- *BOARD OF THE FACULTY OF ENGLISH LANGUAGE AND LITERATURE
- *BOARD OF THE FACULTY OF LAW
- BOARD OF THE FACULTY OF SOCIAL STUDIES
- BOARD OF THE FACULTY OF MATHEMATICAL
SCIENCES
- Honour School of Mathematics 1998
- Honour School of Mathematical Sciences 1999
- Honour School of Mathematics 1999 and Honour School of Mathematical Sciences 1999
- Honour School of Computation 1999
- Honour School of Mathematics and Computation 1999
- M.Sc. in Geometry, Mathematical Physics, and Analysis
- M.Sc. in Mathematics and the Foundations of Computer Science

- STANDING COMMITTEE FOR THE HONOUR SCHOOL OF ENGINEERING AND COMPUTING SCIENCE
- EXAMINATIONS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

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Model Theory

Proof Theory

Axiomatic Set Theory

Gödel's Incompletess Theorems

Group Theory

Lie Algebras

Representation Theory

Algebraic Topology

Manifolds and Differential Geometry

Functional Analysis

Analytic Topology

C* Algebras

Techniques in Applied Mathematics

Continuum Models

Numerical Linear Algebra

Finite Elements for Partial Differential Equations

Patterns and Networks

Bayesian Statistics

Complexity and Cryptography

Randomised Algorithms

Domain Theory

Lambda Calculus

Further Quantum Theory

General Relativity I

Quantum Field Theory

General Relativity II

Algebraic Number Theory

Generalised Linear Models and Survival Analysis

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**2** Teaching mathematics and its relationship
to issues in learning: being an able mathematician is not, by
itself, sufficient to guarantee being an effective teacher of
mathematics, nor an effective unsupported learner of further
mathematics. Mathematical pedagogy will be introduced through an
analysis of mathematical topics and the needs of learners in
coming to understand these topics. We shall draw on research into
the learning and teaching of mathematics at all levels.

**3** Wider issues in the learning and teaching
of mathematics: this strand will explore a range of issues in
mathematics education: for example social and cultural issues and
the roles of technology.

Outline of topics to be covered: Mathematical Thinking: the nature of mathematics; the process of mathematics; convincing and proving; conjecturing; advanced mathematical thinking.

Mathematical Understanding: mathematics and language; visualisation and imagery; children and number; strategies and errors.

Psychology of Learning Mathematics: relational and instrumental understandings; understanding, learning, and knowing; constructivism.

Research in Mathematics Teaching: teaching styles and interactive strategies; constructions of teaching; assessment.

Sociology of Mathematics Teaching: social constructivism and situated cognition; gender, culture, and social class.

Organisation of Mathematics Teaching and Learning: school curricula; classroom learning.

The examination will consist of a three-hour paper with three essay-type questions each relating to one of the strands of the course. Preparation for two of these questions will be done in advance.

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Elementary Number Theory

Lattice Theory

Mathematical Ecology and Biology

Non-Linear Systems

Communication Theory

Applied Probability

Combinatorial Optimisation

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1. Section II.1. Compilers and Operating Systems.

2. Section II.2. Computer Graphics, Splines, and Computational Geometry.

3. Section II.3. Parallel Scientific Computation and Parallel Algorithms.

4. Section II.4. Object-oriented programming.

5. Section II.5. Mathematical Foundation of Programming Languages (*topics may vary from year to year and may include Lambda Calculus, Domain Theory, Semantics of Programming Languages, Application-oriented program semantics).

6. Section II.6. Advanced Mathematical Logic (*topics may vary from year to year and may include Proof Theory, Model Theory, Axiomatic Set Theory, and Gödel's Incompleteness Theorems).

Options 1, 2, and 3 will have 1/6 practical weight and a two- and-a-half-hour examination.

Option 4 will have 1/3 practical weight and a two-hour examination.

Options 5 and 6 will have no practicals and a three-hour examination.

*Synopses of the topics to be offered will be circulated to undergraduates in the Trinity Term preceding the examination.

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Algebraic Topology

Further Quantum Theory

General Relativity I

General Relativity II

Quantum Field Theory

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Group Theory

Lie Algebras

Elementary Number Theory

Lattice Theory

Analytic Topology

Representation Theory

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General Topology

Gödel's Incompleteness Theorems

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Domain Theory

Parallel Algorithms

Unifying Theories of Computation

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Complexity and Cryptography

Communication Theory

Combinatorial Optimisation

Computational Algebra

Computational Number Theory

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Section II.I: Compilers and Operating Systems (as for Section II, Option 1, of the Honour School of Computation 1999)

Section II.2: Computer Graphics, Splines, and Computational Geometry (as for Section II, Option 2, of the Honour School of Computation 1999)

Section II.3: Parallel Scientific Computation and Parallel Algorithms (as for Section II, Option 3, of the Honour School of Computation 1999)

Section II.4: Object Oriented Programming (as for Section II, Option 4, of the Honour School of Computation 1999)

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St Cross Building, Friday, 31 October, 2.15 p.m.

T.I. MILNES, St Hugh's: `Romantic epistemology: Kant and the
paradoxes of creation in English Romantic theory'.

Examination Schools, Wednesday, 19 November, 2 p.m.

*Examiners*: P. Hamilton, A.D. Nuttall.

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Taylor Institution, Friday, 24 October, 2.15 p.m.

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Institute for Chinese Studies, Wednesday, 22 October, 2.30 p.m.

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Department of Engineering Science, Monday, 27 October, 2.15 p.m.

B. STEPHENSON, St Edmund Hall: `The tectonic and metamorphic
evolution of the main central thrust zone and high Himalaya around
the Kishtwar and Kulu windows, north-west India'.

Department of Earth Sciences, Tuesday, 9 December,
10 a.m.

*Examiners*: J.F. Dewey, P.J. Treloar.

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Department of Experimental Psychology, Friday, 24 October, 2.15 p.m.

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Nuffield, Friday, 21 November, 11 a.m.

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Examination Schools, Wednesday, 19 November, 2.15 p.m.

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Templeton, Friday, 24 October, 2 p.m.

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