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We investigate the journal impact factor, focusing on the applied mathematics category. We discuss impact factor manipulation and demonstrate that the impact factor gives an inaccurate view of journal quality, which is poorly correlated with expert opinion.
We have written a Java applet to illustrate the meaning of curved geometry. The applet provides a mapping interface similar to MapQuest or Google Maps; features include the ability to navigate through a space and place permanent point objects and/or shapes at arbitrary positions. The underlying two-dimensional space has a constant, positive curvature, which causes the apparent paths and shapes of the objects in the map to appear distorted in ways that change as you view them from different relative angles and distances.
In this paper we study two operations, Pasting and Reversing, defined from a natural way to be applied over some rings such as the ring of polynomials and the ring of linear differential operators, which is a differential ring. We obtain some properties of these operations over these rings, in particular over the set of natural numbers, in where we rewrite some properties incoming from recreational mathematics.
In this short note we have produced for the first time in the history different kinds of universal bimagic squares. This we have made using only the digits 0,1 and 2. The universal bimagic squares of order 8x8 and 16x16 are with the digits 0 and 1. The universal bimagic square of order 9x9 is with the digits 0, 1 and 2. It is interesting to note that the day 0ctober 10 have only the digits 0 and 1 if we consider it as 10.10.10. If we consider the date as 10.10.2010, then this has the digits 0, 1 and 2.
We summarize the major results in number theory of the last decade.
In this short note we have produced different kinds of bimagic squares using only the digits 0, 1, 2, 5 and 8. The universal bimagic squares presented are of order 8x8, 9x9, 16x16 and 25x25. In order to bring universal bimagic square of order 8x8, we used only the digits 2 and 5. For the order 9x9, we used only the digits 2, 5 and 8. For the universal bimagic square of order 16x16 we used the digits 1, 2, 5 and 8 and finally for the order 25x25, we used five digits 0, 1, 2, 5 and 8. In order to produce these universal bimagic squares we have used the digits in the digital form.
The Calculus Concept Readiness (CCR) instrument is based on the broad body of mathematics education research that has revealed major understandings, representational abilities, and reasoning abilities students need to construct in precalculus level courses to be successful in calculus. The CCR is a 25-item multiple-choice instrument, and the CCR taxonomy articulates what the CCR assesses. The methodology used to develop and validate the CCR is described and illustrated. Results from administering the CCR as a readiness examination in calculus are provided along with data to guide others in using the CCR as a readiness examination for beginning calculus.
This note deals with two topics of linear algebra. We give a simple and short proof of the multiplicative property of the determinant and provide a constructive formula for rotations. The derivation of the rotation matrix relies on simple matrix calculations and thus can be presented in an elementary linear algebra course. We also classify all invariant subspaces of equiangular rotations in 4D.
In this short note we have given an equation based on the date 11.09.2001 and presented some magic squares. The magic squares presented are of order 3x3, 4x4, 5x5, 9x9, 16x16 and 25x25. While the magic square of higher order 9x9, 16x16 and 25x25 are bimagic. These magic squares are based on the digits, 1-6-9, 0-1-2, 0-1-2-9 and 0-1-2-6-9. The interesting fact in all these magic squares is that if we gave them a rotation of 180 degrees, they remain again the magic squares. In order to have this rotation, we have used the numbers in digital forms. Moreover, the day of submission of this work (20.10.2010) has only the digits 0, 1 and 2. Using only these three digits, we have presented magic squares of order 3x3 and 9x9.
We propose a simple real-valued generalization of the well known integer-valued Erdos number as a topological, non-metric measure of the `closeness' felt between two nodes in an undirected, weighted graph. These real-valued Erdos numbers are asymmetric and are able to distinguish between network topologies that standard distance metrics view as identical. We use this measure to study some simple analytically tractable networks, and show the utility of our measure to devise a ratings scheme based on the generalized Erdos number that we deploy on the data from the NetFlix prize, and find a significant improvement in our ratings prediction over a baseline.
This paper was published in French under the title \textit{Sur une méthode d'approximation des racines carrées dans l'Inde antérieurement à la conquête d'Alexandre}, in the Bulletin de la S. M. F., volume 7 (1879), p. 98-102. It argues that the process of approximating the irrational square root of an integer, now commonly known as Newton's method, was known in India since very ancient times.
A problem that enjoys an enduring popularity asks: "what is the least number of pound weights that can be used on a scale pan to weigh any integral number of pounds from 1 to 40 inclusive, if the weights can be placed in either of the scale pans ?" W.W. Rouse Ball attributes the first recording of this problem to Bachet in the early 17th century, calling it "Bachet's Weights Problem". However, Bachet's problem stretches all the way back to Fibonacci in 1202, making it a viable candidate for the first problem of integer partitions. Remarkably, given the age of Bachet's problem, an elegant and succinct solution to this problem when we replace 40 with any integer has only come to light in the last 15 or so years. We hope to expound on this generalization here armed only with our sharp wits and a willingness to induct. In doing so we will discover some of the joys of partitions of integers and enumerative combinatorics. This expository article, while of interest to researchers in combinatorics, integer partitions and the history of mathematics, is written with an impressionable undergraduate audience in mind.
A frequently cited theorem says that for n > 0 and prime p, the sum of the first p n-th powers is congruent to -1 modulo p if p-1 divides n, and to 0 otherwise. We survey the main ingredients in several known proofs. Then we give an elementary proof, using an identity for power sums proven by Pascal in 1654. An application is a simple proof of a congruence for certain sums of binomial coefficients, due to Hermite and Bachmann.
In this short note we shall give connection between the most perfect "Khajuraho" magic square of order 4x4 discovered in 10th century and the "Lo-Shu" magic square of order 3x3 with the day October 1, 2010, i.e., 01.10.2010. The day has only three digits 0, 1 and 2. Here we have given an equivalent version of Khajuraho magic square using only three digits 0, 1 and 2. If we write the above date in two parts, 0110 2010, interestingly, the sum of new magic square is the first part, i.e., 0110, and the numbers appearing in the magic square are from the second part. An equivalent version of "Lo-Shu" magic square of order 3x3 is also given
In this exposition the space of at most 3-element subsets of the circle, first identified by Borsuk and Bott, is used as a motivation to introduce the readers to a variety of methods in (algebraic) topology.
In the present popular-science paper, we find out which rectangles can be dissected into squares. The proof is based on a physical interpretation in terms of electrical networks. Only a secondary school background is assumed in the paper.
The Monty Hall problem is the TV game scenario where you, the contestant, are presented with three doors, with a car hidden behind one and goats hidden behind the other two. After you select a door, the host (Monty Hall) opens a second door to reveal a goat. You are then invited to stay with your original choice of door, or to switch to the remaining unopened door, and claim whatever you find behind it. Assuming your objective is to win the car, is your best strategy to stay or switch, or does it not matter? Jason Rosenhouse has provided the definitive analysis of this game, along with several intriguing variations, and discusses some of its psychological and philosophical implications. This extended review examines several themes from the book in some detail from a Bayesian perspective, and points out one apparently inadvertent error.
The 19th century impressionist movement, as a reaction to "art pompier", is proposed as a comparison with modern evolutions in mathematics.