Yu-Hong Dai1, Roger Fletcher2 1 State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, PO Box 2719, Beijing, 100080, PR China; e-mail: [email protected] 2 Department of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland, UK; e-mail...

Proof theory began in the 1920’s as a part of Hilbert’s program, which aimed to secure the foundations of mathematics by modeling infinitary mathematics with formal axiomatic systems and proving those systems consistent using restricted, finitary means. The program thus viewed mathematics as a system of reasoning with precise linguistic norms, governed by rules that can be described and studied...

Software engineering is a young engineering discipline that is different in many aspects from the classical engineering fields. For me the most distinguishing point is the kind of mathematics that serves the respective fields well. By giving examples I will try to show that classical, calculus based mathematics is of no help for defining central notions in software engineering, like ”abstract d...

We introduce the notion of domain descriptions (D) in order to ensure that software (S) is right and is the right software, that is, that it is correct with respect to written requirements (R) and that it meets customer expectations (D). That is, before software can be designed (S) we must make sure we understand the requirements (R), and before we can express the requirements we must make sure...

8-28-8/1, Tamil Street, Chinna Waltair, Visakhapatnam-530 017, India E-mail: [email protected] Department of Engineering Mathematics, GIT, Gitam University Visakhapatnam-530 045, India E-mail: [email protected] Department of Mathematics, Mrs. A.V.N. College Visakhapatnam -530 001, India E-mail: [email protected] Department of Mathematics, Raghu Engineering College Visakhapatnam-531 1...