Modern mathematical logic is a multifaceted subject, which concerns itself with the strengths and limitations of formal proofs and algorithms and the relationship between language and mathematical structure. Modern mathematical logic also addresses foundational issues that arise in mathematics. This commentary summarizes the groundbreaking results of Malliaris and Shelah (1), recently published...

We present a system, called RZ, for automatic generation of program specifications from mathematical theories. We translate mathematical theories to specifications by computing their realizability interpretations in the ML language augmented with assertions (as comments). While the system is best suited for descriptions of those data structures that can be easily described in mathematical langu...

We commonly think of mathematics as bringing precision to application domains, but its relationship with computer science is more complex. This experience report on the use of Racket and Haskell to teach a required first university CS course to students with very good mathematical skills focusses on the ways that programming forces one to get the details right, with consequent benefits in the m...

chewable ferrous fumarate tablet is the best iron dosage form for children due to better compliance and lower teeth staining compared to the oral drop. because of the different desirable properties of chewable tablets and the opposing effects of fillers on them, the mathematical experimental design was used as the formulation approach. different series of formulations based on single filler (la...

Recent experimental evidence fromdevelopmental psychology and cognitive neuroscience indicates that humans are equippedwith unlearned elementarymathematical skills. However, formal mathematics has properties that cannot be reduced to these elementary cognitive capacities. The question then arises how human beings cognitively deal with more advanced mathematical ideas. This paper draws on the ex...

Accurate interpretations of large-scale assessment results and sound judgments about students’ mathematical literacy depend on these assessments’ validity and reliability. One important type of evidence towards this validation is the dimensionality analysis, which explores the conformity between the intended factorial structure (related closely to defining a construct –e.g., mathematical litera...

We start with the simple case of studying the relationship between a response variable Y and a predictor variable X I . Since we have only one predictor variable, we shall drop the subscript in X I and use X for simplicity. We discuss covariance and correlation coefficient as measures of the direction and strength of the linear relationship between the two variables. Simple linear regression mo...