The chapter on statistical-physics simulations has been enlarged, mainly by a dis­ cussion of multispin coding techniques for the Ising model (bit-by-bit parallel oper­ ations). In the chapter about Reduce, some details of the presentation have been cor­ rected or clarified. The new operator MATEIGEN for the computation of eigenvec­ tors of matrices is explained. The first chapter and the appendix remain unchanged. Needless to say, the field of computational science is advancing so quickly, for ex­ ample with the development of parallel, as opposed to vectorized, algorithms, that it will not be too long before a further edition is called for. Cologne, March 1989 The authors Preface to the First Edition Computers play an increasingly important role in many of today's activities, and correspondingly physicists find employment after graduation in computer­ related jobs, often quite remote from their physics education. The present lectures, on the other hand, emphasize how we can use computers for the purposes of fundamental research in physics. Thus we do not deal with programs designed for newspapers, banks, or travel agencies, i.e., word processing and storage of large amounts of data.

1. Computational Methods in Classical Physics.- 1.1 Preface.- 1.2 Motion of a Classical Point-Like Particle.- 1.3 Short Course in FORTRAN Programming Methodology.- 1.4 Methods of Higher Accuracy (and Efficiency).- 1.5 Finding Extremal Points of Motion.- 1.6 Statics and Dynamics of Strings.- 1.7 Dynamics of Strings.- 1.8 Literature.- 2. Monte Carlo Simulations in Statistical Physics.- 2.1 Introduction.- 2.2 Random Numbers.- 2.3 Ising Model.- 2.4 Cellular Automata (Q2R and Creutz).- 2.5 Diffusion and Percolation.- 2.6 Eden Clusters.- 2.7 Kauffman Model.- 2.8 Summary.- 2.9 Appendix: Principles of Vector Computing.- 2.10 References.- Notes Added to the Second Edition.- 3. Reduce for Beginners. Six Lectures on the Application of Computer-Algebra (CA).- Lecture 1.- 1.1 A first interactive Reduce session.- 1.2 What can CA do for you?.- 1.3 The Reduce character set.- 1.4 Integers, rational and real numbers.- 1.5 Variables named by identifiers.- 1.6 A Reduce program, a follow-up of commands.- 1.7 Assign a temporary result to a variable.- 1.8 Homework.- Lecture 2.- 2.1 Built-in operators.- 2.2 Manipulating Reduce expressions amounts to manipulating formulae.- 2.3 The process of evaluation in Reduce.- 2.4 Repeatedly doing something: Loops.- 2.5 Loops and lists.- 2.6 Multidimensional objects: Arrays.- 2.7 Homework.- Lecture 3.- 3.1 The conditional statement.- 3.2 Combining several statements I: The group statement.- 3.3 Combining several statements II: The compound statement.- 3.4 Some elementary mathematieal functions.- 3.5 Differentiation with DF.- 3.6 Integration with INT.- 3.7 Substitution with SUB.- 3.8 Homework.- Lecture 4.- 4.1 Operators that act on lists.- 4.2 Right and left-hand-side of an equation.- 4.3 Solving (non-)linear equations.- 4.4 Retrieving parts of polynomialsand rational functions.- 4.5 To make elecisions with boolean operators.- 4.6 Writing messages.- 4.7 How to define your own operators.- 4.8 LET rules.- 4.9 Homework.- Lecture 5.- 5.1 Extended LET rules.- 5.2 Examples: Factorials and binomial coefficients.- 5.3 Clearing LET rules.- 5.4 Creating non-commutative algebras, symmetric and antisymmetric operators.- 5.5 Procedures for repeated use of commands.- 5.6 A procedure for l'Hospital's rule and a caveat.- 5.7 Homework.- Lecture 6.- 6.1 Linear algebra package: Matrices.- 6.2 Calculus of exterior differential forms in EXCALC.- 6.3 Turning switches on and off.- 6.4 Reordering expressions.- 6.5 On Reduce input and output.- 6.6 Generating Fortran programs.- 6.7 Concluding remarks.- 6.8 Homework.- References.- A.1 Where can you buy Reduce?.- A.2 Some additional exercises (preliminary).- 4. Appendix: A Short Introduction to FORTRAN.