The Fiftieth Anniversary of the Creation of the Probability Theory Department of the Mechanics and Mathematics Faculty of Moscow University, Founded by A. N. Kolmogorov

1990 ◽  
Vol 34 (1) ◽  
pp. 164-165
Author(s):  
Ya. G. Siani ◽  
A. N. Shiryaev
Keyword(s):  
Probability Theory ◽  
Fiftieth Anniversary ◽  
The Creation ◽  
And Mathematics

scholarly journals Evolution of teaching the probability theory based on textbook by V. P. Ermakov

2021 ◽  
Vol 11 (2) ◽  
pp. 300-314
Author(s):  
Tetiana Malovichko
Keyword(s):  
Probability Theory ◽  
19Th Century ◽  
Mathematical Expectation ◽  
Random Variable ◽  
Total Probability ◽  
Creative Development ◽  
Educational Literature ◽  
And Mathematics ◽  
Kyiv Polytechnic Institute ◽  
The 19Th Century

The paper is devoted to the study of what changes the course of the probability theory has undergone from the end of the 19th century to our time based on the analysis of The Theory of Probabilities textbook by Vasyl P. Ermakov published in 1878. In order to show the competence of the author of this textbook, his biography and creative development of V. P. Ermakov, a famous mathematician, Corresponding Member of the St. Petersburg Academy of Sciences, have been briefly reviewed. He worked at the Department of Pure Mathematics at Kyiv University, where he received the title of Honored Professor, headed the Department of Higher Mathematics at the Kyiv Polytechnic Institute, published the Journal of Elementary Mathematics, and he was one of the founders of the Kyiv Physics and Mathematics Society. The paper contains a comparative analysis of The Probability Theory textbook and modern educational literature. V. P. Ermakov's textbook uses only the classical definition of probability. It does not contain such concepts as a random variable, distribution function, however, it uses mathematical expectation. V. P. Ermakov insists on excluding the concept of moral expectation accepted in the science of that time from the probability theory. The textbook consists of a preface, five chapters, a synopsis containing the statements of the main results, and a collection of tasks with solutions and instructions. The first chapter deals with combinatorics, the presentation of which does not differ much from its modern one. The second chapter introduces the concepts of event and probability. Although operations on events have been not considered at all; the probabilities of intersecting and combining events have been discussed. However, the above rule for calculating the probability of combining events is generally incorrect for compatible events. The third chapter is devoted to events during repeated tests, mathematical expectation and contains Bernoulli's theorem, from which the law of large numbers follows. The next chapter discusses conditional probabilities, the simplest version of the conditional mathematical expectation, the total probability formula and the Bayesian formula (in modern terminology). The last chapter is devoted to the Jordan method and its applications. This method is not found in modern educational literature. From the above, we can conclude that the probability theory has made significant progress since the end of the 19th century. Basic concepts are formulated more rigorously; research methods have developed significantly; new sections have appeared.

IDEAS

1992 ◽  
Vol 40 (4) ◽  
pp. 215-225
Author(s):  
Barbara E. Moses ◽  
Linda Proudfit ◽  
William R. Speer
Keyword(s):  
Problem Solving ◽  
Evaluation Standards ◽  
Classroom Activities ◽  
Grade Levels ◽  
Parents And Children ◽  
The Creation ◽  
And Mathematics

The “IDEAS” section for this month focuses on connections between mathematics and music. including both the interpretation of music and the creation of music and musical tones. Music is very special. As a child listens to music, he or she may feel happy and want to smile or may feel a beat and want to clap or dance or may feel contemplative and want to think or write down some thoughts. The activities offer a variety of classroom happenings that tie together a student's perception of music and some important strands of mathematics. The visions of the Curriculum and Evaluation Standards (NCTM 1989), including mathematics as communication, mathematics as reasoning, and mathematics as problem solving, are an integral part of these activities. Other emphasized standards are those on estimation, measurement. statistics, fractions, and patterns. The reproducible sheets for the “IDEAS” section are designed to be used by multiple grade levels. Included are four classroom activities and an activity sheet that involves parents and children in listening together to the radio.

scholarly journals Every Outcome Counts

2020 ◽  
Vol 3 ◽  
pp. 24-31
Author(s):  
Jeden O. Tolentino
Keyword(s):  
Probability Theory ◽  
Graph Theory ◽  
Group Theory ◽  
Visual Art ◽  
Home Country ◽  
The Philippines ◽  
The Creation ◽  
Young Immigrants

I approached the creation of these four graphics as a convergence of the skills and knowledge that I brought from my home country, the Philippines, and those that I have acquired in Canada. Combining abstract mathematics and visual art, I used concepts from graph theory, group theory, and probability theory to show a pictorial flow comparing the muddled situation in which young immigrants to Canada find themselves to the “optimal” albeit assimilated situation of those who have had time to settle (in multiple senses) into their new lives.

