Name: The Basic Laws of Arithmetic
Brand: Gottlob Frege Translated and Edited by Montgomery Furth
Price: 39.95 USD
Availability: InStock

Gottlob Frege Translated and Edited by Montgomery Furth

The Basic Laws of Arithmetic

$39.95

Basic Laws of Arithmetic: Exposition of the System by Gottlob Frege is a seminal work that aims to establish arithmetic and mathematical analysis as logical systems derived from pure logic. Published in 1893, it represents a cornerstone in the history of mathematical and philosophical thought. Frege’s primary objective was to substantiate logicism, the view that truths of arithmetic are not irreducibly mathematical, synthetic a priori, or empirical, but are instead expressions of logical truths. The book lays out three core tasks: defining logical propositions and rules of inference, and deriving arithmetic's fundamental truths from these logical principles. While Frege’s meticulous approach to these tasks helped establish mathematical logic as a discipline, his work ultimately failed to achieve its purpose, as the set theory underpinning his system proved inconsistent, a flaw brought to his attention by Bertrand Russell.

Despite its failure as Frege envisioned it, the work remains profoundly influential. Frege’s exploration of logical truth and inference pioneered formal logic, including propositional calculus, quantification theory, and set theory. His philosophy of language, embedded within the system’s semantics, offers a deep and nuanced understanding of meaning that continues to resonate within analytical philosophy. Moreover, Frege’s precise and rigorous standards of reasoning surpass many subsequent works, including the more widely adopted Principia Mathematica. Although his logicism is untenable in its original form, Frege’s ideas remain a vital resource for understanding the intersection of logic, mathematics, and language, making his Grundgesetze a crucial study for philosophers, logicians, and historians. This translation of key sections emphasizes its ongoing relevance to modern philosophical inquiries into meaning and language.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.

Richard C. Jeffrey

Studies in Inductive Logic and Probability, Volume II

$29.95

Studies in Inductive Logic and Probability, Volume II—edited by Richard C. Jeffrey—delivers the long-awaited completion of Rudolf Carnap’s “Basic System of Inductive Logic” and, with it, a definitive bridge between logical probability and modern Bayesian thought. Opening with the posthumous Part II of Carnap’s program—on attribute spaces, confirmation across predicate families, and the celebrated λ–γ systems—the volume traces how exchangeability, similarity, and proximity reshape predictive inference beyond the straight rule. Jeffrey’s editorial apparatus situates Carnap’s late revisions and includes the originally withheld §21, offering a rare window onto the extensions Carnap envisaged but did not live to finish.

Surrounding this keystone are landmark contributions that push the program into contemporary terrain. Hintikka and Niiniluoto secure positive confirmation for universal generalizations; Kuipers maps neighboring approaches; de Finetti’s classic paper on partial exchangeability (in translation) anchors the treatment of analogy across families; Link and Diaconis–Freedman supply modern representation theorems; Fenstad reconnects logical languages with probabilistic semantics; and David Lewis’s “Principal Principle” reweaves objective chance into subjective credence. Capped by Douglas Hoover’s note on nonstandard measures, the collection is both capstone and launchpad—indispensable for philosophers of science, statisticians, and decision theorists who want Carnap’s foundations rendered in the idiom that now governs rational belief and inductive learning.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1980.

Richard C. Jeffrey

Studies in Inductive Logic and Probability, Volume II

$95.00

Studies in Inductive Logic and Probability, Volume II—edited by Richard C. Jeffrey—delivers the long-awaited completion of Rudolf Carnap’s “Basic System of Inductive Logic” and, with it, a definitive bridge between logical probability and modern Bayesian thought. Opening with the posthumous Part II of Carnap’s program—on attribute spaces, confirmation across predicate families, and the celebrated λ–γ systems—the volume traces how exchangeability, similarity, and proximity reshape predictive inference beyond the straight rule. Jeffrey’s editorial apparatus situates Carnap’s late revisions and includes the originally withheld §21, offering a rare window onto the extensions Carnap envisaged but did not live to finish.

