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Mina Spiegel Rees (1902-1997) was an American mathematician who had a significant impact on mathematical research and eduction in the United States. She received a PhD in mathematics at the University of Chicago, writing under the direction of L.E. Dickson. She was the head of the Mathematical Sciences Division of the Office of Naval Research during World War II and was the Dean of Graduate Studies at CUNY after the war. This book covers in depth Rees' many contributions to the US mathematical scene.

From the 1890s to the 1920s American mathematical research grew substantially in quantity and quality. However, few mathematicians were able to pursue research exclusively; most mathematicians, whether active researchers or not, were employed as teachers by colleges and universities. Their degree of interest in the teaching role varied greatly: while some shunned instructional issues, a few mathematicians became deeply involved not only in teaching undergraduates but in attempting to influence mathematics education in the secondary and even the elementary schools. This book seeks to understand these divisions among the mathematicians regarding pedagogy, to explore alliances and conflicts between mathematicians and other educators, and to explain the resulting effects on educational institutions and on the mathematicians themselves.

Calculating Curves is a book about a beautiful but forgotten paper of Thomas Hakon Gronwall. Gronwall was a Swedish mathematician and an American immigrant who published over 80 papers in pure and applied mathematics. He was a practicing civil engineer in Europe and the United States as well as a professor at Princeton University. The paper considered in the book was the first work to produce a necessary and sufficient condition for the representability problem of a graphical problem-solving construct called an alignment nomogram. The book includes a biography of Gronwall, a translation of the paper with an extensive commentary and a complete bibliography of Gronwall's work.

An Early History of Recursive Functions and Computability traces the development of recursive functions from their origins in the late nineteenth century, when recursion was first used as a method of defining simple arithmetic functions, up to the mid-1930's, when the class of general recursive functions was introduced by Godel, formalized by Kleene and used by Church in his thesis. The book explains how the proposal given in Church's 1936 paper, now known as Church's thesis, first arose and concludes with the consideration of another class of functions, the Turing computable functions, that were specially created to be equivalent to the class of effectively calculable functions. The book includes previously unpublished letters between the author and many of the key historical figures.

In each period of Irish history, mathematical equations represented not only solutions to technical problems, they also represented a vision of what Ireland could and should be. Mathematicians are not typically thought of as playing an important role in building a nation, but it turns out that mathematics---no less than poetry, drama, and music---has also been a medium for imagining and creating Ireland. In the seventeenth century, William Petty's mathematics (backed by the force of Cromwell's army) was essential to transferring the vast majority of land from Catholics to Protestants. In the eighteenth century, Berkeley highlighted the logical flaws at the heart of the calculus to destroy the arguments of deists and freethinkers that threatened the established Church. In the nineteenth century, Hamilton was convinced that his international reputation in mathematics would prove to the English that the Irish were not intellectually inferior, thereby strengthening Ireland's position within the Union. In the twentieth century, Eamon de Valera created the Dublin Institute for Advanced Studies to bolster the reputation of the fledgling Republic and to keep Ireland's top mathematicians from emigrating. Today, mathematics and data analytics have defined a vision of Ireland as a knowledge economy rooted in global networks of information. This book is about this history.

Natural Propositions is about the desirable consequence of Charles Peirce's conception of propositions; namely, that they are no strangers to a naturalist world-view and thus form natural inhabitants of reality. This is because propositions---in Peirce's generalization: Dicisigns---do not depend upon human language nor upon human consciousness or intentionality, contrary to most standard assumptions. In addition to a careful consideration of Peirce's work, the book includes numerous examples of Dicisigns in nature as firefly signaling and vervet monkey alarm calls.

In the turn from the 19th to the 20th century, reform in education at all levels was in the air in the United States. Particularly in mathematics, a strong movement formed toward initiating graduate education and then modernizing undergraduate education. Diann Porter uses the the work of William Fogg Osgood on the integration of series term by term to characterize this evolution of academic mathematics in antebellum America.

The first third of the nineteenth century was the formative period for American mathematics: Nathaniel Bowditch emerged as a leader with an international reputation; American scientific journals began publishing mathematical papers; and American mathematicians began to turn away from the British-dominated mathematical philosophy of their past and to turn towards the modern mathematical approach as represented by the French textbook authors. Each of these factors contributed to a work-in-progress as American mathematicians struggled to build a foundation upon which a research community would form. This book traces the development of that that foundation.

Perfect Mechanics captures the excitement of Georgian "big science" and the starring roles played by London instrument makers in the scientific expeditions to measure the shape of the earth, to find and map unknown lands in the Pacific, and to explore the heavens. Yet these indispensible practitioners of "mixed mathematics," recognized and honored by the Royal Society through fellowship and the awarding of the Copley Medal, became increasingly marginalized by the gentlemanly FRS after 1800 and the essential tensions between commerce and science, mechanical and craft production, and social classes brought an abrupt halt to this dynamic and inventive period.

The David Eugene Smith archives at Columbia University's Rare Book and Manuscript Library contain the printed material, manuscripts, portraits and medallions, autographs, and mathematical instruments from his collection. The collection is no longer open to the public as an exhibition. This book provides a special look at the collection by using Smith's own words to guide the reader into what he recollected about the piece while also pinpointing what he valued and thought most important in his collection.

Peirce's logic of continuity is explored from a double perspective: (i) Peirce's original understanding of the continuum, alternative to Cantor's analytical Real line, (ii) Peirce's original construction of a topological logic -- the existential graphs -- alternative to the algebraic presentation of propositional and first-order calculi. Peirce's general architectonics, oriented to back-and-forth hierarchical crossings between the global and the local, is reflected with great care both in the continuum and the existential graphs.

In 1881 the American philosopher Charles S. Peirce published a remarkable paper in The American Journal of Mathematics called "On the Logic of Number." Peirce's paper marked a watershed in nineteenth century mathematics, providing the first successful axiom system for the natural numbers. Awareness that Peirce's axiom system exists has been gradually increasing but the conventional wisdom among mathematicians is still that the first satisfactory axiom systems were those of Dedekind and Peano. The book analyzes Peirce's paper in depth, placing it in the context of contemporary work, and provides a proof of the equivalence of the Peirce and Dedekind axioms for the natural numbers.

The book begins with a discussion of Benjamin Peirce's linear associative algebra and then considers this and other early influences on the logic of is son, C. S. Peirce. A discussion of the early algebraic logicians such as Boole, Jevons and De Morgan follows, culminating in a detailed analysis of C. S. Peirce's seminal paper "Description of a Notation for the Logic of Relatives." His further developments of the 1880s, including quantificational logic are also traced. At the end of his life, Peirce looked to his graphical logic system - the existential graphs - to provide the logic of the future.