Principles and applications of algorithmic problem solving
Algorithmic problem solving provides a radically new way of approaching and solving problems in general by using the advances that have been made in the basic principles of correct-by-construction algorithm design. The aim of this thesis is to provide educational material that shows how these advanc...
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
2011
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| Online Access: | https://eprints.nottingham.ac.uk/11707/ |
| _version_ | 1848791339950407680 |
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| author | Ferreira, Joao Fernando Peixoto |
| author_facet | Ferreira, Joao Fernando Peixoto |
| author_sort | Ferreira, Joao Fernando Peixoto |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Algorithmic problem solving provides a radically new way of approaching and solving problems in general by using the advances that have been made in the basic principles of correct-by-construction algorithm design. The aim of this thesis is to provide educational material that shows how these advances can be used to support the teaching of mathematics and computing.
We rewrite material on elementary number theory and we show how the focus on the algorithmic content of the theory allows the systematisation of existing proofs and, more importantly, the construction of new knowledge in a practical and elegant way. For example, based on Euclid’s algorithm, we derive a new and efficient algorithm to enumerate the positive rational numbers in two different ways, and we develop a new and constructive proof of the two-squares theorem.
Because the teaching of any subject can only be effective if the teacher has access to abundant and sufficiently varied educational material, we also include a catalogue of teaching scenarios. Teaching scenarios are fully worked out solutions to algorithmic problems together with detailed guidelines on the principles captured by the problem, how the problem is tackled, and how it is solved. Most of the scenarios have a recreational flavour and are designed to promote self-discovery by the students.
Based on the material developed, we are convinced that goal-oriented, calculational algorithmic skills can be used to enrich and reinvigorate the teaching of mathematics and computing. |
| first_indexed | 2025-11-14T18:26:57Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-11707 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T18:26:57Z |
| publishDate | 2011 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-117072025-02-28T11:15:07Z https://eprints.nottingham.ac.uk/11707/ Principles and applications of algorithmic problem solving Ferreira, Joao Fernando Peixoto Algorithmic problem solving provides a radically new way of approaching and solving problems in general by using the advances that have been made in the basic principles of correct-by-construction algorithm design. The aim of this thesis is to provide educational material that shows how these advances can be used to support the teaching of mathematics and computing. We rewrite material on elementary number theory and we show how the focus on the algorithmic content of the theory allows the systematisation of existing proofs and, more importantly, the construction of new knowledge in a practical and elegant way. For example, based on Euclid’s algorithm, we derive a new and efficient algorithm to enumerate the positive rational numbers in two different ways, and we develop a new and constructive proof of the two-squares theorem. Because the teaching of any subject can only be effective if the teacher has access to abundant and sufficiently varied educational material, we also include a catalogue of teaching scenarios. Teaching scenarios are fully worked out solutions to algorithmic problems together with detailed guidelines on the principles captured by the problem, how the problem is tackled, and how it is solved. Most of the scenarios have a recreational flavour and are designed to promote self-discovery by the students. Based on the material developed, we are convinced that goal-oriented, calculational algorithmic skills can be used to enrich and reinvigorate the teaching of mathematics and computing. 2011-07-13 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/11707/1/thesis.pdf Ferreira, Joao Fernando Peixoto (2011) Principles and applications of algorithmic problem solving. PhD thesis, University of Nottingham. algorithmic problem solving algorithms calculational method algorithm construction algorithm derivation computer science education mathematics mathematics education elementary number theory teaching scenarios |
| spellingShingle | algorithmic problem solving algorithms calculational method algorithm construction algorithm derivation computer science education mathematics mathematics education elementary number theory teaching scenarios Ferreira, Joao Fernando Peixoto Principles and applications of algorithmic problem solving |
| title | Principles and applications of algorithmic problem solving |
| title_full | Principles and applications of algorithmic problem solving |
| title_fullStr | Principles and applications of algorithmic problem solving |
| title_full_unstemmed | Principles and applications of algorithmic problem solving |
| title_short | Principles and applications of algorithmic problem solving |
| title_sort | principles and applications of algorithmic problem solving |
| topic | algorithmic problem solving algorithms calculational method algorithm construction algorithm derivation computer science education mathematics mathematics education elementary number theory teaching scenarios |
| url | https://eprints.nottingham.ac.uk/11707/ |