• Journal for History of Mathematics
• /
• v.20 no.4
• /
• pp.61-70
• /
• 2007

Combinatorics, often called the 21 st century mathematics, has turned out a very important subject for the present information era. Modern combinatorics has started from some mathematical works, for example, Pascal's triangle and the binomial coefficients, and Euler's problems on the partitions of integers and Konigsberg's bridge problem, and so on. In this paper, we investigate the origin of combinatorics by looking over some interesting ancient combinatorial problems and some important problems which have started various subfields of combinatorics. We also discuss a little on the role of combinatorics in mathematics and mathematics education.

• Communications of Mathematical Education
• /
• v.32 no.2
• /
• pp.207-223
• /
• 2018

In this study, we studied Bumwoo KIM Chi Young's cogitation on mathematics, and analyzed his typical 3 essays on mathematics by KoNLP. Approximately 80% of Bumwoo's sentences consist of less than 30. His writing became clearer over the years. It is verified from the mean and standard deviation of the number of words in a sentence are decreasing. Bumwoo emphasized the structure in mathematics, and he was a strong advocate of importancy on axiom, topolized and category as the characteristics of modern mathematics. In particular, it can be seen that the relations between 'mathematics', 'axiom', 'structure', 'Euclid', 'axiomatic system' and 'set' were his main topic.

• Journal for History of Mathematics
• /
• v.18 no.3
• /
• pp.79-90
• /
• 2005

Before the First World War, French mathematicians were leading mathematical community in the world but after the war, there was a vacuum compared with Germany and England. So it was necessary to make everything new in France. Young mathematicians from Ecole Normale Superieur came together to form the Bourbaki group. Bourbaki advanced the view that mathematics is a science dealing with structures, and that it attains its results through a systematic application of the modern axiomatic method. French culture movements, especially structuralism and potential literature, including the Bourbakist endeavor, emerged together, each strengthening the public appeal of the others through constant interaction. In this paper, we investigate Bourbaki's role and their achievements in the twentieth century mathematics, and the decline of Bourbaki.

• Journal of Educational Research in Mathematics
• /
• v.10 no.2
• /
• pp.263-277
• /
• 2000

mathematics holds a key position among the subject-matters of school education. Nevertheless, beyond Its Instrumental one, humanity-educational value of mathematics for the general public has been under estimated. For the past fifty years, in the our country there has not been enough systematic and profound examination and discussion concerning the goals of mathematics education in order to establish the philosophy of mathematics education. Thus, in this thesis we argue how mathematics education could contribute to the humanity education. For this, we examine how western educational theorists have emphasized the value of mathematics as humanity education and how their theories have been reflected in the goals of the modern mathematics education. First of all, we discuss Platonism as a philosophical basis of the traditional mathematics teaching mainly with Euclid's "Elements" since the ancient Greece and the relationship between mathematics education and humanity education in the light of this traditional thought. Next, we examine the thoughts of Pestalozzi, Harbert, Froebel who provided the theoretical basis for the public education since 19th century, and discuss the value of mathematics teaching in their humanistic educational thoughts. Also we examine the humanistic value of mathematics education in Dewey's educational philosophy, which criticized the traditional western ethics and epistemology, and established instrumen talism. Further, we analyze how such a philosophy of mathematics teaching is reflected mathematics education of 20th century, and confirm that the formation of Dewey's rational intelligence is one of the central aims of mathematics education of late 20th century. Finally, we discuss the ideals of humanistic mathematics education ; develop ment of the rational intelligence via 'doing knowledge'and change of mind via 'looking knowledge'. In this paper identify the humanistic values of mathematics education through the historical examination of the philosophies of mathematics education, and we could find significance as a fundamental study for one of the most important problems which Korean mathematics educational society confronts, that is establishing the philosophy of mathematics education.

