Mathematical Competition Research Articles

The Eighty-Fourth William Lowell Putnam Mathematical Competition

The Eighty-Fourth William Lowell Putnam Mathematical Competition

Innovative Research on Improving the Mathematical Competition Ability of Normal Students in Local Normal Universities

Innovative Research on Improving the Mathematical Competition Ability of Normal Students in Local Normal Universities

The Eighty-Third William Lowell Putnam Mathematical Competition

The Eighty-Third William Lowell Putnam Mathematical Competition

Construction and Practice of the "Three Levels - Four Dimensions" System for Basic Disciplines Competitions

Mathematical modeling competition, mathematical competition, physical competition, physical experiment competition, mechanics competition and graphics competition are basic discipline competitions in university. These basic discipline competitions of “Mathematics-Physics-Mechanics-Graphics” are an effective carrier to cultivate students' ability of practice, innovation and entrepreneurship, which are also an effective means to stimulate students' potential and creativity. With the increase of the number of participants, the number of awards and the level in recent years, the basic discipline competitions system of “Mathematics-Physics-Mechanics-Graphics” is studied and practiced from the three levels of "School-City-Country" and the four dimensions of "Foundation-Training-Competition-Tracking", which has achieved certain results. The "three levels" enables more students to participate in basic discipline competitions, which is helpful to improve the number and level of awards. The "Four Dimensions" covers the pre competition, competition and post competition. It can not only promote the teaching reform of public basic courses, but also let the basic discipline competition run through the students' four-year college study, which makes the basic discipline competitions more effective in serving the professional training objectives and provides an effective way to cultivate the talents of applied, complex and innovative.

The Eighty-Second William Lowell Putnam Mathematical Competition

The Eighty-Second William Lowell Putnam Mathematical Competition

Mathematical competitions in Africa: their prevalence and relevance to students and teachers.

Mathematical competitions feature in most developed countries as a part of the secondary school experience, but to a lesser extent in developing countries. In this paper we investigate how widespread these competitions are in Africa, both historically as well as currently, focussing both on national Olympiads and on the participation of African countries in competitions beyond their borders, such as the continent-wide Pan African Mathematical Olympiad and the global International Mathematical Olympiad. Since we could not find a consolidated source of information on African competitions, we include many details and links, hoping that this paper will serve as a valuable starting point for future investigators. Next, we present some survey findings on the attitudes towards and experiences of mathematical competitions, both from the perspective of teachers in secondary schools as well as from secondary school students, and whether these experiences have served to improve or degrade their perceptions of mathematics in general. Among other results, we find that teachers view their students’ participation in mathematics competitions as being important, with the biggest barrier to participation being that there are not enough competitions at appropriate levels available, and that students enjoy mathematics competitions and are more likely to pursue a STEM career because of them. Finally, we present some suggestions on how this research may be taken further, and on how the state of mathematical competition culture in Africa may be improved.

Short-Term Load Forecasting Based on a Hybrid Neural Network and Phase Space Reconstruction

Most current short-term load forecasting models have difficulty in simultaneously taking into account the time-series nature of load data, the non-linear characteristics, and the ineffectiveness of extracting potential high-dimensional features from historical series. To solve this problem, we propose a hybrid neural algorithm model (DPCL). In the DPCL, we use convolutional neural networks to obtain the high-dimensional spatial features of the phase space reconstruction of the load time series. Then, we combine the obtained high-dimensional spatial features with the external influence features extracted in the Pearson correlation analysis. Long and short-term memory networks retrieve Spatio-temporal features through the connection layer and obtain prediction results. In addition, there are problems of network gradient degradation and overfitting during the training process, We use an improved differential evolutionary algorithm to optimize the topology and time step of the hybrid neural network. We use the public dataset of a European utility and the loaded dataset of a Chinese mathematical competition as practical arithmetic examples. Experiments have higher prediction accuracy and faster prediction speed compared with other traditional algorithms.