Surrounding this keystone are landmark contributions that push the program into contemporary terrain. Hintikka and Niiniluoto secure positive confirmation for universal generalizations; Kuipers maps neighboring approaches; de Finetti’s classic paper on partial exchangeability (in translation) anchors the treatment of analogy across families; Link and Diaconis–Freedman supply modern representation theorems; Fenstad reconnects logical languages with probabilistic semantics; and David Lewis’s “Principal Principle” reweaves objective chance into subjective credence. Capped by Douglas Hoover’s note on nonstandard measures, the collection is both capstone and launchpad—indispensable for philosophers of science, statisticians, and decision theorists who want Carnap’s foundations rendered in the idiom that now governs rational belief and inductive learning.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1980.

Richard C. Jeffrey

Studies in Inductive Logic and Probability, Volume II

$49.95

Studies in Inductive Logic and Probability, Volume II—edited by Richard C. Jeffrey—delivers the long-awaited completion of Rudolf Carnap’s “Basic System of Inductive Logic” and, with it, a definitive bridge between logical probability and modern Bayesian thought. Opening with the posthumous Part II of Carnap’s program—on attribute spaces, confirmation across predicate families, and the celebrated λ–γ systems—the volume traces how exchangeability, similarity, and proximity reshape predictive inference beyond the straight rule. Jeffrey’s editorial apparatus situates Carnap’s late revisions and includes the originally withheld §21, offering a rare window onto the extensions Carnap envisaged but did not live to finish.

Surrounding this keystone are landmark contributions that push the program into contemporary terrain. Hintikka and Niiniluoto secure positive confirmation for universal generalizations; Kuipers maps neighboring approaches; de Finetti’s classic paper on partial exchangeability (in translation) anchors the treatment of analogy across families; Link and Diaconis–Freedman supply modern representation theorems; Fenstad reconnects logical languages with probabilistic semantics; and David Lewis’s “Principal Principle” reweaves objective chance into subjective credence. Capped by Douglas Hoover’s note on nonstandard measures, the collection is both capstone and launchpad—indispensable for philosophers of science, statisticians, and decision theorists who want Carnap’s foundations rendered in the idiom that now governs rational belief and inductive learning.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1980.

Lucien M. Le Cam

Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume III

$44.95

The Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability continues the tradition of this esteemed series, which has been held every five years since 1945. This iteration, spanning multiple sessions from 1970 to 1971, reflects the breadth and evolution of probability theory, statistical analysis, and their applications to emerging scientific challenges. The symposium was structured to cover not only theoretical advances in statistics and probability but also pressing interdisciplinary issues such as molecular evolution, biological health, and environmental pollution, demonstrating the increasingly expansive role of statistical methodologies in scientific inquiry.

Comprising over 3,000 pages of research, these proceedings serve as a vital compendium of contemporary thought in probability and statistics. The volumes include contributions from leading mathematicians and scientists worldwide, fostering collaboration across disciplines and nations. Notably, the symposium acknowledges the loss of two intellectual giants, William Feller and Alfred Rényi, whose influence on probability theory remains profound. With rigorous editorial oversight and contributions from experts across academia and government research agencies, these proceedings exemplify the enduring impact of the Berkeley Symposia in shaping the future of mathematical sciences and their application to real-world problems.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1972.

Lucien M. Le Cam

Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume I

$44.95

This title was originally published in 1972.

This title was originally published in 1972.

Cover image for Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume I, isbn: 9780520325883

Lucien M. Le Cam

Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume II, Part II

$32.95

The Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability represents a monumental effort in advancing the discourse on probability theory and statistical applications across a wide range of scientific disciplines. Held every five years, the Berkeley Symposia have established themselves as crucial platforms for stimulating research and fostering collaboration among scholars from around the world. The Fifth Symposium, extending over two sessions in 1965 and organized by renowned statisticians Lucien Le Cam and Jerzy Neyman, brought together leading minds to discuss both theoretical and applied aspects of probability and statistics.

Divided into multiple volumes, this extensive compilation reflects the breadth of topics covered, from foundational statistical theory and probability to specialized applications in astronomy, meteorology, biology, medicine, and even artificial weather modification. The inclusion of interdisciplinary research highlights the growing impact of probabilistic and statistical methodologies beyond pure mathematics, influencing fields as diverse as genetics, epidemiology, and climate science. The symposium's Proceedings provide not only a record of cutting-edge research at the time but also a valuable resource for contemporary statisticians and scientists seeking to understand the evolution of these crucial disciplines.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1967.

