Abstract—Integral Calculus II is a second-year undergraduate course offered by the Department of Pure and Applied Mathematics at Maseno University. It is one of the 20 foundational courses with a high enrolment of about 800 students drawn from the school of Mathematics, Education, Science, and Business. Because of the large number of enrollments in these foundational courses, and the small number of teaching staff, instructors face challenges in providing immediate personalized feedback that can guide learning. Systems for Teaching and Assessment which use Computer Algebra Kernerl, STACK, a computer-aided assessment plug-in that provides a sophisticated assessment in mathematics-related disciplines, was used to deploy Continuous Assessment Tests (CAT) in the course for 370 students. This paper reports on the findings of the course based on a comparison between student test scores in STACK and in the final course exam.
Abstract—Systems for Teaching and Assessment using Computer Algebra Kernel (STACK) is a computer-aided assessment plug-in for the Moodle learning management system that provides sophisticated tools for student assessment in mathematics and related disciplines, with emphasis on formative assessment. In the last four years, IDEMS international has supported the School of Mathematics at Maseno to integrate STACK and use it in the teaching, learning, and assessment of undergraduate students in nine courses. One of the courses was “Introduction to Complex Analysis'', a third-year course shared by students taking mathematics-related programs from different faculties within Maseno. This paper reports on an evaluation of learner behavior in the Complex Analysis course using data from the STACK weekly quizzes done in that course, the final exam, 20 key informant interviews, and 4 focus group discussions.
We construct a class of quadratic irrationals having continued fractions of period \(n\geq2\) with `small' partial quotients for which specific integer multiples have periodic continued fractions with the length of the period being \(1\), \(2\) or \(4\), and with 'large' partial quotients. We then show that numbers in the period of the new continued fraction are functions of the numbers in the periods of the original continued fraction. We also show how polynomials arising from generalizations of these continued fractions are related to Chebyshev and Fibonacci polynomials and, in some cases, have hyperbolic root distribution.
A well-known theorem of Lagrange states that the simple continued fraction of a real number α is periodic if and only if α is a quadratic irrational. We examine non-periodic and non-simple continued fractions formed by two interlacing geometric series and show that in certain cases they converge to quadratic irrationalities. This phenomenon is connected with certain sequences of polynomials whose properties we examine further.
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