MATHEMATICS IN CONTEXT: THEMES FOR DISCUSSION I

A. What is Mathematics?
    1.  Notation:
       a) improvements in notation through the ages
            1) numbers
            2) graphs
            3) geometry
            4) algebra
       b) current notations
       c) computers
    2. Argument and logic
          a) origins of logic
          b) logic and computers
                  1) The history of computers
                  2) The next generation of computers
                  3) Artificial intelligence
          c) probability
     3. Calculation
            a) numbers
            b) areas and volumes
            c) speeds and derivatives
            d) interest
            e) estimation
            f) computers
     4. Concepts
             a) groups
             b) symmetry
             c) number
             d) function
     5. Problem solving
           a) Methods
           b) Strategies

B. The extent of new Mathematics
           1. Numbers of mathematicians in universities
           2. Numbers of Mathematics undergraduates
                   a) in UK
                   b) in EEC
                   c) in world
           3.Quantity of research output
           4. Quality of research output
C. The funding of Mathematics
         1. University teaching
         2. FE and HE teaching
         3. Research
              a) Total funding
              b) Comparison with other science subjects

D. The importance of Mathematics for science
              1. Physics
              2. Chemistry
              3. Biology
              4. Engineering

E. The importance of Mathematics for technology
               1. Engineering
               2. Computer science
               3. Physics
F. The importance of Mathematics for commerce and finance
           1. Use of old established techniques
           2. Use of recent Mathematics
                  a) Cryptography
                  b) Optimisation
G. The teaching of Mathematics
            1. Mathematics as a core subject in schools
            2. The relevance (or otherwise) of university Mathematics
            3. New methods of teaching Mathematics in schools
                      a) GCSE
                      b) Investigations
                      c) Where should A-level go?
                      d) Skills v understanding
            4. The teaching of communication skills
            5. The teaching of writing skills
            6. The teaching of problem solving skills
            7. The teaching of problem formulation skills
H. The public image of Mathematics
          1. Measures of the public impression of Mathematics
          2. Mathematics and numerical skills
          3. Improving the public image of Mathematics
          4. Mathematical recreations

K. The employment of mathematicians
          1. Where do mathematicians get employment?
          2. The McLone report
          3. Mathematics and computer science
          4. Mathematics and software

    A. Nature of Mathematics
          1. Notion of proof
              a) Any subject has criteria of validity.
              b) Lakatos
              c) Creativity versus rigour
              d) Influence of computers - the proof of the four
                   colour theorem
              e) Large proofs - the classification of finite simple groups
              f) Stochastic theorems - article in the Scientific American
          2. What is interesting or good Mathematics
          3. Current view of Mathematics as based on logic and set theory
              a) Lawvere view
              b) Current programming debate on functional programming
              c) Constructive Mathematics, many valued logics, fuzzy Mathematics
          4. Undecidability and computability
              a) Limits on mathematical applications
          5. Infinitesimals and non-standard analysis
          6. Category theory and Mathematics as the study of structure
          7. Logic and computers - complexity
    B. Applications of Mathematics
          1. The influence of applications on the development of Mathematics
          2. Catastrophe theory: a case study in theory and applications
          3. Mathematics and biology:
                a) Zeeman's Presidential Address
                b) Thom
                c) Dawkins and the evolution controversies
                d) Knots and DNA
          4. The importance of probability in applications
          5. Topological ideas in Mathematics and its applications:
                   differential equations and physics
          6. Operational research, optimisation, finite Mathematics, Mathematics
               and management
    C. Mathematics and society
          1. Provision of teachers of Mathematics
          2. The funding of Mathematics
                  a)University funding
                        1) UK
                        2) USA
                        3) France