Cover image for Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume II, Part II, isbn: 9780520325340

Jerzy Neyman

Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Volume I

$23.95

This title was originally published in 1956.

This title was originally published in 1956.

Cover image for Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Volume I, isbn: 9780520313880

Richard Bellman

Mathematical Optimization Techniques

$29.95

Mathematical Optimization Techniques offers a comprehensive exploration of optimization methods and their applications, as presented at the 1960 Symposium on Mathematical Optimization Techniques in Santa Monica, California. Bringing together mathematicians, scientists, and engineers, the symposium emphasized the interdisciplinary significance of optimization in areas such as linear and nonlinear programming, dynamic programming, and variational processes. The volume delves into mathematical modeling and control systems, examining their role in solving complex problems in flight trajectories, structural design, communication systems, and adaptive controls. The discussions underscore the interplay between mathematical theory and real-world applications, bridging descriptive studies with control processes.

The book is divided into four sections, each tackling a vital aspect of optimization. The first explores variational methods in trajectory optimization, presenting new approaches to balancing differential equations and constraints. The second addresses signal processing, decision-making, and statistical estimation, while the third focuses on linear and nonlinear programming, offering geometric and computational insights into maximizing functions under constraints. The final section examines control processes and automation, highlighting dynamic programming's theoretical and practical advances. Contributors like Bellman, Kalman, and others provide cutting-edge perspectives, making this collection a foundational text for researchers and practitioners in optimization, applied mathematics, and systems engineering.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1963.

Cover image for Mathematical Optimization Techniques, isbn: 9780520319875

Edited by Lucien M. Le Cam, Jerzy Neyman, and Elizabeth L. Scott

Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume III

$75.00

The Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability continues the tradition of this esteemed series, which has been held every five years since 1945. This iteration, spanning multiple sessions from 1970 to 1971, reflects the breadth and evolution of probability theory, statistical analysis, and their applications to emerging scientific challenges. The symposium was structured to cover not only theoretical advances in statistics and probability but also pressing interdisciplinary issues such as molecular evolution, biological health, and environmental pollution, demonstrating the increasingly expansive role of statistical methodologies in scientific inquiry.

Comprising over 3,000 pages of research, these proceedings serve as a vital compendium of contemporary thought in probability and statistics. The volumes include contributions from leading mathematicians and scientists worldwide, fostering collaboration across disciplines and nations. Notably, the symposium acknowledges the loss of two intellectual giants, William Feller and Alfred Rényi, whose influence on probability theory remains profound. With rigorous editorial oversight and contributions from experts across academia and government research agencies, these proceedings exemplify the enduring impact of the Berkeley Symposia in shaping the future of mathematical sciences and their application to real-world problems.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1972.

Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume III

Edited by Lucien M. Lecam and Jerzy Neyman

Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume II, Part II

$55.00

The Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability represents a monumental effort in advancing the discourse on probability theory and statistical applications across a wide range of scientific disciplines. Held every five years, the Berkeley Symposia have established themselves as crucial platforms for stimulating research and fostering collaboration among scholars from around the world. The Fifth Symposium, extending over two sessions in 1965 and organized by renowned statisticians Lucien Le Cam and Jerzy Neyman, brought together leading minds to discuss both theoretical and applied aspects of probability and statistics.

Divided into multiple volumes, this extensive compilation reflects the breadth of topics covered, from foundational statistical theory and probability to specialized applications in astronomy, meteorology, biology, medicine, and even artificial weather modification. The inclusion of interdisciplinary research highlights the growing impact of probabilistic and statistical methodologies beyond pure mathematics, influencing fields as diverse as genetics, epidemiology, and climate science. The symposium's Proceedings provide not only a record of cutting-edge research at the time but also a valuable resource for contemporary statisticians and scientists seeking to understand the evolution of these crucial disciplines.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1967.

Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume II, Part II

Edited by Lucien M. Le Cam, Jerzy Neyman, and Elizabeth L. Scott

Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume III

$115.00

The Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability continues the tradition of this esteemed series, which has been held every five years since 1945. This iteration, spanning multiple sessions from 1970 to 1971, reflects the breadth and evolution of probability theory, statistical analysis, and their applications to emerging scientific challenges. The symposium was structured to cover not only theoretical advances in statistics and probability but also pressing interdisciplinary issues such as molecular evolution, biological health, and environmental pollution, demonstrating the increasingly expansive role of statistical methodologies in scientific inquiry.

Comprising over 3,000 pages of research, these proceedings serve as a vital compendium of contemporary thought in probability and statistics. The volumes include contributions from leading mathematicians and scientists worldwide, fostering collaboration across disciplines and nations. Notably, the symposium acknowledges the loss of two intellectual giants, William Feller and Alfred Rényi, whose influence on probability theory remains profound. With rigorous editorial oversight and contributions from experts across academia and government research agencies, these proceedings exemplify the enduring impact of the Berkeley Symposia in shaping the future of mathematical sciences and their application to real-world problems.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1972.

Edited by Lucien M. Lecam and Jerzy Neyman

Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume II, Part II

$95.00

The Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability represents a monumental effort in advancing the discourse on probability theory and statistical applications across a wide range of scientific disciplines. Held every five years, the Berkeley Symposia have established themselves as crucial platforms for stimulating research and fostering collaboration among scholars from around the world. The Fifth Symposium, extending over two sessions in 1965 and organized by renowned statisticians Lucien Le Cam and Jerzy Neyman, brought together leading minds to discuss both theoretical and applied aspects of probability and statistics.

Divided into multiple volumes, this extensive compilation reflects the breadth of topics covered, from foundational statistical theory and probability to specialized applications in astronomy, meteorology, biology, medicine, and even artificial weather modification. The inclusion of interdisciplinary research highlights the growing impact of probabilistic and statistical methodologies beyond pure mathematics, influencing fields as diverse as genetics, epidemiology, and climate science. The symposium's Proceedings provide not only a record of cutting-edge research at the time but also a valuable resource for contemporary statisticians and scientists seeking to understand the evolution of these crucial disciplines.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1967.

Edited by Richard Bellman

Mathematical Optimization Techniques

$95.00

Mathematical Optimization Techniques offers a comprehensive exploration of optimization methods and their applications, as presented at the 1960 Symposium on Mathematical Optimization Techniques in Santa Monica, California. Bringing together mathematicians, scientists, and engineers, the symposium emphasized the interdisciplinary significance of optimization in areas such as linear and nonlinear programming, dynamic programming, and variational processes. The volume delves into mathematical modeling and control systems, examining their role in solving complex problems in flight trajectories, structural design, communication systems, and adaptive controls. The discussions underscore the interplay between mathematical theory and real-world applications, bridging descriptive studies with control processes.

The book is divided into four sections, each tackling a vital aspect of optimization. The first explores variational methods in trajectory optimization, presenting new approaches to balancing differential equations and constraints. The second addresses signal processing, decision-making, and statistical estimation, while the third focuses on linear and nonlinear programming, offering geometric and computational insights into maximizing functions under constraints. The final section examines control processes and automation, highlighting dynamic programming's theoretical and practical advances. Contributors like Bellman, Kalman, and others provide cutting-edge perspectives, making this collection a foundational text for researchers and practitioners in optimization, applied mathematics, and systems engineering.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1963.

Edited by Richard Bellman

Mathematical Optimization Techniques

$49.95

Mathematical Optimization Techniques offers a comprehensive exploration of optimization methods and their applications, as presented at the 1960 Symposium on Mathematical Optimization Techniques in Santa Monica, California. Bringing together mathematicians, scientists, and engineers, the symposium emphasized the interdisciplinary significance of optimization in areas such as linear and nonlinear programming, dynamic programming, and variational processes. The volume delves into mathematical modeling and control systems, examining their role in solving complex problems in flight trajectories, structural design, communication systems, and adaptive controls. The discussions underscore the interplay between mathematical theory and real-world applications, bridging descriptive studies with control processes.