The Eighty-First William Lowell Putnam Mathematical Competition

The Eighty-First William Lowell Putnam Mathematical Competition

Guide for the establishment of the decomposition model of the probability density function based on the hyphal extension rate of fungi

The main purpose of this paper is to provide readers with a guide to mathematical modeling. The idea of establishing a model is roughly as follows: extract the probability factors of the research object, analyze the research object itself, observe the changes of the research object, and observe the effects of environmental changes on the research object. In this article, taking the 2021 American Mathematical Competition in Modeling (MCM) as an example, using the proposed modeling guidelines, a mathematical model was established to describe the decomposition of woody fiber by fungi, and the independent variable was set to hyphal extension rate, temperature conditions, climate conditions, etc. Set the dependent variable to decomposition rate, and fit a series of logarithmic expression and exponential expression according to the data provided by references[1][2]. Establish a community evolution model to realize the dynamic evolution of the interaction between different types of fungi, fungi with a higher competitive ranking will have a higher hyphal extension rate than the original without the interaction. As a result, fungi with a higher competitive ranking is in a dominant position in the colony, and fungi with a lower competitive ranking is in a subordinate or inferior position in the colony. In order to use the relative advantages and disadvantages of various fungi in different environments to predict the exact composition of fungi in the colony, considering the influence of initial climatic conditions on the evolution of the community, and bring about relative changes in the competitive ranking of different types of fungi. The model example in this article reflects the correctness of the modeling guidelines.

数学建模竞赛驱动下大学生创新能力培养模式的探索

数学建模竞赛驱动下大学生创新能力培养模式的探索

Interspecific competition between two self-fertile and one related sexual species of tadpole shrimp Triops (Branchiopoda, Notostraca) with reproductive interference, Allee effect and environmental fluctuation

Invasive alien species of tadpole shrimp Triops, originated from America, were first introduced into rice fields of Japan in the 1910s and have spread around Japan. In the 1950s, a European species of Triops also seems to have entered Japan. Originally, Japanese paddy fields had Asian Triops species as a prehistoric naturalised animal. A new invasive Triops from Western Australia has been reported in the south part of Japan, occasionally forming mixed populations. The expansion of Triops has resulted in negative ecological and potential economic impact. Longhursts revision did not contain any specimens of the richest collection in the world, i.e., Daday Collection in the Hungarian Natural History Museum. And therefore, Naganawa surveyed at least 20 times as many samples as those by Longhurst, and number the named Triops granarius s.l. species group from Africa-India to Siberia-Asia at eight species, organised in the same genus. As for the establishment or extinction patterns, based on Tilmans competition model, we built a simple mathematical competition model between two self-fertile and one related sexual species of Japan, incorporating reproductive interference. To make the mathematical model more natural, we also assumed environmental fluctuation and Allee effect, which reduces the population growth rate of sexual species with low density. Intense reproductive interference drove the competition to sexual exclusion of self-fertile species. However, even under intense reproductive interference, Allee effect allowed self-fertile species to survive when the competition started with the lower densities; contrary to the survival of sexual species when the competition started with the higher densities.

Optimal design of protective clothing based on difference equation

The temperature distribution and thickness design of high temperature protective clothing are studied in this paper. Based on the data provided by China mathematical modeling competition in 2018. We establish the temperature distribution model and skin layer heat conduction and burn model. The interface continuous conditional difference method, differential iterative method, least squares method and the chasing method are used to solve the given temperature distribution on the protective clothing in the environment, and analyze protective clothing meeting the actual needs.

The Seventy-Eighth William Lowell Putnam Mathematical Competition

The 78th William Lowell Putnam Mathematical Competition took place on December 2, 2017. There were 4,638 undergraduates who participated in the competition at 575 institutions across the United Sta...