Evaluating a Teaching Intervention for Teaching STEM and Programming Concepts Through the Creation of a Weather-Forecast App for Smart Mobile Devices

2020 ◽  
pp. 31-53 ◽  
Author(s):  
Stamatios Papadakis
Keyword(s):  
High School Students ◽  
Mobile Devices ◽  
Weather Forecast ◽  
Thinking Skills ◽  
Scientific Discipline ◽  
Second Grade ◽  
The Creation ◽  
And Mathematics ◽  
Smart Mobile ◽  
Smart Mobile Devices

The last two decades have necessitated the need for an interdisciplinary approach to mathematics, science, and technology (STEM) as contemporary problems are too multidimensional to be tackled by a single scientific discipline as was the case with classical school curricula. Teaching programming has the potential to contribute to this vision as it is effective in helping students develop critical thinking skills. This work presents an educational approach that combines STEM learning with the basic concepts of programming through the creation of a weather-forecast app for smart mobile devices with the programming environment MIT App Inventor. This approach was implemented with second grade high school students as a school project. The evaluation results are considered encouraging as the students engaged in authentic learning activities and research related to the STEM field while, at the same time, enhanced their interest and knowledge in pursuing careers involving programming, science, technology, engineering, and mathematics.

The Remarkable Story

2019 ◽  
pp. 1-14 ◽  
Author(s):  
Steven J. Osterlind
Keyword(s):  
Probability Theory ◽  
World War I ◽  
Historical Context ◽  
Conditional Probabilities ◽  
World War ◽  
Bell Curve ◽  
The Everyday ◽  
History Of ◽  
Napoleonic Era ◽  
And Mathematics

This chapter introduces the extraordinary story of “quantification,” the perception of seeing things—both the everyday and the extraordinary—through the lens of quantifiable events (i.e., via odds, probability, and likelihood). This concept arose when people learned how to measure uncertainty, through the development of probability theory. The chapter presents many examples of using probability for measuring uncertainty and sets the historical context for the following chapters by showing how the idea of quantification developed during a relatively brief period in history, roughly from the end of Napoleonic era through the start of World War I. This era saw a torrent of mathematical developments, specifically, the invention of probability theory, the bell curve, regressions, Bayesian conditional probabilities, and psychometrics. The chapter also explains that this book is not a history of probability theory but a story of how history and mathematics came together to fashion the current worldview.

2. Characteristica universalis , logical calculus, and mathematics

2016 ◽  
pp. 13-31
Author(s):  
Maria Rosa Antognazza
Keyword(s):  
Natural Language ◽  
Scientific Discovery ◽  
Intellectual Life ◽  
Universal System ◽  
Logical Calculus ◽  
The Core ◽  
Scientific Advancement ◽  
The Creation ◽  
And Mathematics ◽  
Characteristica Universalis

How did Leibniz propose to pursue his all-embracing programme of scientific advancement? What were the core projects that held his wide-ranging intellectual life together? ‘Characteristica universalis, logical calculus, and mathematics’ explains that Leibniz nurtured the dream of developing an alphabet of human thoughts leading to the creation of a characteristica universalis: a universal system of signs designed to eliminate the ambiguity of natural language. This project progressed into the development of a logical calculus. Over and above the provision of a means of universal and unambiguous communication, however, the characteristica universalis was conceived by Leibniz as a powerful tool of scientific discovery and judgement on the model of algebra.

scholarly journals Doob: A Half-Century on

2005 ◽  
Vol 42 (01) ◽  
pp. 257-266
Author(s):  
N. H. Bingham
Keyword(s):  
Stochastic Process ◽  
Probability Theory ◽  
Seventeenth Century ◽  
Stochastic Processes ◽  
Fiftieth Anniversary ◽  
Process Theory ◽  
Dynamic Aspect ◽  
Half Century ◽  
Classic Work

Probability theory, and its dynamic aspect stochastic process theory, is both a venerable subject, in that its roots go back to the mid-seventeenth century, and a young one, in that its modern formulation happened comparatively recently - well within living memory. The year 2003 marked the seventieth anniversary of Kolmogorov's Grundbegriffe der Wahrscheinlichkeitsrechnung, usually regarded as having inaugurated modern (measure-theoretic) probability theory. It also marked the fiftieth anniversary of Doob's Stochastic Processes. The profound and continuing influence of this classic work prompts the present piece.

scholarly journals INNOVATIVE APPROACH TO SOLVING COMBINATIC ELEMENTS AND SOME PROBLEMS OF NEWTON BINOMY IN SCHOOL MATHEMATICS COURSE

2021 ◽  
pp. 45-54
Keyword(s):  
Probability Theory ◽  
School Mathematics ◽  
Mathematical Statistics ◽  
Innovative Approach ◽  
The Future ◽  
The Creation ◽  
Mathematics Course

This article provides information on the elements of combinatorics in the school mathematics course and solutions to some problems related to the Newtonian binomial. This article is also aimed at solving problems related to the indepth study of the elements of combinatorics in the school course, the creation of a sufficient basis for the study of probability theory and mathematical statistics in the future.

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