The book is divided into four sections, each tackling a vital aspect of optimization. The first explores variational methods in trajectory optimization, presenting new approaches to balancing differential equations and constraints. The second addresses signal processing, decision-making, and statistical estimation, while the third focuses on linear and nonlinear programming, offering geometric and computational insights into maximizing functions under constraints. The final section examines control processes and automation, highlighting dynamic programming's theoretical and practical advances. Contributors like Bellman, Kalman, and others provide cutting-edge perspectives, making this collection a foundational text for researchers and practitioners in optimization, applied mathematics, and systems engineering.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1963.

Sze-Tsen Hu

Threshold Logic

$29.95

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1965.

Cover image for Threshold Logic, isbn: 9780520329560

Rudolf Carnap

Studies in Inductive Logic and Probability, Volume I

$23.95

Rudolf Carnap and Richard C. Jeffrey’s Studies in Inductive Logic and Probability, Volume I gathers seminal work charting Carnap’s late-career re-architecture of inductive logic. Moving beyond the single preferred c\*-method of Logical Foundations of Probability (1950), this volume documents the shift to a “continuum” of c-functions and then to a still broader framework sensitive to analogy and similarity, informed by de Finetti’s representation theorem and contemporary probability/statistics. Anchored by Carnap’s “Basic System” (presented here in detail) and complemented by foundational essays—including the programmatic “Inductive Logic and Rational Decisions”—the collection recasts logical probability in the idiom of events, models, and conditionalization, aligning formal inductive methods with Bayesian decision theory while distinguishing logical from statistical notions of information and entropy.

Framed by Jeffrey’s editorial introduction and Carnap’s own historical notes, the book doubles as an intellectual roadmap through the 1950s–60s renaissance in formal epistemology: collaborations with John Kemeny, dialogue with Savage and Putnam, and the systematic adoption of mathematical tools that were absent from Carnap’s earlier work. For philosophers of science, statisticians, and decision theorists, Volume I offers both a definitive statement of Carnap’s mature foundations and a launch pad for the unfinished upper stories—issues of confirmation, learning from analogy, and representation—that Volume II continues. It’s essential reading for anyone who wants to see how inductive logic became conversant with modern probability while retaining a distinctly logical—normative—conception of rational belief.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1971.

Edited by Rudolf Carnap and Richard C. Jeffrey

Studies in Inductive Logic and Probability, Volume I

$95.00

Rudolf Carnap and Richard C. Jeffrey’s Studies in Inductive Logic and Probability, Volume I gathers seminal work charting Carnap’s late-career re-architecture of inductive logic. Moving beyond the single preferred c\*-method of Logical Foundations of Probability (1950), this volume documents the shift to a “continuum” of c-functions and then to a still broader framework sensitive to analogy and similarity, informed by de Finetti’s representation theorem and contemporary probability/statistics. Anchored by Carnap’s “Basic System” (presented here in detail) and complemented by foundational essays—including the programmatic “Inductive Logic and Rational Decisions”—the collection recasts logical probability in the idiom of events, models, and conditionalization, aligning formal inductive methods with Bayesian decision theory while distinguishing logical from statistical notions of information and entropy.

Framed by Jeffrey’s editorial introduction and Carnap’s own historical notes, the book doubles as an intellectual roadmap through the 1950s–60s renaissance in formal epistemology: collaborations with John Kemeny, dialogue with Savage and Putnam, and the systematic adoption of mathematical tools that were absent from Carnap’s earlier work. For philosophers of science, statisticians, and decision theorists, Volume I offers both a definitive statement of Carnap’s mature foundations and a launch pad for the unfinished upper stories—issues of confirmation, learning from analogy, and representation—that Volume II continues. It’s essential reading for anyone who wants to see how inductive logic became conversant with modern probability while retaining a distinctly logical—normative—conception of rational belief.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1971.

Edited by Rudolf Carnap and Richard C. Jeffrey

Studies in Inductive Logic and Probability, Volume I

$39.95

Rudolf Carnap and Richard C. Jeffrey’s Studies in Inductive Logic and Probability, Volume I gathers seminal work charting Carnap’s late-career re-architecture of inductive logic. Moving beyond the single preferred c\*-method of Logical Foundations of Probability (1950), this volume documents the shift to a “continuum” of c-functions and then to a still broader framework sensitive to analogy and similarity, informed by de Finetti’s representation theorem and contemporary probability/statistics. Anchored by Carnap’s “Basic System” (presented here in detail) and complemented by foundational essays—including the programmatic “Inductive Logic and Rational Decisions”—the collection recasts logical probability in the idiom of events, models, and conditionalization, aligning formal inductive methods with Bayesian decision theory while distinguishing logical from statistical notions of information and entropy.

