Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe Stable Matching Problem and Sudoku
89
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Are you having trouble getting married? These days, there are lots of products on the market for dating, from apps to websites and matchmakers, but we know a simpler way! Thats right -- your path to coupled life isnt through Tinder: its through Sudoku! Read our fabulous paper where we explore the Stable Marriage Problem to help you find happiness and stability in marriage through math. As a bonus, you get two Sudoku puzzles with a new flavor.
rate research
Read More
The Stable Marriage Problem is to find a one-to-one matching for two equally sized sets of agents. Due to its widespread applications in the real world, especially the unique importance to the centralized match maker, a very large number of questions have been extensively studied in this field. This article considers a generalized form of stable marriage problem, where different numbers of men and women need to be matched pairwise and the emergence of single is inevitable. Theoretical analysis and numerical simulations confirm that even small deviations from equal number of two sides can have a large impact on matching solution of Gale-Shapley Algorithm. These results provide insights to many of the real-world applications when matching two sides with unequal number.
This is an English translation of G.N. Chebotarevs classical paper On the Problem of Resolvents, which was originally written in Russian and published in Vol. 114, No. 2 of the Scientific Proceedings of the V.I. Ulyanov-Lenin Kazan State University. In this paper, Chebotarev extends the method in Wimans On the Application of Tschirnhaus Transformations to the Reduction of Algebraic Equations to argue that the general polynomial of degree 21 admits a solution using algebraic functions of at most 15 variables. However, his and Wimans proofs assume that certain intersections in affine space are generic without proof.
Problem-based learning (PBL) is a constructivist learner-centered instructional approach based on the analysis, resolution and discussion of a given problem. It can be applied to any subject, indeed it is especially useful for the teaching of mathematics. When compared to traditional teaching, the PBL approach requires increased responsibility for the teachers (in addition to the presentation of mathematical knowledge, they need to engage students in gathering information and using their knowledge to solve given problems). It thus become crucial that the future teachers become aware of its effectiveness. One of the main obstacle to this awareness lies usually on the fact that future teachers did not find this methodology in their own pre-service training. In this paper we will describe the attempt to introduce PBL in University courses so to have future maths teacher experience mathematics themselves.
We suggest a method of solving the problem of existence of a triangle with prescribed two bisectors and one third element which can be taken as one of the angles, the sides, the heights or the medians, or the third bisector.
The Coupon Collectors Problem is one of the few mathematical problems that make news headlines regularly. The reasons for this are on one hand the immense popularity of soccer albums (called Paninimania) and on the other hand that no solution is known that is able to take into account all effects such as replacement (limited purchasing of missing stickers) or swapping. In previous papers we have proven that the classical assumptions are not fulfilled in practice. Therefore we define new assumptions that match reality. Based on these assumptions we are able to derive formulae for the mean number of stickers needed (and the associated standard deviation) that are able to take into account all effects that occur in practical collecting. Thus collectors can estimate the average cost of completion of an album and its standard deviation just based on elementary calculations. From a practical point of view we consider the Coupon Collectors problem as solved. ----- Das Sammelbilderproblem ist eines der wenigen mathematischen Probleme, die regelma{ss}ig in den Schlagzeilen der Nachrichten vorkommen. Dies liegt einerseits an der gro{ss}en Popularitat von Fu{ss}ball-Sammelbildern (Paninimania genannt) und andererseits daran, dass es bisher keine Losung gibt, die alle relevanten Effekte wie Nachkaufen oder Tauschen berucksichtigt. Wir haben bereits nachgewiesen, dass die klassischen Annahmen nicht der Realitat entsprechen. Deshalb stellen wir neue Annahmen auf, die die Praxis besser abbilden. Darauf aufbauend konnen wir Formeln fur die mittlere Anzahl benotigter Bilder (sowie deren Standardabweichung) ableiten, die alle in der Praxis relevanten Effekte berucksichtigen. Damit konnen Sammler die mittleren Kosten eines Albums sowie deren Standardabweichung nur mit Hilfe von elementaren Rechnungen bestimmen. Fur praktische Zwecke ist das Sammelbilderproblem damit gelost.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
