Section 47 Infinite numerical series

The Turkish Languages are unusually rich in numerical series, and there are pecularities in their numerical system which are, I believe, unparallelled elsewhere. The main facts are well known, and it might be thought that there was nothing more to be said about them; but several interesting points have never been properly discussed. The purpose of this paper is to call attention to them.

Download Full-text

Software tools for teaching numerical series at the university level

2019 38th International Conference of the Chilean Computer Science Society (SCCC) ◽

10.1109/sccc49216.2019.8966439 ◽

2019 ◽

Author(s):

Veronica Baran ◽

Adriana Frausin ◽

Ma. de los Milagros Gutierrez

Keyword(s):

Software Tools ◽

Numerical Series ◽

University Level ◽

The University

Download Full-text

Applying Computer-based Testing in Palestine: Assessing Fourth and Fifth Graders Inductive Reasoning

Journal of Studies in Education ◽

10.5296/jse.v9i3.14799 ◽

2019 ◽

Vol 9 (3) ◽

pp. 1 ◽

Cited By ~ 1

Author(s):

Mojahed Mousa ◽

Gyöngyvér Molnár

Keyword(s):

School Achievement ◽

Inductive Reasoning ◽

School Curriculum ◽

Educational Systems ◽

Numerical Series ◽

Online Data ◽

Online Test ◽

Reasoning Test ◽

Computer Based ◽

Computer Based Testing

Computer-based assessment offers unique possibilities for collecting data about student’s cognitive development and using this data to improve learning. Its innovative approach to assessment (Thurlow, et al., 2010) encourages educational systems worldwide to involve it. This study introduces and tests the applicability of computer-based testing in the Palestinian schools by measuring fourth (N=123) and fifth (N=125) graders (age ± 9-10) inductive reasoning skills. The online test consists of 60 items measuring figural series (18 items), figural analogy (18 items), numerical series (16 items) and numerical analogy (8 items). Automatic scoring was used and at the end of the test instant feedback was provided for the students. The online data collection was carried out via the eDia platform (Molnár & Csapó, 2019) using the schools’ infrastructure. The time spent to complete the test was approximately 60 minutes. The reliability (Cronbach-alpha) of the inductive reasoning test was .807. The test proved to be difficult for the students M=25.29% SD=10.94%. There were no significant gender differences (M_girls=26.75, M_boys=24.13; t=-1,92, p>.05). Students with higher school achievement proved to be more developed in inductive reasoning skill (M_school_advanced=40.08, M_school_average=25.48; M_school_low=14.50, F=528.16, p<.001; r=.89, p<.001), which indicates that its assessment and development must be included in the Palestine school curriculum. This study provided evidence that (1) computer-based testing can be introduced in the Palestinian school system even at early ages; (2) the development of inductive reasoning is an integral part of the Palestinian school curriculum, thus the stimulation of it is pursued explicitly in Palestinian schools.

Download Full-text

An Iterative Method of General Planetary Theory

Symposium - International Astronomical Union ◽

10.1017/s0074180900070522 ◽

1974 ◽

Vol 62 ◽

pp. 139-155

Author(s):

V. A. Brumberg

Keyword(s):

Power Series ◽

Equations Of Motion ◽

Slight Modification ◽

Planetary Motion ◽

Planetary Theory ◽

Exponential Series ◽

Numerical Series ◽

Satellites Of Jupiter ◽

General Planetary Theory ◽

The Right

This paper deals with an iterative version of the general planetary theory. Just as in Airy's Lunar method the series in powers of planetary masses are replaced here by the iterations to achieve improved approximations for the coefficients of planetary inequalities. The right-hand members of the equations of motion are calculated in closed formulas, and no expansion in powers of small corrections to the planetary coordinates is needed. For the N-planet case this method requires the performance of the analytical operations on a computer with power series of 4N polynomial variables, the coefficients being the exponential series of N-1 angular arguments. To obtain numerical series of planetary motion one has to solve the secular system using Birkhoff's normalization or the Taylor series in powers of time. A slight modification of the method in the resonant case makes it valid for the treatment of the main problem of the Galilean satellites of Jupiter.

Download Full-text