12,908 research outputs found
A Unifying Project for a TEX/CAS Course
We describe a CAS and TEX usage course for mathematics majors. As a unifying project, each student selects two primes p and q with pq \u3c 100, explores mathematical pq ideas, and generates associated graphs, figures, tables for a final TEX paper. We summarize several pq explorations: stu- dents render page pq from Schwartzâs picture book about primes, You Can Count on Monsters, via Mathematica and TEXâs picture environment; students generate fractal images of pq; and students discover the primes of the ring Z râpql
Reports on a Course for Prospective High School Mathematics Teachers
The author describes his design for a course entitled Secondary School Mathematics from an Advanced Viewpoint. He adds subjective comments on how his design has worked in practice
Symbolic Manipulators Affect Mathematical Mindsets
Symbolic calculators like Mathematica are becoming more commonplace among
upper level physics students. The presence of such a powerful calculator can
couple strongly to the type of mathematical reasoning students employ. It does
not merely offer a convenient way to perform the computations students would
have otherwise wanted to do by hand. This paper presents examples from the work
of upper level physics majors where Mathematica plays an active role in
focusing and sustaining their thought around calculation. These students still
engage in powerful mathematical reasoning while they calculate but struggle
because of the narrowed breadth of their thinking. Their reasoning is drawn
into local attractors where they look to calculation schemes to resolve
questions instead of, for example, mapping the mathematics to the physical
system at hand. We model the influence of Mathematica as an integral part of
the constant feedback that occurs in how students frame, and hence focus, their
work
A mathematicaâbased CAL matrixâtheory tutor for scientists and engineers
Under the TLTP initiative, the Mathematics Departments at Imperial College and Leeds University are jointly developing a CAL method directed at supplementing the level of mathematics of students entering science and engineering courses from diverse Aâlevel (or equivalent) backgrounds. The aim of the joint project is to maintain â even increase â the number of students enrolling on such firstâyear courses without lowering the coursesâ existing mathematical standards
Symbolic Maximum Likelihood Estimation with Mathematica
Mathematica is a symbolic programming language that empowers the user to undertake complicated algebraic tasks. One such task is the derivation of maximum likelihood estimators, demonstrably an important topic in statistics at both the research and expository level. In this paper, a Mathematica package is provided that contains a function entitled SuperLog. This function utilises pattern-matching code that enhances Mathematica's ability to simplify expressions involving the natural logarithm of a product of algebraic terms. This enhancement to Mathematica's functionality can be of particular benefit for maximum likelihood estimation
Computational Economics: Help for the Underestimated Undergraduate
Our concern in this paper is that the capability of economics undergraduates is substantially underestimated in the design of the present college curriculum and that our students are insufficiently challenged and motivated. Students enter our classrooms with substantial previous knowledge about computers and computation and we are not taking full advantage of this opportunity. We suggest a set of examples from computational economics which are challenging enough to motivate students and simple enough that they can master them within a few hours. By encouraging the students to modify the models in directions of their own interest avenues for creative endeavor are opened which deeply involve the students in their own education.teaching computational economics
Active Learning in Sophomore Mathematics: A Cautionary Tale
Math 245: Multivariate Calculus, Linear Algebra, and Differential Equations with Computer I is the first half of a year-long sophomore sequence that emphasizes the subjects\u27 interconnections and grounding in real-world applications. The sequence is aimed primarily at students from physical and mathematical sciences and engineering. In Fall, 1998, as a result of my affiliation with the Science, Technology, Engineering, and Mathematics Teacher Education Collaborative (STEMTEC), I continued and extended previously-introduced reforms in Math 245, including: motivating mathematical ideas with real-world phenomena; student use of computer technology; and, learning by discovery and experimentation. I also introduced additional pedagogical strategies for more actively involving the students in their own learningâa collaborative exam component and in-class problem-solving exercises. The in-class exercises were well received and usually productive; two were especially effective at revealing normally unarticulated thinking. The collaborative exam component was of questionable benefit and was subsequently abandoned. Overall student performance, as measured by traditional means, was disappointing. Among the plausible reasons for this result is that too much material was covered in too short a time. Experience here suggests that active-learning strategies can be useful, but are unlikely to succeed unless one sets realistic limits to content coverage
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