We walk through an optimization problem step by step, clearly explaining how to identify variables, set up the correct function, apply derivatives, and find maximum or minimum values. Each step is ...

An illustration of a magnifying glass. An illustration of a magnifying glass.

Abstract: Neural networks (NNs) are commonly used to approximate functions based on data samples, as they are a universal function approximator for a large class of ...

Ohio's math problem: Students struggle in math with scores still below pre-COVID lows Ohio, like much of the country, has a math problem that teachers, college and district leaders, parents and others ...

Working memory is like a mental chalkboard we use to store temporary information while executing other tasks. Scientists worked with more than 200 elementary students to test their working memory, ...

Ask the publishers to restore access to 500,000+ books. An icon used to represent a menu that can be toggled by interacting with this icon. A line drawing of the Internet Archive headquarters building ...

Practical word problems are often considered one of the most complex parts of elementary school mathematics. They require students to understand the context of a math problem, identify what the ...

This research was supported in part by the U.S. Air Force under Contracts AF 49(638)-382 and AF 33(657)-8559 as well as by the National Aeronautical and Space Administration under Contract NASr-103.

Author's present address, Department of Mathematics, Harvard University. This paper was written while the author was engaged on a project sponsored by the Office of Naval Research (Contract N6-ori, ...