Oxford Mathematician Dr Tom Crawford looks through some of the oldest maths textbooks at the University of Oxford with assistance from the @StEdmundHall Librarian James Howarth. Link for Maple Learn worksheet below.

Maple Learn worksheet on Parallelograms here: https://learn.maplesoft.com/doc/6p665268db/trm-parallelograms

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List of books covered in the video:
1. Euclid's "Elements"
2. William Leybourne's "Cursus Mathematicus"
3. Galileo's "System of the World"
4. Kepler's "On The Six-Angled Snowflake"
5. Robert Hooke's "Micrographia"
6. Isaac Newton's "Principia Mathematica"
7. Lewis Carroll's "The Game Of Logic"

Highlights include: Galileo's drawing of the heliocentric solar system with planets orbiting the sun; Robert Hooke's drawings of snowflakes seen under a microscope for the first time; and Lewis Carroll's game of logic meant to be played by children.

Some notes from James on the books.

Fol. C 8 Mathematical collections and translations: the first tome.
London: Printed by William Leybourn, MD CLXI [1661].
Translations of Galileo, Kepler etc. First volume only, almost all copies of vol. 2 destroyed in the Great fire of London.

Fol. O 13 William Leybourn Cursus Mathematicus, London: Printed for Thomas Basset, Benjamin Tooke, Thomas Sawbridge, Awnsham and John Churchill,1690
9 book, 900 page course in mathematics – tons of diagrams including practical ones for calculating field area or height of buildings etc. Full title is fun: Cursus mathematicus. Mathematical sciences, in nine books. : Comprehending arithmetick, vulgar, decimal, instrumental, algebraical. Geometry, plain, solid. Cosmography, cœlestial, terrestrial. Astronomy, theorical, practical. Navigation, plain, spherical.

4° G 18 (1-7) Sammelband of 7 mathematical pamphlets including Kepler on Snowflakes.
Two of the tracts we have the only copy in Oxford, two where it’s only us and the Box. Given by Timothy Goodwyn who transferred to Oxford from Leyden and became Bishop of Kildare.

JJ94, John Newton, The scale of interest: or The use of decimal fractions, and the table of logarithmes, in the most easie and exact resolving all questions in anatocism, or compound interest; with tables of simple interest also at 6. per cent. per annum. Together with their use in the measuring of board, timber, stone, and gauging of cask, &c. very necesary for all carpenters, joyners, masons, glasiers, and all tradesmen whatsoever.

Check your working using the Maple Calculator App – available for free on Google Play and the App Store.

Android: https://play.google.com/store/apps/details?id=com.maplesoft.companion&hl=en
Apple: https://apps.apple.com/us/app/maple-companion/id1466659419

Don’t forget to check out the other videos in the ‘Oxford Calculus’ series – all links below.

Full playlist: https://www.youtube.com/playlist?list=PLMCRxGutHqflZoTY8JCm1GRzCdGXvZ3_S

Finding critical points for functions of several variables: https://youtu.be/Leomuu82-u8

Classifying critical points using the method of the discriminant: https://www.youtube.com/watch?v=5M_ts8Q2LEM

Partial differentiation explained: https://youtu.be/RVwcBGzQcT8

Second order linear differential equations: https://youtu.be/F54yhRB9qDI

Integrating factors explained: https://www.youtube.com/watch?v=ftqKuOfOX3E

Solving simple PDEs: https://youtu.be/uztjxrGY6Jw

Jacobians explained: https://www.youtube.com/watch?v=YqMelRryG8U

Separation of variables integration technique explained: https://youtu.be/zk41c0vs9XQ

Solving homogeneous first order differential equations: https://youtu.be/uqvqjbAcbL8

Taylor’s Theorem explained with examples and derivation: https://www.youtube.com/watch?v=DULzJmUHN5g

Heat Equation derivation: https://youtu.be/rz3cdzZXQms

Separable Solutions to PDEs: https://www.youtube.com/watch?v=hcm-CgHFbwI

How to solve the Heat Equation: https://youtu.be/l6spigOZCOs

Fourier Series Derivation: https://youtu.be/LEonZYoW6sk

Find out more about the Maple Calculator App and Maple Learn on the Maplesoft YouTube channel: https://www.youtube.com/channel/UCq2MmZQ8-kqEVAnmL2GSMsQ

Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: https://www.seh.ox.ac.uk/people/tom-crawford

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