the Materials Genome Initiative (MGI) "to help businesses discover, develop, and deploy new materials twice as fast" and at a fraction of the cost. The MGI brings together academic institutions, small businesses, large industrial enterp
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Mini project : ROM based sine wave generator : document transcript
This is Mini Project documentation introducing a ROM-Based Sine Wave Generator. It is part of the 2009/10 BEng in Digital Systems and Computer Engineering (course number 2ELE0065) from the University of Hertfordshire. All the mini projects are designed as level two modules of the undergraduate programmes. It includes an introduction, project briefs for days 1 and 2 and a preparation session. This project requires the establishment of a communication protocol between two 68000-based microco
Author(s): University of Hertfordshire, School of Electronic

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South Royalton After 40 Years
From the panel recorded at the 2014 Austrian Economics Research Conference in Auburn, Alabama, on 22 March 2014. Sponsored by Jing Jin and Wai Chan.

12.086 Modeling Environmental Complexity (MIT)
This course provides an introduction to the study of environmental phenomena that exhibit both organized structure and wide variability—i.e., complexity. Through focused study of a variety of physical, biological, and chemical problems in conjunction with theoretical models, we learn a series of lessons with wide applicability to understanding the structure and organization of the natural world. Students will also learn how to construct minimal mathematical, physical, and computational mod
Author(s): Rothman, Daniel

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8.6 Research skills

This kind of work teaches some very valuable skills:

  • how to set about an enquiry

  • how and where to find source material and information

  • how to make your own investigations

  • strategic planning

  • time management

  • cutting corners and being pragmatic

  • analysing and interpreting primary and secondary source material

  • forming your own conclusions<
    Author(s): The Open University

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2.1 Two examples
This unit introduces ‘voice-leading’ or ‘Schenkerian’ analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the first in the AA314 series of three units on this form of harmonic analysis, and concentrates on the ‘foreground level’ of voice leading. As you work through this unit, you will become familiar with five complete movements of Mozart’s piano
Author(s): The Open University

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Virtual Maths - Shapes, Space and Measure, Theodolite Survey simulation
Simulation of using a thodolite to calculate the height of a building.
Author(s): Leeds Metropolitan University

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Hendrik Lenstra, University of Leiden: "Escher and the Droste Effect" - April 3, 2007
In 1956 the Dutch graphic artist M. C. Escher made an unusual lithograph with the title "Print Gallery." It shows a young man viewing a print in an exhibition gallery. Among the buidlings depicted on the print, he sees paradoxically the very same gallery that he is standing in. A lot is known about the way in which Escher made his lithograph. It is not nearly as well known that it contains a hidden "Droste effect," or infinite repetition; but this is brought to light by a mathematical analysis o
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