Part III of the Mathematical Tripos

Part III of the Mathematical Tripos (officially Master of Mathematics/Master of Advanced Study) is a one year Masters-level taught course in mathematics offered at the Faculty of Mathematics, University of Cambridge. It is regarded as one of the hardest and most intensive mathematics courses in the world and is taken by over 200 students each year. Roughly one third of the students take the course as a fourth year of mathematical study at Cambridge (after Parts IA, IB, and II), whilst the remaining two thirds take the course as a one year course.

History

The Smith's Prize Examination was founded by bequest of Robert Smith upon his death in 1768 to encourage the study of more advanced mathematics than that found in the undergraduate course. T. W. Körner notes

In 1883 this was replaced by an exam called Part III and the Smith's Prize awarded for an essay rather than examination. In 1886 this exam was renamed Part II, and later in 1909 Part II, Schedule B. In 1934 it was again renamed Part III. In the 1980s the Certificate of Advanced Study in Mathematics was introduced, and in 2010 CASM was replaced by two new degrees, the Master of Mathematics (M.Math.) and Master of Advanced Study (M.A.St.). All those who have taken the course since 1962 have the right to proceed to these new degree titles. The first retrospective M.Math and M.A.St. degrees were conferred in October 2010. The course is often still referred to as Part III.

Available seat miles

Available seat miles (ASM) or Available seat kilometres (ASK) is a measure of an airline flight's passenger carrying capacity. It is equal to the number of seats available multiplied by the number of miles or kilometres flown. An available seat mile is the fundamental unit of production for a passenger-carrying airline. A unit in this case is one seat, available for sale, flown one mile. For example, an aircraft with 300 seats available for sale flying 1,000 statute miles would generate 300,000 ASMs for that particular flight. That the seats are available for sale is critical. An aircraft that had 300 seats but which was limited (for regulatory or technical reasons) to selling only 250 of them on a particular flight of 1,000 miles would generate 250,000 ASMs on that flight, not 300,000. Similarly, if passenger seats on a particular flight are dedicated to crew rest purposes, such seats would not be included in the calculation of ASMs for that flight.

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