Our curriculum has become math-phobic!

Tucker, Allen B.; Kelemen, Charles; Bruce, Kim B.

doi:10.1145/366413.364593

Cited by 16 publications

(15 citation statements)

References 3 publications

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“…Yet, this is still a long-term option, since curriculum design lags behind insights in formal methods [80]. Meanwhile one should work at lowering the threshold formal methods still present in practice, but without sacrificing the safety and effectiveness that only mathematics can provide for users of automated tools.…”

Section: Improving Accessibility For Practiciansmentioning

confidence: 99%

Pointfree expression and calculation: from quantification to temporal logic

Boute

2010

Form Methods Syst Des

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Pointfree formulation means suppressing domain variables to focus on higherlevel objects (functions, relations). Advantages are algebraic-style calculation and abstraction as formal logics pursue by axiomatization. Various specific uses are considered, starting with quantification in the wider sense (∀, ∃, , etc.). Pointfree style is achieved by suitable functionals that prove superior to pointwise conventions such as the Eindhoven notation. Pointwise calculations from the literature are reworked in pointfree form. The second use considered is in describing systems, with generic functionals capturing signal flow patterns. An illustration is the mathematics behind a neat magician's trick, whose implementation allows comparing the pointfree style in Funmath, LabVIEW, TLA + , Haskell and Maple. The third use is making temporal logic calculational, with a simple generic Functional Temporal Calculus (FTC) for unification. Specific temporal logics are then captured via endosemantic functions. The example is TLA + . Calculation is illustrated by deriving various theorems, most related to liveness issues, and discovering results by calculation rather than proving them afterwards. To conclude, various ramifications, style and abstraction issues are discussed, in relation to engineering mathematics in general and to categorical formulations.

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Section: Improving Accessibility For Practiciansmentioning

confidence: 99%

Pointfree expression and calculation: from quantification to temporal logic

Boute

2010

Form Methods Syst Des

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“…Given the preceding remarks, wide use of formal methods in industry is best served by a constant supply of well-prepared students [12]. Yet, this is still a long-term option, since curriculum design lags behind insights in formal methods [35]. Meanwhile we should attempt lowering the threshold formal methods still represent in practice, but without sacrificing the safety and effectiveness that only mathematics can provide for tool users.…”

Section: Diversity Versus Disparitymentioning

confidence: 99%

Making Temporal Logic Calculational: A Tool for Unification and Discovery

Boute

2009

FM 2009: Formal Methods

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Abstract. In temporal logic, calculational proofs beyond simple cases are often seen as challenging. The situation is reversed by making temporal logic calculational, yielding shorter and clearer proofs than traditional ones, and serving as a (mental) tool for unification and discovery. A sideeffect of unifying theories is easier access by practicians. The starting point is a simple generic (software tool independent) Functional Temporal Calculus (FTC). Specific temporal logics are then captured via endosemantic functions. This concept reflects tacit conventions throughout mathematics and, once identified, is general and useful. FTC also yields a reasoning style that helps discovering theorems by calculation rather than just proving given facts. This is illustrated by deriving various theorems, most related to liveness issues in TLA + , and finding strengthenings of known results. Educational issues are addressed in passing.

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“…in computer science to be more of the same, plus programming. 3 Students like these are often frustrated by the major in their junior and senior years. The second year that the course was taught, the New Media major was offered on campus for the first time.…”

Section: Retention Of Studentsmentioning

confidence: 99%

“…• The details of programming often distracted students from more conceptual information presented in CS-I and II (see also [3]). Success with this strategy in early courses caused some students in upper-level courses to spend their time on programming assignments to the exclusion of studying the theoretical material presented in the course.…”

Section: Introductionmentioning

confidence: 99%

Teaching entering students to think like computer scientists

Turner¹,

Turner²

2005

Proceedings of the 36th SIGCSE Technical Symposium on Computer Science Education

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This paper describes a new course developed at the University of Maine to help students better understand the discipline of computer science and to aid us in recruiting and retaining majors. The course provides an overview of computer science, but also, through focusing on particular topics at an advanced level, begins to teach students how computer scientists think about problems. The course has been taught in

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Our curriculum has become math-phobic!

Cited by 16 publications

References 3 publications

Pointfree expression and calculation: from quantification to temporal logic

Pointfree expression and calculation: from quantification to temporal logic

Making Temporal Logic Calculational: A Tool for Unification and Discovery

Teaching entering students to think like computer scientists

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