The Zeros of Riemann Zeta Partial Sums Yield Solutions to f(x) + f(2x) + · · · + f(nx) = 0

This paper proves that every zero of any n th , n ≥ 2, partial sum of the Riemann zeta function provides a vector space of basic solutions of the functional equation f(x)+f(2x)+⋯+f(nx)=0,x∈R . The continuity of the solutions depends on the sign of the real part of each zero.

On the Analytic Solutions of the Functional Equations w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0

In this paper, it is showed that, given an integer number n ≥ 2, each zero of an exponential polynomial of the form w1az1+w2az2+⋯+wnazn, with non-null complex numbers w 1,w 2,…,w n and a 1,a 2,…,a n , produces analytic solutions of the functional equation w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0 on certain domains of C, which represents an extension of some existing results in the literature on this functional equation for the case of positive coefficients a j and w j.

Deposition of Andrew Eliot against Nathan Prince, Nov. 26, 1741

In this deposition, Eliot describes Prince's anger at John Winthrop's selection as Hollis Professor of Mathematics and Natural Philosophy, which he believed was done "to vex and torture" him. Eliot claims that Prince said: "they have chosen that Boy Winthrop professor, I could teach him his A. B. C. in the Mathematicks, they want to get me away from College."

Rules and orders relating to a Professor of the Mathematicks, of Natural and Experimental Philosophy, in Harvard College, 18 January 1726

This folder contains a single document describing the "rules and orders" of the Hollis Professor of Mathematics and Natural Philosophy. The document begins by defining the subjects to be taught by the Hollis Professor including natural and experimental philosophy, elements of geometry, and the principles of astronomy and geography. It then outlines the number of public and private lectures to be given to students, how much extra time the professor should spend with students reviewing any difficulties they may encounter understanding class subject matter discussed, and stipulates that the professor's duties shall be restricted solely to his teaching activities and not involve him in any religious activities at the College or oblige him to teach any additional studies other than those specified for the Hollis Professor of Mathematics and Natural Philosophy. Furthermore, the rules establish the professor's salary at £80 per year and allow the professor to receive from students, except those students studying theology under the Hollis Professor of Divinity, an additional fee as determined by the Corporation and Board of Overseers, to supplement his income. Moreover, the rules assert that all professorship candidates selected by the Harvard Corporation must be approved by Thomas Hollis during his lifetime or by his executor after his death. Finally, the rules state that the Hollis professor take an oath to the civil government and declare himself a member of the Protestant reformed religion. This document is signed by Thomas Hollis and four witnesses, John Hollis, Joshua Hollis, Richard Solly, and John Williams.

The summary of a course of experimental lectures in natural philosophy by Dr. John Winthrop (manuscript copy), 1772-1774

Notebook with a handwritten copy of lecture summaries for a physics course given by Harvard Professor John Winthrop. The notes were made by Timothy Foster in 1772 and 1773. The volume contains twenty-five lectures with some diagrams.

Student lecture notes of Benjamin Peirce, 1797-1798

This collection contains approximately twenty-three handwritten lecture summaries on six leaves made by Harvard undergraduate Benjamin Peirce between September 1797 and November 22, 1798. The summaries generally provide a few sentences describing the topic covered and primarily pertain to lectures on English grammar delivered by Eliphalet Pearson, the Hollis Professor of Hebrew and other Oriental Languages. There are also summaries for single lectures by David Tappan, the Hollis Professor Divinity; Samuel Webber, the Hollis Professor of Mathematics and Natural Philosophy; and John Snelling Popkin, the Greek Tutor from 1795 to 1798, and later the Eliot Professor of Greek Literature. There is also an undated summary of a lecture by Benjamin Waterhouse, the Hersey Professor of Theory and Practice of Physic.

Rubbing of the gravestone of Harvard librarian Nathaniel Ward made by David S. Ferriero, October 15, 1972

Large rubbing of the gravestone of Nathaniel Ward, librarian of Harvard college for one week in 1768. The rubbing was made by David S. Ferriero, and is signed and dated October 15, 1972 in the lower right corner.

Rings of operators.

"Prepared with the assistance of a grant from the Research Corporation."

Game theory and programming; National Science Foundation summer mathematics institute notes.

Bibliography: leaves [87]-[88]

On the roots of matrices.

Reprinted from the American journal of mathematics, v.14.

The mechanics of tires. Final report.

National Bureau of Standards, Washington, D.C.

Higher mathematics. A text-book for classical and engineering colleges.

"Bibliography ... general works on the history of mathematics in the nineteenth century": p. 568-570.

Outlines of mathematical science for the school room.

"An abridgment, with some changes and modifications, of the larger work, 'Logic and utility of mathematics'".--Pref.

Lectures on mathematics /

Mode of access: Internet.