The likelihood of social choice violations in rank sum scoring: algorithms and evidence from NCAA cross country running

Recent contributions have used combinatorial algorithms to determine the likelihood of particular social choice violations in rank sum scoring. Given the broad importance of rank sum scoring (e.g., in non-parametric statistical testing, sporting competition, and mathematical competition), it is important to establish the level of ambiguity generated by this aggregation rule. Combinatorial likelihoods are naive, however, in that they assume each possible outcome sequence for an event to be equally likely. We develop a computational algorithm to extend upon previous combinatorial results as to the likelihood of a violation of transitivity or independence in rank sum scoring. We use a similar computational scoring approach to analyze the empirically-observed likelihood of each such violation across fourteen NCAA Cross Country Championships. Within the data, rank sum scoring fails to specify a robust winning team (i.e., one that also rank sum wins against each possible subset of opponents) in 4 of 14 cases. Overall, we find that empirical likelihoods of social choice violations are consistently (significantly) overestimated by combinatorial expectations. In the NCAA data, we find correlated ability (quality) levels within team (group) and discuss this as a cause of lower empirical likelihoods. Combinatorial analysis proves reliable in predicting the order of empirical likelihoods across violation type and event setting.

The Downtown Problem: Variations on a Putnam Problem

SummaryThe following problem appeared in the afternoon session of the Fiftieth William Lowell Putnam Mathematical Competition in 1989. A dart, thrown at random, hits a square target. Assuming that any two parts of the target of equal area are equally likely to be hit, find the probability that the point hit is nearer to the center than to any edge. In general, which points are closer to the center of a square (or cube) than to any of the four edges (six faces)? And what do we mean by “closer”? Using a variety of distance functions (metrics), we will investigate these questions and pose several additional open problems for the reader to explore.

Seventy-Five Years of the Putnam Mathematical Competition

We review the 75-year history of the world's foremost college-level mathematics competition. Evidence is provided to support the assertion that exceptional performance in premier secondary-school-level and college-level mathematics competitions correlates well with an exceptional research career in mathematics.

Karjeras kompetenču veidošana ārpusprogrammas aktivitātēs

Mathematics is one of the basic subjects of the study program at school / technical university. Teaching Mathematics is a complex task, because the amount of the acquired study topic is wide, requiring great effort and regular work from pupils / students. Mathematical Olympiad and competitions is to promote interest in mathematics among young people, it is an opportunity to promote its creatives application and cooperation between young people with similar interests. The article gives a brief insight in the beginnings Mathematical Olympiad in Europe, about all mathematical Olympiads and competitions available for pupils and technical university students in Latvia: National Mathematical Olympiad, Meridian Mathematical Competition (MMC), International Mathematical Competition “Kangaroo”, Latvian Open Mathematical Olympiad, International Student Scientific Mathematical Olympiad, International Students and Pupils Mathematical Olympiad.

The Seventy-Sixth William Lowell Putnam Mathematical Competition

The Seventy-Sixth William Lowell Putnam Mathematical Competition

Mathematical Problem Solving with Technology: the Techno-Mathematical Fluency of a Student-with-GeoGebra

This study offers a view on students’ technology-based problem solving activity through the lens of a theoretical model which accounts for the relationship between mathematical and technological knowledge in successful problem solving. This study takes a qualitative approach building on the work of a 13-year-old girl as an exemplary case of the nature of young students’ spontaneous mathematical problem solving with technology. The empirical data comprise digital records of her approaches to two problems from a web-based mathematical competition where she resorted to GeoGebra and an interview where she explains and describes her usual problem solving activity with this tool. Based on a proposed model for describing the processes of mathematical problem solving with technologies (MPST), the main results show that this student’s solving and expressing the solution are held from the early and continuing interplay between mathematical skills and the perception of the affordances of the tool. The analytical model offers a clear picture of the type of actions that lead to the solution of each problem, revealing the student’s ability to deal with mathematics and technology in problem solving. By acknowledging this as a case of a human-with-media in solving mathematical problems, the students’ efficient way of merging technological and mathematical knowledge is portrayed in terms of her techno-mathematical fluency.

An Application of a Theorem of Orthohomological Triangles

In this note we prove a problem given at a Romanian student mathematical competition, and we obtain an interesting result by using a Theorem of Orthohomological Triangles.