• Communications of the Korean Mathematical Society
• /
• v.22 no.2
• /
• pp.219-225
• /
• 2007

Since the time of Euler, the dilogarithm and polylogarithm functions have been studied by many mathematicians who used various notations for the dilogarithm function $Li_2(z)$. These functions are related to many other mathematical functions and have a variety of application. The main objective of this paper is to present corrected versions of two equivalent factorization formulas involving the Legendre's Chi-function $\chi_2$ and an evaluation of a class of integrals which is useful to evaluate some integrals associated with the dilogarithm function.

• Journal of the Korean Society for Library and Information Science
• /
• v.24
• /
• pp.53-71
• /
• 1993

In 1926, Alfred Lotka examined the frequency distribution of scientific productivity of chemists and physicists. He observed that the number of persons making n contributions is about $1/ n^2$ of those making one and the proportion of all contributions that make a single contribution is about $60\%$. Investigator studing the applicability of 'Lotka's Law' to Mathematics and to Mechanical engineers have fitted Lotka's Law and concluded that the law applied to these subject fields.

• Communications of the Korean Mathematical Society
• /
• v.28 no.4
• /
• pp.799-807
• /
• 2013

We defined and studied a naturally extended hyperbolic space (see [1] and [2]). In this study, we describe Sforza's formula [7] and Santal$\acute{o}$'s formula [6], which were rediscovered and later discussed by many mathematicians (Milnor [4], Su$\acute{a}$rez-Peir$\acute{o}$ [8], J. Murakami and Ushijima [5], and Mednykh [3]) in the spherical space in an elementary way. Thereafter, using the extended hyperbolic space, we apply the same method to prove their results in the hyperbolic space.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.2
• /
• pp.315-326
• /
• 2021

Korobov type polynomials are introduced and extensively investigated many mathematicians ([1, 8-10, 12-14]). In this work, we define unified Apostol Korobov type polynomials and give some recurrences relations for these polynomials. Further, we consider the q-poly Korobov polynomials and the q-poly-Korobov type Changhee polynomials. We give some explicit relations and identities above mentioned functions.

• Journal of applied mathematics & informatics
• /
• v.29 no.5_6
• /
• pp.1221-1228
• /
• 2011

Recently, several mathematicians have studied some interesting relations between extended q-Euler number and Bernstein polynomials(see [3, 5, 7, 8, 10]). In this paper, we give some interesting identities on the Genocchi polynomials and Bernstein polynomials.

• Research in Mathematical Education
• /
• v.12 no.4
• /
• pp.271-281
• /
• 2008

Quarter a century ago, I founded the Colorado Mathematical Olympiad. The Colorado Mathematical Olympiad is the largest essay-type in-person mathematical competition in the United States, with 600 to 1,000 participants competing annually for prizes. In this article, I explain what it is, how it works, give examples of problems and solutions, and share with the reader careers of some of the Olympiad's winners.

• Research in Mathematical Education
• /
• v.8 no.3
• /
• pp.145-155
• /
• 2004

Mathematics, by its nature, is a creative activity. Creativity can be developed either through considering its intrinsic beauty or by examining the role that it plays in applications to real world problems. Many of the great mathematicians have been vitally interested in applications and gained inspiration in developing new mathematics from the mathematical descriptions of physical phenomena. In this paper we will examine the processes of applying mathematics by looking at how mathematical models are formed and used. Applications from sport, the environment and populations are used as illustrations.

• Journal for History of Mathematics
• /
• v.16 no.3
• /
• pp.1-26
• /
• 2003

Gougu Rule for the right triangles is the Chinese Pythagorean theorem. In the late age of the Chosun Dynasty, mathematicians of Chosun pioneered the study of the Chinese Nine Chapters and other advanced mathematical problems as well as the Easternism in spite of the various difficulties after the Imchinoeran(임진왜란), Chungyuchairan(정유재란) and Byungchahoran(병자호란) The technologies of the addition and addition twice are the methods of the solution of the problems in the right triangles. This paper is intended to introduce some problems using these methods of solution.

• Journal for History of Mathematics
• /
• v.15 no.1
• /
• pp.83-92
• /
• 2002

Gator Szego was one of the most brilliant Mathematicians. Mathematical science owes him several fundamental contributions in such fields as theory of functions of a complex variables, conformal mapping, Fourier series, theory of orthogonal polynomials, and many others. He wrote the famous Polya-Szego Problems and Theorem in Analysis which is the two volume of concentrated mathematical beauty. In this paper, we mention Szego's life, Szego's work, and Szego reproducing kernel.

• Research in Mathematical Education
• /
• v.10 no.1 s.25
• /
• pp.1-11
• /
• 2006

In today's world, it is not enough to be proficient at computation or at memorizing rote procedures to solve routine problems. These skills are important, but even more important are the abilities to recognize and define problems, generate multiple solutions or paths toward solution, reason, justify conclusions, and communicate results. These are not abilities that one is born with and they do not generally develop on their own. For students to become gifted, promising, and creative mathematicians, these talents must be cultivated and nurtured.