Computation in Science (Second Edition). Konrad Hinsen

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3.1 From manual computation to rewriting rules

       3.2 From computing machines to automata theory

       3.3 Computability

       3.4 Restricted models of computation

       3.5 Computational complexity

       3.6 Computing with numbers

       3.6.1 Floating-point numbers

       3.6.2 Rational numbers

       3.6.3 Computable numbers

       3.7 Further reading

       References

       4 Automating computation

       4.1 Computer architectures

       4.1.1 Processors and working memory

       4.1.2 Processor instruction sets

       4.1.3 Special-purpose processors

       4.1.4 Parallel computers

       4.2 Programming languages

       4.2.1 Design choices

       4.2.2 Social and psychological aspects

       4.3 Observing program execution

       4.3.1 Debuggers: watching execution unfold

       4.3.2 Profilers: measuring execution time

       4.4 Software engineering

       4.5 Further reading

       References

       5 Taming complexity

       5.1 Chaos and complexity in computation

       5.2 Verification, validation, and testing

       5.2.1 Verification versus validation

       5.2.2 Independent repetition

       5.2.3 Testing

       5.2.4 Redundancy

       5.2.5 Proving the correctness of software

       5.2.6 The pitfalls of numerical computation

       5.3 Abstraction

       5.3.1 Program abstractions

       5.3.2 Data abstractions

       5.3.3 Object-oriented programming

       5.3.4 The cost of abstraction

       5.4 Managing state

       5.4.1 Identifying state in a program

       5.4.2 Stateless computing

       5.4.3 State protection

       5.5 Incidental complexity and technical debt

       5.6 Further reading

       References

       6 Computational reproducibility

       6.1 Reproducibility: a core value of science

       6.2 Repeating, reproducing, replicating

       6.3 The role of computation in the reproducibility crisis

      

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