Framed by Jeffrey’s editorial introduction and Carnap’s own historical notes, the book doubles as an intellectual roadmap through the 1950s–60s renaissance in formal epistemology: collaborations with John Kemeny, dialogue with Savage and Putnam, and the systematic adoption of mathematical tools that were absent from Carnap’s earlier work. For philosophers of science, statisticians, and decision theorists, Volume I offers both a definitive statement of Carnap’s mature foundations and a launch pad for the unfinished upper stories—issues of confirmation, learning from analogy, and representation—that Volume II continues. It’s essential reading for anyone who wants to see how inductive logic became conversant with modern probability while retaining a distinctly logical—normative—conception of rational belief.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1971.

Sze-Tsen Hu

Threshold Logic

$49.95

Threshold Logic by Sze-Tsen Hu offers the first comprehensive treatment of logical elements based on the threshold principle, devices that had attracted growing attention in the wake of McCulloch and Pitts’s 1943 neuron models and von Neumann’s investigations into reliability. Threshold devices—including paramétrons, magnetic core switches, and Esaki diode circuits—function as complex logical units that extend well beyond the simplicity of “AND” and “OR” gates. Because a single device can generate relatively intricate switching functions, they hold the potential to increase the speed and efficiency of electronic digital computers while reducing the number of components required. This efficiency has made threshold logic a key subject in computing research during the postwar era, and the book situates the field at the intersection of mathematical theory, hardware design, and computational application.

Hu’s study surveys and advances work in three major areas: defining the conditions a switching function must meet to qualify as a threshold function, devising algorithms to test and implement these functions, and developing synthesis methods for networks composed of threshold gates. The book is designed both as a reference consolidating contributions from the previous decade and as a research monograph introducing Hu’s own results, much of which had been confined to Lockheed Missiles and Space Company technical reports. The early chapters cover the theory of threshold functions and decision conditions; subsequent chapters detail algorithms for classification and realization; the concluding chapter presents Hu’s mathematically rigorous process for constructing minimal threshold networks, moving beyond the heuristic techniques that had dominated the field. With an eye to accessibility, Hu deliberately emphasizes clarity in his proofs and explanations, ensuring that both engineers and mathematicians can use the book as a foundation for further exploration of threshold logic in the design of high-speed computing systems.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1965.

Sze-Tsen Hu

Threshold Logic

$95.00

Threshold Logic by Sze-Tsen Hu offers the first comprehensive treatment of logical elements based on the threshold principle, devices that had attracted growing attention in the wake of McCulloch and Pitts’s 1943 neuron models and von Neumann’s investigations into reliability. Threshold devices—including paramétrons, magnetic core switches, and Esaki diode circuits—function as complex logical units that extend well beyond the simplicity of “AND” and “OR” gates. Because a single device can generate relatively intricate switching functions, they hold the potential to increase the speed and efficiency of electronic digital computers while reducing the number of components required. This efficiency has made threshold logic a key subject in computing research during the postwar era, and the book situates the field at the intersection of mathematical theory, hardware design, and computational application.

Hu’s study surveys and advances work in three major areas: defining the conditions a switching function must meet to qualify as a threshold function, devising algorithms to test and implement these functions, and developing synthesis methods for networks composed of threshold gates. The book is designed both as a reference consolidating contributions from the previous decade and as a research monograph introducing Hu’s own results, much of which had been confined to Lockheed Missiles and Space Company technical reports. The early chapters cover the theory of threshold functions and decision conditions; subsequent chapters detail algorithms for classification and realization; the concluding chapter presents Hu’s mathematically rigorous process for constructing minimal threshold networks, moving beyond the heuristic techniques that had dominated the field. With an eye to accessibility, Hu deliberately emphasizes clarity in his proofs and explanations, ensuring that both engineers and mathematicians can use the book as a foundation for further exploration of threshold logic in the design of high-speed computing systems.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1965.

