MA232A: Syllabus For Examination at the Annual Examination 2016
For examination purposes, the examination questions on Euclid have been
based on the diagrams and (where approppriate) the statements in John
Casey’s edition of Euclid, originally published in 1885 and available through
Project Gutenberg. Verbatim reproduction of the exact wording of the proofs
in John Casey’s edition is not expected, or necessarily recommended. It is
suggested that candidates present proofs in their own words, guided by the
labelled figures that occur on the examination paper.
Euclid, Book I
The following propositions from Euclid Book I are examinable:
Statements (not proofs) of Book I, Propositions 4, 5 and 6.
Statement of Book I, Proposition 7, together with the first part
of the proof covering the case where the point D lies outside the
triangle ABC.
Statements (not proof) of Book I, Propositions 8, 13, 14 and 15.
Statements and proofs of Book I, Propositions 16, 17, 18, 19, 20,
Statement (not proof) of Book I, Proposition 24.
Statements and proofs of Book I, Propositions 26 to 38 inclusive,
Statement and proof of Book I, Proposition 47.
Euclid, Book III
Construction of Book III, Proposition 1.
Statements and proofs of Book III, Propositions 2, 3, 4, 7, 8, 11,
12, 16.
Construction of Book III, Proposition 17.
Statements and proofs of Book III, Propositions 18, 19, 20, 21
and 22.
Section 5: Vector Algebra and Spherical Trigonometry
All material in Subsections 5.3 – 5.9 inclusive.
Section 6: Notes on Smooth Surfaces
No examinable material.
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Section 7: Curvature of Smooth Surfaces in Three-Dimensional
Space
Examinable material consists of subsections 7.1, 7.3, 7.4. 7.5, 7.6 and 7.7
only.
Section 8: The Hyperbolic Plane
Examinable material consists of Sections 8.1, 8.2 and 8.3 up to, but not including Proposition 8.5. The formulae in Section 8.1 expressing the quantity
4(EG−F 2 )2 k in terms of the partial derivatives of E, F and G are not examinable. Thus, with the exception of these complicated formulae, everything
in Section 8 prior to Proposition 8.5 is examinable.
(The material from Proposition 8.5 onwards is not examinable, because
it was not possible to complete this material in lectures, though a general
programme for completing the section was sketched out at the end of the
final lecture and the notes were subsequently completed.)
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