Managing Mathematical Projects - with Success!

<P>&nbsp;</P>1. Introduction and Organisation<BR>1.1 Individual Projects <BR>1.2 Group Projects <BR>1.3 Case Studies <BR>2. Assessment <BR>2.1 Introduction <BR>2.2 Interim Reports <BR>2.3 Verbal Presentations <BR>2.4 Final Report <BR>2.5 Moderating <BR>2.6 Assessment of Case Studies <BR>3. Individual Projects <BR>3.1 Introduction <BR>3.2 Selecting a Project <BR>3.3 Report Writing <BR>3.4 Non-Euclidean Geometry <BR>3.4.1 Scope <BR>3.4.2 Project Details <BR>3.5 Boomerangs <BR>3.5.1 Scope <BR>3.5.2 Project Details <BR>3.6 Hurricane Dynamics <BR>3.6.1 Scope <BR>3.6.2 Project Details <BR>3.7 Hypergeometric Functions <BR>3.7.1 Scope <BR>3.7.2 Project Details <BR>3.8 Summary <BR>3.9 Project Examples <BR>4. Group Projects <BR>4.1 Introduction <BR>4.2 Setting up Group Projects <BR>4.2.1 Peer Assessment <BR>4.2.2 Dividing into Groups <BR>4.3 Estuarial Diffusion <BR>4.4 Graphs and Networks <BR>4.5 Fourier Transforms <BR>4.6 Orbital Motion <BR>4.7 Conclusion <BR>4.8 Further Suggestions <BR>5. Case Studies <BR>5.1 Introduction <BR>5.2 Ocean Surface Dynamics <BR>5.3 Non-linear Oscillations <BR>5.4 Traffic Flow <BR>5.5 Contour Integral Solutions to ODEs <BR>5.6 Optimisation <BR>5.7 Euler and Series <BR>5.8 Summary <BR>5.9 Exercises <BR>A. Project Example 1: Topics in Galois Theory<BR>A.1 Galois' Approach <BR>A.1.1 Preparation <BR>A.1.2 The Galois Resolvent <BR>A.1.3 The Galois Group <BR>A.1.4 Soluble Equations and Soluble Groups<BR>A.2 The Modern Approach <BR>A.2.1 Field Extension <BR>A.2.2 The Galois Group <BR>A.2.3 Applying Galois Theory <BR>A.3 Soluble Groups <BR>A.3.1 Normal Subgroup Series <BR>A.3.2 Normal Subgroups <BR>A.3.3 Simple Groups <BR>A.3.4 p-Groups <BR>A.4 Geometrical Constructions <BR>A.4.1 Constructible Points <BR>A.4.2 Impossibility Proofs <BR>A.4.3 Performing Algebraic Operations by Construction<BR>A.4.4 Regular n-gons <BR>B. Project Example 2: Algebraic Curves <BR>B.1 Basic De.nitions and Properties <BR>B.1.1 Complex Algebraic Curves and Real Algebraic CurvesB.1.2 Projective Spaces <BR>B.1.3 A.ne and Projective Curves <BR>B.1.4 Singular Points<BR>B.2 Intersection of Two Curves and Points of Inflection<BR>B.2.1 Bezout's Theorem <BR>B.2.2 Points of Inflection on a Curve <BR>B.3 Conics and Cubics <BR>B.3.1 Conics <BR>B.3.2 Cubics <BR>B.3.3 Additive Group Structure on a Cubic <BR>B.4 Complex Analysis <BR>B.4.1 Holomorphic Functions and Entire Functions<BR>B.4.2 Closed Curve Theorem and Line Integrals<BR>B.4.3 Liouville's Theorem and Fundamental Theorem of Algebra<BR>B.4.4 Properties of Holomorphic Functions <BR>B.4.5 General Cauchy Closed Curve Theorem<BR>B.4.6 Isolated Singularities and Removable Singularities<BR>B.4.7 Laurent Expansions <BR>B.4.8 Residue Theorem <BR>B.4.9 Conformal Mapping <BR>B.5 Topology and Riemann Surfaces <BR>B.5.1 Topology of Complex Algebraic Curves<BR>B.5.2 Riemann Surfaces <BR>B.5.3 Degeneration of a Cubic <BR>B.5.4 Singularities and Riemann Surfaces <BR>B.6 Further Topics <BR>B.6.1 The Weierstrass Function <BR>B.6.2 Differential Forms on a Riemann Surface<BR>B.6.3 Abel's Theorem <BR>C. Project Example 3: Water Waves on a Sloping Beach<BR>C.1 Abstract <BR>C.2 Introduction <BR>C.3 Surface Waves <BR>C.3.1 The Current <BR>C.3.2 The Boundary Conditions <BR>C.3.3 A Separable Solution of Laplace's Equation<BR>C.4 [No Title] <BR>C.4.1 The Velocity of the Waves <BR>C.4.2 The Group Velocity of the Waves <BR>C.4.3 The Motion of the Particles <BR>C.4.4 Breaking Waves in Shallow Water <BR>C.5 [No Title] <BR>C.5.1 Plane Waves <BR>C.5.2 Wave Rays <BR>C.5.3 The Waves Approaching a Beach <BR>C.5.4 Wave rays in shallow water <BR>C.6 [No Title] <BR>C.6.1 Conclusion and Discussion <BR>Index