Knowledge is so expensive!!!!

GROUPS 24 lectures

Examples of groups       Lagrange’s theorem      Group actions       Quotient groups

Matrix groups         Permutations

Appropriate books

M.A. Armstrong Groups and Symmetry. Springer–Verlag 1988 (£33.00 hardback).

† Alan F Beardon Algebra and Geometry. CUP 2005 (£21.99 paperback, £48 hardback).

R.P. Burn Groups, a Path to Geometry. Cambridge University Press 1987 (£20.95 paperback).

J.A. Green Sets and Groups: a first course in Algebra. Chapman and Hall/CRC 1988 (£38.99 paperback).

W. Lederman Introduction to Group Theory. Longman 1976 (out of print).

VECTORS AND MATRICES 24 lectures

Complex numbers         Vectors              Matrices

Eigenvalues and Eigenvectors

Appropriate books

Alan F Beardon Algebra and Geometry. CUP 2005 (£21.99 paperback, £48 hardback).

D.M. Bloom Linear Algebra and Geometry. Cambridge University Press 1979 (out of print).

D.E. Bourne and P.C. Kendall Vector Analysis and Cartesian Tensors. Nelson Thornes 1992 (£30.75

paperback).

E. Sernesi Linear Algebra: A Geometric Approach. CRC Press 1993 (£38.99 paperback).

D. Smart Linear Algebra and Geometry. Cambridge University Press 1988 (out of print).

NUMBERS AND SETS 24 Lectures

Introduction to numbers systems and logic              Sets, relations and functions

The integers            Elementary number theory             The real numbers

Countability and uncountability

Appropriate books
R.B.J.T. Allenby Numbers and Proofs. Butterworth-Heinemann 1997 (£19.50 paperback).
R.P. Burn Numbers and Functions: steps into analysis. Cambridge University Press 2000 (£21.95
paperback).
H. Davenport The Higher Arithmetic. Cambridge University Press 1999 (£19.95 paperback).
A.G. Hamilton Numbers, sets and axioms: the apparatus of mathematics. Cambridge University Press
1983 (£20.95 paperback).
C. Schumacher Chapter Zero: Fundamental Notions of Abstract Mathematics. Addison-Wesley 2001
(£42.95 hardback).

DIFFERENTIAL EQUATIONS 24 lectures

Basic calculus          First-order linear differential equations

Nonlinear first-order equations           Higher-order linear differential equations

Multivariate functions: applications

Appropriate books
W.E. Boyce and R.C. DiPrima Elementary Differential Equations and Boundary-Value Problems. Wiley,
2004 (£34.95 hardback).
D.N. Burghes and M.S. Borrie Modelling with Differential Equations. Ellis Horwood 1981 (out of print).
W. Cox Ordinary Differential Equations. Butterworth-Heinemann 1996 (£14.99 paperback).
F. Diacu An introduction to Differential Equations: Order and Chaos. Freeman 2000 (£38.99 hardback).
N. Finizio and G. Ladas Ordinary Differential Equations with Modern Applications. Wadsworth 1989
(out of print).
D. Lomen and D. Lovelock Differential Equations: Graphics-Models-Data. Wiley 1999 (£80.95 hardback).
R.E. O’Malley Thinking about Ordinary Differential Equations. Cambridge University Press 1997
(£19.95 paperback).
D.G. Zill and M.R. Cullen Differential Equations with Boundary Value Problems. Brooks/Cole 2001
(£37.00 hardback).
I. Stewart and D. Tall The Foundations of Mathematics. Oxford University Press 1977 (£22.50 paperback).

ANALYSIS I 24 lectures

Limits and convergence             Continuity             Differentiability

Power series           Integration

Appropriate books
H. Anton Calculus. Wiley 2002 (£41.71 paperback with CD-ROM).
T.M. Apostol Calculus. Wiley 1967-69 (£181.00 hardback).
J.C. Burkill A First Course in Mathematical Analysis. Cambridge University Press 1978 (£18.95 paperback).
J.B. Reade Introduction to Mathematical Analysis. Oxford University Press (out of print).
M. Spivak Calculus. Addison–Wesley/Benjamin–Cummings 1967 (out of print).

