MU

The Mathematics Understander (MU)

Contact: Dr Edmund Furse
E-mail: efurse@glam.ac.uk
Telephone: 01443 482240

Others involved:

Dr Rod Nicolson (University of Sheffield)
Glenn Morgan (University of Sheffield)

Start date: 1985

Summary of Research

The Mathematics Understander (MU) is a computational model of how undergraduates learn pure mathematics at university from the reading of texts. The texts are expressed in the Formal Expression Language (FEL), and MU is able to learn a number of different branches of mathematics. This research is primarily about learning rather than mathematics per se, and is the state of the art in the complexity of the material it can learn from no previous mathematical knowledge.
How do students learn maths from books?

MU has built-in procedural knowledge about mathematics proof checking and general purpose problem solving heuristics, but no declarative knowledge of mathematical results other than those learned from reading texts. MU has successfully checked proofs in classical analysis and solved simple problems in group theory.
Could a machine learn maths from a book?

MU's learning is based upon the Contextual Memory System (CMS). Morgan has developing an extension to MU to enable new heuristics to be learned known as the Hueristic/Applier Learner (HAL). There are several possible further research projects in this area including advanced problem solving, and the learning of procedural knowledge.
Could a machine pass a maths exam?

Research into MU has been published in IJCAI-93 and IJCAI-95, and a video is available from Morgan Kaufman. MU will shortly be available to Beta test sites by FTP access. Expected release date June 1996.

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Page by Edmund Furse
Last updated 15/April/96

The Mathematics Understander (MU) is a computational model of how undergraduates learn pure mathematics at university from the reading of texts. The texts are expressed in the Formal Expression Language (FEL), and MU is able to learn a number of different branches of mathematics. This research is primarily about learning rather than mathematics per se, and is the state of the art in the complexity of the material it can learn from no previous mathematical knowledge.	How do students learn maths from books?
MU has built-in procedural knowledge about mathematics proof checking and general purpose problem solving heuristics, but no declarative knowledge of mathematical results other than those learned from reading texts. MU has successfully checked proofs in classical analysis and solved simple problems in group theory.	Could a machine learn maths from a book?
MU's learning is based upon the Contextual Memory System (CMS). Morgan has developing an extension to MU to enable new heuristics to be learned known as the Hueristic/Applier Learner (HAL). There are several possible further research projects in this area including advanced problem solving, and the learning of procedural knowledge.	Could a machine pass a maths exam?