Elena Anne Marchisotto

An Invitation to Integration in Finite Terms

Elena Anne Marchisotto, a professor of mathematics at California State University, Northridge, earned her Ph.D. from New York University. Her research interests are foundations of geometry and the work of the geometer Mario Pieri (1860-1913). She is collaborating with Francisco Rodriguez-Consuegra on a book about Pieris philosophy of geometry, and with Phil Davis and Reuben Hersh on a second edition of The Mathematical Experience for use in the college classroom.

In the shadow of giants: The work of mario pieri in the foundations of mathematics

A discussion is given of the research in the foundations of mathematics of Mario Pieri (1860-1913) and how it compares with the works of Christian von Staudt (1798-1867), Giuseppe Peano (1858-1932), David Hubert (1862-1943), and Alfred Tarski (1902-1983). The author demonstrates that the acceptance of Pieri’s results was overshadowed by the research of these four scholars, and argues that Pieri’s work merits a more significant place in the history of mathematics than it currently enjoys

Lines without order

ion sets mathematicians free Of spatial limits and times interludes. Abstraction lets them add infinitudes To reach a still vaster infinity, To postulate points as transcendently Unreal as pixies in solemn moods, To fete a shadowy whole that includes The part which equals it resplendently. Creators of their own strange universe, Mathematicians can transcend the earth, Just as the spirit can transcend the flesh. More liltingly than Irishmen speak Erse, Their image sing of the lyric birth Of paradoxes woven in a mesh.

From Certainty to Fallibility

IF YOU DO mathematics every day, it seems the most natural thing in the world. if you stop to think about what you are doing and what you means, it seems one of the most mysterious. How are we able to tell about things no one has ever seen, and understand them better than the solid objects of daily life? Why is Euclidean geometry still correct, while Aristotelian physics is dead long since? What do we know in mathematics, and how do we know it?

SMALL STEPS TO A STUDENT-CENTERED CLASSROOM

ABSTRACT Research supports the view that students should play an active role in the mathematics classroom. This paper describes several techniques that have been used in a variety of mathematics classes (remedial, pre-calculus, liberal arts mathematics, calculus, and geometry) to shift the mathematics classrooms experience from an instructor-centered one to a student-centered one.

A Case Study in Reuben Hersh’s Philosophy: Bézout’s Theorem

I met Reuben Hersh, in person, in 1989. However, I knew of him well before that. I had a read on The Mathematical Experience ([11] 1981), a book he had coauthored with Philip Davis that won the National Book Award in 1983. Written for a general audience, this book sought to promote an understanding of mathematics from historical, philosophical, and psychological perspectives.

Varieties of Mathematical Experience

THERE IS A LIMITIED amount of knowledge, practice, and aspiration which is currently manifested in the thoughts and activites of contemporary mathematicians. The mathematics that is frequently used or is in the process of emerging is part of the current consciousness. This is the material which—to use a metaphor from computer science—is in the high speed memory or storage cells. What is done, created, practiced, at any given moment of time can be viewed in two distinct ways: as part of the larger cultural and intellectual consciousness and milieu, frozen in time, or as part of a changing flow of consciousness.

Selected Topics in Mathematics

THE HEART of the mathematical experience is, of course, mathematics itself. This is the material in the technical journals, monographs, and, if deemed sufficiently intersting and important, the material that is taught. Whilke it is not the purpose of this book to teach any portion of mathematics in a systematic way, it would be a serious omission if we did not expound a number of individual topics. We have selected six.

The Mathematical Landscape

ANIVE DEFINITION, adequate for the dictiuonary and for an initial understanding, is that mathematics is the science of quality and space. Expanding this definition a bit, one might add that mathematics also deals with the symbolism relating to quantity and to space.

Foundations of Geometry in the School of Peano

The question that motivated this paper — why Pieri made an analogy to Peano’s affinities when he introduced segmental transformations — revealed several plausible answers. But perhaps more importantly, seeking to answer the question provided an opportunity to explore the commonalities and differences about the scholars’ views and treatments of projective geometry and its transformations. In this regard, there is one more avenue to explore. What is not evident from his axiomatizations, but is clear from his lectures37 to students, is the evolution of Pieri’s thoughts about projective geometry. In his (1891) notes for a course in projective geometry at the Military Academy — prior to writing his first axiomatization, but after he had translated Staudt (1847) — Pieri took the same approach to projective geometry as had Peano38. But in his notes for the University of Parma (1909–10), after he had written all his foundational papers in projective geometry, Pieri alerted students to the more “desirable” direction of Staudt as opposed to that pursued by J. Poncelet, Mobius, J. Steiner and Chasles, who studied projective geometry as an extension of elementary geometry.