R. K. Luneburg

Mathematical Theory of Optics

$29.95

Mathematical Theory of Optics by Dr. Rudolf K. Luneburg stands as a monumental work in the field of optical theory, offering a rigorous and innovative approach to understanding instrumental optics through the lens of Maxwell's electromagnetic equations. First presented as a lecture series at Brown University in 1944, and later refined into these notes, Luneburg’s work connects geometrical optics and scalar diffraction optics as systematic extensions of electromagnetic theory. This unification was groundbreaking, as these disciplines were previously treated as distinct fields. Luneburg’s formulation of geometrical optics as exact solutions to Maxwell's equations, rather than simply as asymptotic approximations, redefined the theoretical landscape and laid the groundwork for future developments in optics.

The volume meticulously explores topics such as Hamilton's theory of geometrical optics, the mathematical treatment of optical aberrations, and the now-famous Luneburg lens, which has become a key component in microwave antenna technology. Later chapters delve into diffraction theory, introducing Luneburg diffraction integrals that extend classical results and address complex problems such as resolution improvements. With additional appendices and notes by prominent scholars, the book not only consolidates Luneburg's profound insights but also enriches the field with practical applications and theoretical advancements. Recognized as one of the most significant contributions to optical theory, this volume remains a foundational text for physicists and engineers engaged in advanced optical research.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.

Cover image for Mathematical Theory of Optics, isbn: 9780520328266

Saloman Bochner

Harmonic Analysis and the Theory of Probability

$23.95

Harmonic Analysis and the Theory of Probability by Salomon Bochner is a landmark monograph that rigorously links two central domains of modern mathematics: Fourier analysis and probability theory. Written during the author’s time at the Statistical Laboratory at Berkeley under the direction of Jerzy Neyman, the book develops a unified account of approximation, Fourier expansions, Laplace and Mellin transforms, stochastic processes, and their deep interrelations. Bochner’s treatment moves fluidly from classical tools—kernels, summability formulas, spherical harmonics—to more advanced concepts such as infinitely divisible processes, characteristic functionals, and the closure properties of Fourier transforms, always with an eye to their probabilistic interpretations.

This volume demonstrates how probability theory gains analytic depth when recast in the language of harmonic analysis, and how harmonic methods are enriched by probabilistic intuition. It offers precise theorems on convergence, moment conditions, and stochastic functionals, while also exploring zeta integrals, random paths, and the analysis of stationary processes. As part of the California Monographs in Mathematical Sciences series, it speaks to mathematicians, statisticians, and theoretical physicists seeking rigorous frameworks for randomness and structure. Bochner’s synthesis not only advanced mid-twentieth-century probability but also laid groundwork for contemporary research in functional analysis, statistical mechanics, and stochastic modeling.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1955.

Salomon Bochner

Harmonic Analysis and the Theory of Probability

$39.95

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1955.

Salomon Bochner

Harmonic Analysis and the Theory of Probability

$95.00

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1955.

R. K. Luneburg

Mathematical Theory of Optics

$49.95

Mathematical Theory of Optics by Dr. Rudolf K. Luneburg stands as a monumental work in the field of optical theory, offering a rigorous and innovative approach to understanding instrumental optics through the lens of Maxwell's electromagnetic equations. First presented as a lecture series at Brown University in 1944, and later refined into these notes, Luneburg’s work connects geometrical optics and scalar diffraction optics as systematic extensions of electromagnetic theory. This unification was groundbreaking, as these disciplines were previously treated as distinct fields. Luneburg’s formulation of geometrical optics as exact solutions to Maxwell's equations, rather than simply as asymptotic approximations, redefined the theoretical landscape and laid the groundwork for future developments in optics.

The volume meticulously explores topics such as Hamilton's theory of geometrical optics, the mathematical treatment of optical aberrations, and the now-famous Luneburg lens, which has become a key component in microwave antenna technology. Later chapters delve into diffraction theory, introducing Luneburg diffraction integrals that extend classical results and address complex problems such as resolution improvements. With additional appendices and notes by prominent scholars, the book not only consolidates Luneburg's profound insights but also enriches the field with practical applications and theoretical advancements. Recognized as one of the most significant contributions to optical theory, this volume remains a foundational text for physicists and engineers engaged in advanced optical research.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.

