Jae Duck Kim

This study analyzed the correlation between a student's learning background and their academic achievement in college-level calculus. By focusing on A university cases, this study seeks ways to improve the college calculus curriculum according to changes in the curriculum and the College Scholastic Ability Test (SAT) system. In particular, the academic achievement of college calculus was compared and analyzed according to whether calculus was completed in high school, or if calculus was selectively taken in the SAT. Through this study, it was confirmed that the relationship between one's academic achievement and one's learning background in college calculus differs depending on the student's basic academic ability. In other words, there was a difference in the academic achievement of college calculus according to whether students with a certain level of basic academic ability selectively took calculus in the SAT. On the other hand, it was also confirmed that there was a difference in the academic achievement of college calculus for students who lacked basic academic ability depending on whether or not they had completed calculus in high school. Therefore, universities should prepare a curriculum for college calculus according to the educational background of students by conducting a basic academic ability assessment before granting them admission in order to more accurately grasp their particular educational backgrounds.

In order to reform both the curriculum and the contents of university calculus, changes in secondary education courses and the College Scholastic Ability Test are inevitable. In particular, from the 2022 academic year onwards, not only will there be no distinction between liberal arts and the natural sciences in the College Scholastic Ability Test, but the difference in basic academic ability among college freshmen is expected to widen due to the subject selection system, which is a feature of the 2015 revised curriculum. Therefore, the purpose of this study is to find ways to improve the college calculus curriculum in response to changes in the basic learning ability of the students, based on an accurate understanding of the 2015 revised curriculum. To that end, 20 high schools were analyzed for the current status of the 2015 revised curriculum. We also analyzed changes in mathematics subjects and changes in mathematics field subjects of the College Scholastic Ability Test. As a result, we found that whether ‘calculus’ was selected in high school, and whether ‘calculus’ was selected in the math section of the SAT, became an important criterion for improving the curriculum of college calculus. Therefore, this study suggests that the curriculum should not only be redesigned to better account for the prerequisite concepts of college mathematics that have not been learned in secondary education courses, but also to improve the curriculum so that students can learn in a step-by-level manner, and at a level that matches their basic academic ability.

RENEWAL AND RENEWAL REWARD THEORIES FOR T-INDEPENDENT FUZZY RANDOM VARIABLES N(S)Fuzzy sets;(I)Stochastic processes;Fuzzy renewal process;Renewal reward theories;Possibility measure; Recently, Wang et al. [Computers and Mathematics with Ap-plications 57 (2009) 1232-1248.] and Wang and Watada [Information Sci-ences 179 (2009) 4057-4069.] studied the renewal process and renewal reward process with fuzzy random inter-arrival times and rewards under the T-independence associated with any continuous Archimedean t-norm. But, their main results do not cover the classical theory of the random elementary renewal theorem and random renewal reward theorem when fuzzy random variables degenerate to random variables, and some given assumptions relate to the membership function of the fuzzy variable and the Archimedean t-norm of the results are restrictive. This paper improves the results of Wang and Watada and Wang et al. from a mathematical per-spective. We release some assumptions of the results of Wang and Watada and Wang et al. and completely generalize the classical stochastic renewal theorem and renewal rewards theorem.