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Over the last decade, there has been an increasing, widespread pedagogical interest in developing various types of integrated curricula for science and engineering programs. Over the last three years, a year-long Integrated Math/Physics course has been developed at Union College. This paper will focus on a model for a one-quarter integrated course organized around a traditional set of electricity and magnetism (E&M) physics topics, integrated with appropriate mathematical topics. Traditional, nonintegrated E&M physics students often struggle with challenging vector calculus ideas which may have been forgotten, not yet encountered, or introduced with different notation in different contexts. Likewise, traditional vector calculus mathematics students are often unable to gain intuitive insight, or fail to grasp the physical significance of many of the vector calculus ideas they are learning. Many of these frustrations are due to the fact that at many schools, the physics and calculus teachers teaching separate courses probably have little or no idea what their fellow educators are actually doing in these courses. Substantial differences in context, notation, and philosophy can cause breakdowns in the transfer of knowledge between mathematics and physics courses. We will discuss the methods, philosophy, and implementation of our course, and then go on to present what we feel were the substantial strengths and insights gained from a thoughtful integration of the two subjects. In addition, some problem areas and recommendations for probable student difficulties will be addressed.

In this paper we consider various generalizations of the notion of hugeness. We remind the reader that a cardinal κ is huge if there exist a cardinal λ > κ, an inner model M which is closed under λ-sequences, and an elementary embedding i: V → M with critical point κ such that i(κ) = λ. We shall call λ a target for κ and shall write κ → (λ) to express this fact. Equivalently, κ is huge with target λ if and only if there exists a normal ultrafilter on P=κ(λ) = {X ⊆ λ:X has order type κ}. For the proof and additional facts on hugeness, see [3].We assume that the reader is familiar with the notions of measurability and supercompactness. If κ is γ-supercompact for each γ < λ, we shall say that κ is < λ-supercompact. We note that if κ → (λ), it follows immediately that κ is < λ-supercompact.Throughout the paper, n shall be used to denote a positive integer, the letters α, β, and δ shall denote ordinals, while κ, λ, γ, and η shall be reserved for cardinals. All addition is ordinal addition. V denotes the universe of all sets.All results except for Theorems 6b and 6c and Lemma 6d can be formalized in ZFC.This paper was written while the first named author was at Rochester Institute of Technology, Rochester, New York. We wish to thank the department of mathematics at R.I.T. for secretarial time and facilities.

We define a strengthening of the notions of fair and envy-free cake division, which we call super envy-free cake division. We establish that there exists a super envy-free partition of a "cake" among n people if and only if the n measures used by these people to evaluate sizes of pieces of cake are linearly independent.