This study investigated (a) mathematics achievement (Test of Academic Progress) of 589 female and 644 male, predominantly white, 9th-12th grade students enrolled in mathematics courses from four schools, controlling for mathematics background and general ability (Quick Word Test); (b) relationships to mathematics achievement, and to sex-related differences in mathematics achievement, of spatial visualization (Differential Aptitude Test), eight attitudes measured by the Fennema-Sherman Mathematics Attitudes Scales, a measure of Mathematics Activities outside of school, and number of Mathematics Related Courses and Space Related Courses taken. Complex results were obtained. Few sex-related cognitive differences but many attitudinal differences were found. Analyses of variance, covariance, correlation, and principal components analysis techniques were used. The results showed important relationships between socio-cultural factors and sex-related cognitive differences.

Sex-related defferences in mathematics achievement, spatial visualization, and affective factors

A generalized hybrid unsupervised learning algorithm, which is termed as rough-fuzzy possibilistic C-means (RFPCM), is proposed in this paper. It comprises a judicious integration of the principles of rough and fuzzy sets. While the concept of lower and upper approximations of rough sets deals with uncertainty, vagueness, and incompleteness in class definition, the membership function of fuzzy sets enables efficient handling of overlapping partitions. It incorporates both probabilistic and possibilistic memberships simultaneously to avoid the problems of noise sensitivity of fuzzy C-means and the coincident clusters of PCM. The concept of crisp lower bound and fuzzy boundary of a class, which is introduced in the RFPCM, enables efficient selection of cluster prototypes. The algorithm is generalized in the sense that all existing variants of C-means algorithms can be derived from the proposed algorithm as a special case. Several quantitative indices are introduced based on rough sets for the evaluation of performance of the proposed C-means algorithm. The effectiveness of the algorithm, along with a comparison with other algorithms, has been demonstrated both qualitatively and quantitatively on a set of real-life data sets.

https://www.isical.ac.in/~sankar/paper/SMC_B_07_PAJI_SKP.pdf

Rough Set Based Generalized Fuzzy $C$ -Means Algorithm and Quantitative Indices

https://isiarticles.com/bundles/Article/pre/pdf/23029.pdf

Trademark image retrieval using synthetic features for describing global shape and interior structure

http://www2.eng.cam.ac.uk/~sdg/preprint/shellmodel.pdf

Bistable composite slit tubes II: a shell model

This article examines the role of gradable properties in referring expressions from the perspective of natural language generation. First, we propose a simple semantic analysis of vague descriptions (i.e., referring expressions that contain gradable adjectives) that reflects the context-dependent meaning of the adjectives in them. Second, we show how this type of analysis can inform algorithms for the generation of vague descriptions from numerical data. Third, we ask when such descriptions should be used. The article concludes with a discussion of salience and pointing, which are analyzed as if they were gradable adjectives.

