## Section 3.3 Organizational Meeting

Table 3.3.1 lists the five invited speakers at the very first meeting of the Philadelphia Section, held November \(27\text{,}\) \(1926\text{,}\) at Lehigh University. There are several ways in which this meeting differed from all others. For instance, three of the five speakers were associated with institutions in the Lehigh Valley, two from Lehigh University. One of them, Joseph Reynolds, was given the opportunity to be the section’s very first speaker in honor of his role in founding the section. The second speaker was Howard Mitchell, another founder. Leroy Smail and Will Smith were the other two speakers from the Lehigh Valley, with Smail from Lehigh and Smith from Lafayette. Mitchell hailed from Penn.

Speaker | Title |

Reynolds | The evolutes of a certain type of symmetrical plane curves |

Mitchell | The analogue for ideals of the Lagrange-Gauss theory of quadratic forms |

Smail | A new treatment of exponentials and logarithms on the basis of |

a modified Dedekind theory of irrationals | |

Smith | The derivation and solution of certain ordinary differential equations |

Foberg | The state course of study in mathematics |

The final speaker was J. A. Foberg, the Director of Science and Mathematics for Pennsylvania who had been a co-chairman of the MAA

^{ 1 }’s National Committee on Mathematical Requirements. In the introduction to his talk Foberg expressed his view on the section’s role in pre-college education. He stated, “The attention consistently given by the Mathematical Association to the interests of mathematical instruction in the secondary school makes it appropriate that discussion of mathematics instruction in the public schools should form part of the program of this initial meeting of the Philadelphia Section.” Foberg told the audience that “mathematics is a required study through the first nine school years – thereafter it is elective.” Nonetheless, “the state program of studies in Pennsylvania contemplates a continuous twelve-year program in such major subjects as mathematics.” His concluding remarks encouraged a symbiotic relationship between high school teachers and college professors. “A number of colleges and universities in Pennsylvania now admit applicants upon a showing of twelve units of work done in the three-year senior high school. It is hoped and expected that this plan will become general in the near future.”Three of the other four lectures dealt with themes from the undergraduate curriculum. Joseph Reynolds spoke about a topic from analytic geometry, a subject that was then a typical second-year course taken before calculus. Reynolds demonstrated nine properties of a curve and its evolutes for analytic symmetrical plane curves having continuous evolutes, one infinite branch, and no point singularities. He presented the parabola as an example of the type of curve he was discussing.

Smail and Smith lectured on topics from an undergraduate analysis course. Smail, who became known for his highly successful calculus book, presented material at the boundary of graduate and undergraduate education. He introduced a modified form of Dedekind’s definition of irrational numbers to treat rational and irrational exponents and logarithms without explicit use of the theory of limits. Smith’s topic fit neatly into the undergraduate curriculum as enrichment material for the usual course in differential equations. He presented an expository account of the derivation of various kinds of differential equations, including the Riccati equation, equations of forced, damp vibrations, and certain others with solutions “arising from a kind of maintained vibration in which the force of restitution ... is subject to an imposed periodic variation.”

Only one of the lectures appears to be at the graduate level, meaning that it was aimed mainly for the edification of the college professors in the audience. In the talk Howard Mitchell discussed the determination of the number of classes of ideals in quadratic fields by methods used in the theory of binary quadratic forms.

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