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College Mathematics Journal Contents—November 2015

The final issue of volume 46 completes The College Mathematics Journal's series of lead articles from Pólya Award and other MAA writing award winners. In this issue, read about a student who caught Bud Brown teaching the same theorem in two classes and join in her understanding of the connection between the contexts. There are two other pages inspired by the MAA's centennial celebration. Brian Beasley and David Stone consider the history of posing mathematical problems from Johann Bernoulli up through the vibrant Problems and Solutions sections of the MAA journals, considering how these popular sections contribute to research and teaching. The review section this time consists of excerpts from 18 interviews posted on the MAA's centennial website; enjoy finding out more about some of the individuals who help make the MAA so lively and effective. -Brian Hopkins

Vol 46 No 5, pp 324-400


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Saints and Scoundrels and Two Theorems That Are Really the Same

Ezra Brown

The Chinese remainder theorem and the polynomial interpolation theorem are foundational theorems of number theory and numerical analysis, respectively. These two theorems are special cases of a construct in a more general setting and we describe a scenario—namely, two back-to-back classes—in which students can discover this fact. We end by describing that general setting, in which the key idea is an ability to write 1 in a special way.

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Proof Without Words: Centered Triangular Numbers

Roger B. Nelsen

We wordlessly prove a theorem relating centered triangular numbers to the ordinary triangular numbers.

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Journal Problems Sections: Modern Challenges and Teaching Tools

Brian D. Beasley and David R. Stone

As the Mathematical Association of America enters its second century, this article cites some historical mathematical challenges, relating this unique disciplinary practice to the problems sections in today's journals. It presents some results of a survey conducted with the editors of problems sections in various journals and with several mathematicians active throughout their careers as posers and solvers of problems. For example, it includes their views on the general role of problem solving in the mathematical enterprise, their experience with specific applications in both teaching and research, and a sample of their all-time favorite problems.

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Proof Without Words: Bounding the Euler–Mascheroni Constant

Meiyue Shao

We show bounds for the Euler–Mascheroni constant using the trapezoidal and midpoint approximations for integrals.

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A Sufficient Condition for Subgroups with Prime Indices to Be Normal

Cosmin Pohoata and Richard Stong

We extend two group theory exercises to determine a necessary condition for a prime index finite subgroup to be normal.

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Predicting Wins and Losses: A Volleyball Case Study

Elizabeth Knapper and Hope McIlwain

For a sports fan, predicting whether a favored team will win or lose can be an enticing past time. Using the mathematical ranking method known as the Massey method, we use data from volleyball matches to rate and rank teams. We then use our rankings to predict the outcome of future matches. As an example, we apply these methods to the 2013 women's indoor volleyball season of the Atlantic Sun Conference.

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Explicit Form of the Faulhaber Polynomials

José Luis Cereceda

Hersh recently showed that the Faulhaber polynomials, related to sums of consecutive powers, can be expressed as even or odd polynomials in the variable offset by one-half. In this article, we use generating functions to give explicit formulas for all terms in these polynomials.

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Classroom Capsules

A Short Proof of Symmetric Inequalities

Kambiz Razminia

We present a general simple approach for proving symmetric inequalities and apply it to several examples.

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A Note on the Fundamental Theorem of Calculus

Zengxiang Tong

We redeem some “bad” choices for antiderivatives in applications of the fundamental theorem of calculus and suggest a revision for its statement.

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Problems and Solutions

Problems and Solutions: 369-376

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Book Review

Excerpts From MAA Interviews

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Media Highlights

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George Pólya Awards for 2015

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