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Surfaces
Science, Maths & Technology

Surfaces

...change. [Figure 43] Figure 43 To sum up, two surfaces in space are homeomorphic if we can bend, stretch, squeeze or shrink one into the other and/or if we can cut one and then, after some bending, stretching, squeezing or shrinking, glue it back together (making sure to join the points on either side of the cut exactly as beforehand) to form the other. We thus have a...
View course Surfaces
Level 3: Advanced 20 hrs
Diagrams, charts and graphs
Science, Maths & Technology

Diagrams, charts and graphs

...changed over a period of nearly 30 years. NUMBER OF PEOPLE IN HOUSEHOLD 1961 (%) 1971 (%) 1981 (%) 1991 (%) 1 14 18 22 27 2 30 32 32 34 3 23 19 17 16 4 18 17 18 16 5 9 8 7 5 6 or more 7 6 4 2 Number of households surveyed/millions 16.3 18.6 20.2 22.4 Average household size (number of people) 3.1 2.9 2.7 2.5 (Office for National Statistics, Social Trends 29, 1999, Crown...
View course Diagrams, charts and graphs
Level 1: Introductory 5 hrs
Getting started with Spanish 3
Languages

Getting started with Spanish 3

...changing the settings in your mobile phone to Spanish? You will pick up some useful vocabulary without even realising it. Don’t forget to speak Spanish as often as you can. You can also have mini-conversations with yourself and practise spelling out your name. Listen to the audios again and try to repeat aloud what you hear. Next week you’ll be learning how to make...
View course Getting started with Spanish 3
Level 1: Introductory 8 hrs
Voice-leading analysis of music 3: the background
History & The Arts

Voice-leading analysis of music 3: the background

...changes) in the bass which you think will indicate the harmonisation of these notes in the top line. Identify these moments by putting the bar number over each note you have added. Example 6 Beethoven, Symphony No.8, third movement, bars 45–78: preliminary background graph Click to open graph (Example 6). You may wish to listen through to the trio a couple of times...
View course Voice-leading analysis of music 3: the background
Level 3: Advanced 20 hrs
Machine translation in language learning and teaching
Languages

Machine translation in language learning and teaching

...changing, and improving. Today’s top translation websites (see below) use Neural Machine Translation to emulate human intelligence and aim to replicate complex sentence structures, slang, and even humour. As well as specific translation websites, many browsers also offer the option to automatically translate content written in another language, which you will look at in...
View course Machine translation in language learning and teaching
Level 1: Introductory 12 hrs
Cynorthwywyr addysgu: Cymorth ar waith
Education & Development

Cynorthwywyr addysgu: Cymorth ar waith

...changes every term!’ Gall cynorthwywyr addysgu gael eu symud o gwmpas yr ysgol fel y gallant weithio gydag unigolion a grwpiau o blant yn ôl yr angen. Fel y gwyddoch efallai, yn Lloegr, cyflwynodd strategaethau llythrennedd a rhifedd cenedlaethol y llywodraeth nifer fawr o raglenni dal i fyny ('catch-up') ac atgyfnerthu ('booster') i blant nad ydynt yn cyflawni...
View course Cynorthwywyr addysgu: Cymorth ar waith
Level 1: Introductory 4 hrs
Intermediate French: Understanding spoken French
Languages

Intermediate French: Understanding spoken French

...change in lifestyle took place at a defined moment in the past (almost 25 years ago) [Passé composé] Activity 18 Now write sentences about yourself using each of these verb forms to convey the senses described above. Discussion Here is a sample answer using all of the verb forms. Je suis maintenant propriétaire de restaurant depuis 9 mois. Après quelques années à...
View course Intermediate French: Understanding spoken French
Level 1: Introductory 6 hrs
Estimating the cost of equity
Money & Business

Estimating the cost of equity

...changes in market volatility during the period of research. If you are interested in the empirical evidence gathered by academic researchers Elroy Dimson, Paul Marsh and Mike Staunton, find and read ‘Global evidence on the equity risk premium’ (Dimson, et al., 2003). Point to note... By now you will appreciate why many corporate finance textbooks acknowledge the...
View course Estimating the cost of equity
Level 3: Advanced 9 hrs