10,994 research outputs found
Composition of Integers with Bounded Parts
In this note, we consider ordered partitions of integers such that each entry is no more than a fixed portion of the sum. We give a method for constructing all such compositions as well as both an explicit formula and a generating function describing the number of k-tuples whose entries are bounded in this way and sum to a fixed value g
Book Review: How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics
If you think about it, mathematics is really just one big analogy. For one example, the very concept of the number three is an drawing an analogy between a pile with three rocks, a collection of three books, and a plate with three carrots on it. For another, the idea of a group is drawing an analogy between adding real numbers, multiplying matrices, and many other mathematical structures. So much of what we do as mathematicians involves abstracting concrete things, and what is abstraction other than a big analogy? [excerpt
The Power of X
In his recent book, The Math Myth: And Other STEM Delusions, political scientist Andrew Hacker argues, among other things, that we should not require high school students to take algebra.
Part of his argument, based on data some have questioned, is that algebra courses are a major contributor to students dropping out of high school. He also argues that algebra is nothing more than an enigmatic orbit of abstractions that most people will never use in their jobs. [excerpt
On Pi Day, A Serving of Why We Need Math
Today, our Facebook feeds will be peppered with references to Pi Day, a day of celebration that has long been acknowledged by math fans and that Congress recognized in 2009. Every high schooler learns that pi is the ratio of the circumference of a circle to its diameter and that its decimal expansion begins 3.14 and goes on infinitely without repeating. [excerpt
Klein Four Actions on Graphs and Sets
We consider how a standard theorem in algebraic geometry relating properties of a curve with a (ℤ/2ℤ)2-action to the properties of its quotients generalizes to results about sets and graphs that admit (ℤ/2ℤ)2-actions
Math Quiz on the Radio
What word, often spelled with an umlaut, is used to identify a point on a two-dimensional graph?
Many of you probably already figured out the answer is coordinate. But that\u27s because you are sitting comfortably in your dorm room rather than being on a stage with bright lights in front of a few hundred people being recorded for national broadcast on public radio. [excerpt
Life After Calculus: 20 Years Later
In 1996 Math Horizons interviewed a group of students at the Joint Mathematics Meetings; now, 20 years later, one of those students, Darren Glass, interviews another group of students
PREP Workshop Report: Expository Writing
A significant part of the job of a mathematician involves writing - between research papers, expository writing, grant applications, letters of recommendation, and materials for our teaching, I know that I spend much of my days writing something or other. Yet most of us are never really trained to write mathematics, and even in our jobs we rarely find time to talk about the actual writing of the mathematics which has taken place. With this in mind, I chose to attend a PREP workshop held by the Mathematical Association of America at their headquarters in Washington, DC dedicated to the art of mathematical exposition. [excerpt
Klein-Four Covers of the Projective Line in Characteristic Two
In this paper we examine curves defined over a field of characteristic 2 which are (Z/2Z)2-covers of the projective line. In particular, we prove which 2-ranks occur for such curves of a given genus and where possible we give explicit equations for such curves
Fair-Weather Fans: The Correlation Between Attendance and Winning Percentage
In Rob Neyer\u27s chapter on San Francisco in his Big Book of Baseball Lineups, he speculates that there aren\u27t really good baseball cities, and that attendance more closely correlates with winning percentage than with any other factor. He also suggests that a statistically minded person look at this. I took the challenge and have been playing with a lot of data
- …