/pdf/generating-referring-expressions-that-involve-gradable-3g7xqxgw39.pdf

Generating Referring Expressions that Involve Gradable Properties

Table of Contents Chapter 1: Numbers, Algebra and Geometry 1.1 Introduction 1.2 Number and arithmetic 1.3 Algebra 1.4 Geometry 1.5 Numbers and accuracy 1.6 Engineering applications 1.7 Review exercises Chapter 2: Functions 2.1 Introduction 2.2 Basic definitions 2.3 Linear and quadratic functions 2.4 Polynomial functions 2.5 Rational functions 2.6 Circular functions 2.7 Exponential, logarithmic and hyperbolic functions 2.8 Irrational functions 2.9 Numerical evaluation of functions 2.10 Engineering application: a design problem 2.11 Review exercises Chapter 3: Complex Numbers 3.1 Introduction 3.2 Properties 3.3 Powers of complex numbers 3.4 Loci in the complex plane 3.5 Functions of a complex variable 3.6 Engineering application: alternating currents in electrical networks 3.7 Review exercises Chapter 4: Vector Algebra 4.1 Introduction 4.2 Basic definitions and results 4.3 The vector treatment of the geometry of lines and planes 4.4 Engineering application: spin-dryer suspension 4.5 Engineering application: cable stayed bridge 4.6 Review exercises Chapter 5: Matrix Algebra 5.1 Introduction 5.2 Definitions and properties 5.3 Determinants 5.4 The inverse matrix 5.5 Linear equations 5.6 Rank 5.7 The eigenvalue problem 5.8 Engineering application: spring systems 5.9 Engineering application: steady heat transfer through composite materials 5.10 Review exercises Chapter 6: An Introduction to Discrete Mathematics 6.1 Introduction 6.2 Set theory 6.3 Switching and logic circuits 6.4 Propositional logic and methods of proof 6.5 Engineering application: expert systems 6.6 Engineering application: control 6.7 Review exercises Chapter 7: Sequences, Series and Limits 7.1 Introduction 7.2 Sequences and series 7.3 Finite sequences and series 7.4 Recurrence relations 7.5 Limit of a sequence 7.6 Infinite series 7.7 Power series 7.8 Functions of a real variable 7.9 Continuity of functions of a real variable 7.10 Engineering application: insulator chain 7.11 Engineering application: approximating functions and Pade approximants 7.12 Review exercises Chapter 8: Differentiation and Integration 8.1 Introduction 8.2 Differentiation 8.3 Techniques of differentiation 8.4 Hiderivatives 8.5 Applications of optimization problems 8.6 Numerical differentiation 8.7 Integration 8.8 Techniques of integration 8.9 Applications of integration 8.10 Numerical evaluation of integrals 8.11 Engineering application: design of prismatic channels 8.12 Engineering application: harmonic analysis of periodic functions 8.13 Review exercises Chapter 9: Further Calculus 9.1 Introduction 9.2 Improper integrals 9.3 Some theorems with applications to numerical methods 9.4 Taylor's theorem and related results 9.5 Calculus of vectors 9.6 Functions of several variables 9.7 Taylor's theorem for functions of two variables 9.8 Engineering application: deflection of built-in column 9.9 Engineering application: streamlines in fluid dynamics 9.10 Review exercises Chapter 10: Introduction to Ordinary Differential Equations 10.1 Introduction 10.2 Engineering examples 10.3 The classification of differential equations 10.4 Solving differential equations 10.5 first-order ordinary differential equations 10.6 Numerical solution of first-order ordinary differential equations 10.7 Engineering application: analysis of damper performance 10.8 Linear differential equations 10.9 Linear constant-coefficient differential equations 10.10 Engineering application: second-order linear constant-coefficient differential equations 10.11 Numerical solution of second-and higher-order differential equations 10.12 Qualitative analysis of second-order differential equations 10.13 Review exercises Chapter 11: Introduction to Laplace Transforms 11.1 Introduction 11.2 The Laplace transform 11.3 Solution of differential equations 11.4 Engineering applications: electrical circuits and mechanical vibrations 11.5 Review exercises Chapter 12: Introduction to Fourier Series 12.1 Introduction 12.2 Fourier series expansion 12.3 Functions defined over a finite interval 12.4 Differentiation and integration of Fourier series 12.5 Engineering application: analysis of a slider-crank mechanism 12.6 Review exercises Chapter 13: Data Handling and Probability Theory 13.1 Introduction 13.2 The raw material of statistics 13.3 Probabilities of random events 13.4 Random variables 13.5 Important practical distributions 13.6 Engineering application: quality control 13.7 Engineering application: clustering of rare events 13.8 Review exercises Appendix I Tables Answers to Exercises Index

Modern Engineering Mathematics

Various factors were considered by lecturers at two neighbouring universities wishing to devise appropriate and relevant assessments for first-year service mathematics courses for science and engineering. These factors included the changing mathematical background of entrant students, their attitudes to mathematics and their difficulties in applying mathematics. The response was to introduce extended investigative tasks but in different formats at the two universities. At the new university, a single group project was set but at the ancient university ten individual tasks were set spread through the year. This paper describes the introduction and the evaluation of the effectiveness of the tasks. The aspects which were studied in the evaluation included the effect of tasks on attitudes to mathematics, on students' examination results and on their ability to apply mathematics in context. Factors which influenced students' performance in their mathematics course were identified and errors made in examination...

The Effectiveness of Coursework Assessment in Mathematics Service Courses--Studies at Two Universities.

The reorganization and reform of mathematics courses in Scottish Colleges of Further Education is described. The teaching and learning approaches for the new courses are discussed and an evaluation is made of their implementation in one such course.

Creating a learning environment for 16+ mathematics

The effects of a modern mathematics programme and of a self learning project on girls' attainment is described, and an interpretation offered.

J. W. Searl

Papers

Modern Engineering Mathematics

The Effectiveness of Coursework Assessment in Mathematics Service Courses--Studies at Two Universities.

Creating a learning environment for 16+ mathematics

Factors Affecting Girls' Learning of Mathematics in Sudan

Creating a Learning Environment for 16+ Mathematics