• Korean Journal of Mathematics
• /
• v.22 no.1
• /
• pp.45-56
• /
• 2014

Modern society demands leaders who are trained with competence to not only approach knowledge but also create new knowledge by comprehensively understanding and applying it, and a leader with character and commitment to share one's ideas with others and be able to accept criticisms. In response to these societal changes, universities are increasingly adopting 'small group discussion-based classes with an attempt to develop and strengthen communication skills through reading, writing and speaking. This paper seeks to introduce a case of a math lecture, where discussion-based class was applied to mathematical education, requiring practical problem-solving through an argumentative thought process.

• Research in Mathematical Education
• /
• v.11 no.2
• /
• pp.143-151
• /
• 2007

Nowadays there are practically no mathematical courses in which Computer Algebra Systems (CAS) programs, such as MATHEMATlCA, Maple, and TI-89/92, are not used to some extent. However, generally the usage of these programs is reduced to illustration of computing processes: calculation of integrals, differentiation, solution of various equations, etc. This is obtained by usage of standard command of type: Solve [...] in MATHEMATICA. At the same time the main difficulties arise at teaching nonconventional mathematical courses such as coding theory, discrete mathematics, cryptography, Scientific computing, which are gaining the increasing popularity now. Now it is impossible to imagine a modern engineer not having basic knowledge in discrete mathematics, Cryptography, coding theory. Digital processing of signals (digital sound, digital TV) has been introduced in our lives.

• Research in Mathematical Education
• /
• v.15 no.2
• /
• pp.105-114
• /
• 2011

During the 20th century, the secondary school mathematics teaching in China had been developing from the an old-style private school form with individual instruction to classroom teaching with Chinese characteristics, which experienced three stages of development; the stage for the formation of modern teaching system (1902-1949), the stage for development (1950-1976), and the stage for innovation (1977-2000). The characteristics and journey for the transformation will exert great for reference and effects for the reform of secondary school mathematics teaching nowadays.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.2
• /
• pp.265-270
• /
• 2007

The modern approach for wavelets imposes a Bayesian prior model on the wavelet coefficients to capture the sparseness of the wavelet expansion. The idea is to build flexible probability models for the marginal posterior densities of the wavelet coefficients. In this note, we derive exact expressions for a popular model for the marginal posterior density.

• Communications of Mathematical Education
• /
• v.27 no.2
• /
• pp.165-177
• /
• 2013

Mathematics teaching is often more effective when teachers connect the contents of mathematics with history, culture, and social events. In the history of mathematics, the 'paradigm' theory from Thomas Kuhn's scientific revolution is very effective to explain the revolutionary process of development in mathematics, and his theory has been widely quoted in the history of science and economics. However, it has not been appropriate to use his theory in the other fields. This is due to the fact that the scope of Kuhn's paradigm theory is limited to mathematics and science. In this study, this researcher introduced pan-paradigm as a general concept that encompasses all, since through any relation in the field of mathematics and architecture, Thomas Kuhn's theory of paradigm does not explain the phenomena. That is, at the root of various cultures there exist always a 'collective unconsciousness' and 'demands of the times,' and these two factors by synergism form values and controlling principles common to various parts of the culture, and this synergism leads the cultural activities, the process of which is a phenomenon called pan-paradigm.

• Journal for History of Mathematics
• /
• v.19 no.2
• /
• pp.59-76
• /
• 2006

This research focuses on the relationship between mathematics and visual art from a perspective of chaos theory which emerged under the influence of post-modernism. Culture and history, which transform dynamically with the passing of time, are models of complexity. Especially, when the three periods of Medieval, Renaissance, and 17-18 Centuries are observed, the Renaissance period is phase transition phenomenon era between Medieval and 17-18 Centuries. The transition stage between the late Medieval times and the Renaissance; and the stage between the Renaissance and the Modern times are also phase transitions. These phenomena closely resemble similarity in Fractal theory, which includes the whole in a partial structure. Phase transition must be preceded by fluctuation. In addition to the pioneers' prominent act of creation in the fields of mathematics and visual an serving as drive behind change, other socio-cultural factors also served as motivations, influencing the transformation of the society through interdependency. In particular, this research focuses on the fact that scientific minds of artists in the Renaissance stimulated the birth of Perspective Geometry.