PROBABILITY 24 lectures

Basic concepts            Axiomatic approach

Discrete random variables           Continuous random variables

Inequalities and limits

Appropriate books
W. Feller An Introduction to Probability Theory and its Applications, Vol. I. Wiley 1968 (£73.95 hardback).
† G. Grimmett and D. Welsh Probability: An Introduction. Oxford University Press 1986 (£23.95 paperback).
† S. Ross A First Course in Probability. Wiley 2002 (£39.99 paperback).
D.R. Stirzaker Elementary Probability. Cambridge University Press 1994/2003 (£19.95 paperback).

VECTOR CALCULUS 24 lectures

Curves in R^3             Integration in R2 and R3              Vector operators

Integration theorems             Laplace’s equation              Cartesian tensors in R3

Appropriate books
H. Anton Calculus. Wiley Student Edition 2000 (£33.95 hardback).
T.M. Apostol Calculus. Wiley Student Edition 1975 (Vol. II £37.95 hardback).
M.L. Boas Mathematical Methods in the Physical Sciences. Wiley 1983 (£32.50 paperback).
† D.E. Bourne and P.C. Kendall Vector Analysis and Cartesian Tensors. 3rd edition, Nelson Thornes
1999 (£29.99 paperback).
E. Kreyszig Advanced Engineering Mathematics. Wiley International Edition 1999 (£30.95 paperback,
£97.50 hardback).
J.E. Marsden and A.J.Tromba Vector Calculus. Freeman 1996 (£35.99 hardback).
P.C. Matthews Vector Calculus. SUMS (Springer Undergraduate Mathematics Series) 1998 (£18.00
paperback).
† K. F. Riley, M.P. Hobson, and S.J. Bence Mathematical Methods for Physics and Engineering. Cambridge
University Press 2002 (£27.95 paperback, £75.00 hardback).
H.M. Schey Div, grad, curl and all that: an informal text on vector calculus. Norton 1996 (£16.99
paperback).
M.R. Spiegel Schaum’s outline of Vector Analysis. McGraw Hill 1974 (£16.99 paperback).

DYNAMICS AND RELATIVITY 24 lectures

Basic concepts                 Newtonian dynamics of a single particle

Newtonian dynamics of systems of particles              Rigid bodies

Special relativity

Appropriate books
† D.Gregory Classical Mechanics. Cambridge University Press 2006 (£26 paperback).
A.P. French and M.G. Ebison Introduction to Classical Mechanics. Kluwer 1986 (£33.25 paperback).
T.W.B Kibble and F.H. Berkshire Introduction to Classical Mechanics. Kluwer 1986 (£33 paperback).
M. A. Lunn A First Course in Mechanics. Oxford University Press 1991 (£17.50 paperback).
G.F.R. Ellis and R.M. Williams Flat and Curved Space-times. Oxford University Press 2000 (£24.95 paperback).
† W. Rindler Introduction to Special Relativity. Oxford University Press 1991 (£19.99 paperback).
E.F. Taylor and J.A. Wheeler Spacetime Physics: introduction to special relativity. Freeman 1992 (£29.99 paperback).

MECHANICS (non-examinable) 10 lectures

Lecture 1:Brief introduction
Lecture 2: Kinematics of a single particle
Lecture 3: Equilibrium of a single particle
Lecture 4: Equilibrium of a rigid body
Lecture 5: Dynamics of particles
Lecture 6: Dynamics of particles
Further examples, including motion of a projectile with air-resistance.
Lecture 7: Energy
Lecture 8: Momentum
Lecture 9: Springs, strings and SHM
Lecture 10: Motion in a circle
Appropriate books
J. Hebborn and J. Littlewood Mechanics 1, Mechanics 2 and Mechanics 3 (Edexel). Heinemann, 2000 (£12.99 each paperback).
Anything similar to the above, for the other A-level examination boards

CONCEPTS IN THEORETICAL PHYSICS (non-examinable) 8 lectures

Hamilton’s Principle                Fluid Dynamics

Chaos and Integrability             Electrodynamics

General Relativity                  Quantum Mechanics

Particle Physics                     Cosmology