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Cartesian Products and Relations - Foundations of Pure Mathematics - Dr Joel Feinstein
The eighth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers definitions and examples of Cartesian products and (binary) relations, including order relations and congruence modulo k.
These videos are also available for download on iTunes U at: https://itunes.apple.com/us/itunes-u/foundations-pure-mathematics/id950755120
Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com
Dr Joel Feinstein is an Associate Professor in Pure Mathematics at t
Big Ideas for Geograph
ideas for projects involving either the Geograph Website, or the Geograph Image Archive
The Slave Trade
The slave trade touched the lives of people around the globe, explains Colonial Williamsburg's Educational Program Development director Bill White.
September 11 - Film by Jules and Gedeon Naudet
In 2001, Gedeon and Jules Naudet were filming a documentary about a young New York City firefighter from Engine 7, Ladder 1. While Jules was at the scene of a gas leak, the first attack on the World Trade Center took place. (58:32)
Jules (who was still learning his craft) filmed Flight 11 as it crashed into the North Tower. In this clip, from an interview with Charlie Rose, Jules and his brother relate what happened on the September 11 morning when America was attacked.
3.7 Analytical notation
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
3.6 A second reduction: analytical levels
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
3.5 Making a foreground reduction
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
3.4 The concept of prolongation
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
3.3 Categories of dissonance in tonal music
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
3.2 Simple reductive processes
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
3.1 Introduction to the elements of voice-leading analysis
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
2.2 Listening for lines within the harmony
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
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
1.4 Some introductory listening
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
1.3 The origins of voice-leading analysis
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
1.2 Analysing harmony
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
1.1 Overview of Mozart's sonatas
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
Introduction
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
21A.215 Medical Anthropology (MIT)
Examination of how medicine is practiced cross-culturally, with particular emphasis on Western biomedicine. Analysis of medical practice as a cultural system, focusing on the human, as opposed to the biological, side of things. Also, examines how we and people in other cultures think of disease, health, body, and mind.