R. K. Luneburg

Mathematical Theory of Optics

$95.00

Mathematical Theory of Optics by Dr. Rudolf K. Luneburg stands as a monumental work in the field of optical theory, offering a rigorous and innovative approach to understanding instrumental optics through the lens of Maxwell's electromagnetic equations. First presented as a lecture series at Brown University in 1944, and later refined into these notes, Luneburg’s work connects geometrical optics and scalar diffraction optics as systematic extensions of electromagnetic theory. This unification was groundbreaking, as these disciplines were previously treated as distinct fields. Luneburg’s formulation of geometrical optics as exact solutions to Maxwell's equations, rather than simply as asymptotic approximations, redefined the theoretical landscape and laid the groundwork for future developments in optics.

The volume meticulously explores topics such as Hamilton's theory of geometrical optics, the mathematical treatment of optical aberrations, and the now-famous Luneburg lens, which has become a key component in microwave antenna technology. Later chapters delve into diffraction theory, introducing Luneburg diffraction integrals that extend classical results and address complex problems such as resolution improvements. With additional appendices and notes by prominent scholars, the book not only consolidates Luneburg's profound insights but also enriches the field with practical applications and theoretical advancements. Recognized as one of the most significant contributions to optical theory, this volume remains a foundational text for physicists and engineers engaged in advanced optical research.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.

Gottlob Frege

The Basic Laws of Arithmetic

$23.95

Basic Laws of Arithmetic: Exposition of the System by Gottlob Frege is a seminal work that aims to establish arithmetic and mathematical analysis as logical systems derived from pure logic. Published in 1893, it represents a cornerstone in the history of mathematical and philosophical thought. Frege’s primary objective was to substantiate logicism, the view that truths of arithmetic are not irreducibly mathematical, synthetic a priori, or empirical, but are instead expressions of logical truths. The book lays out three core tasks: defining logical propositions and rules of inference, and deriving arithmetic's fundamental truths from these logical principles. While Frege’s meticulous approach to these tasks helped establish mathematical logic as a discipline, his work ultimately failed to achieve its purpose, as the set theory underpinning his system proved inconsistent, a flaw brought to his attention by Bertrand Russell.

Despite its failure as Frege envisioned it, the work remains profoundly influential. Frege’s exploration of logical truth and inference pioneered formal logic, including propositional calculus, quantification theory, and set theory. His philosophy of language, embedded within the system’s semantics, offers a deep and nuanced understanding of meaning that continues to resonate within analytical philosophy. Moreover, Frege’s precise and rigorous standards of reasoning surpass many subsequent works, including the more widely adopted Principia Mathematica. Although his logicism is untenable in its original form, Frege’s ideas remain a vital resource for understanding the intersection of logic, mathematics, and language, making his Grundgesetze a crucial study for philosophers, logicians, and historians. This translation of key sections emphasizes its ongoing relevance to modern philosophical inquiries into meaning and language.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.

Cover image for The Basic Laws of Arithmetic, isbn: 9780520312364

Stanton A. Glantz

Mathematics for Biomedical Applications

$29.95

Mathematics for Biomedical Applications bridges the gap between introductory calculus and advanced mathematical techniques, offering a practical framework for biomedical students and professionals. Originating from a course developed in Stanford University's Cardiology Division, this text equips readers with the tools to model, analyze, and solve real-world biomedical problems using applied mathematics. The author prioritizes a pragmatic approach, ensuring that even a traditionally skeptical audience finds value in the mathematical concepts presented.

The book begins by formulating biomedical problems into differential equations, gradually building to solutions using direct methods and advanced techniques like the Laplace transform and Fourier analysis. It integrates these mathematical tools into biological contexts, such as signal processing, to demonstrate their relevance. The inclusion of numerical methods and guidance for interpreting algorithms provides a stepping stone for readers to delve into more specialized texts or computational tools. Supplementary appendices review calculus basics, properties of complex numbers, and key integral tables, making this a comprehensive yet accessible resource for students aiming to integrate mathematical rigor into their biomedical expertise.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1979.

Cover image for Mathematics for Biomedical Applications, isbn: 9780520323094

Gottlob Frege Translated and Edited by Montgomery Furth

The Basic Laws of Arithmetic

$95.00

Basic Laws of Arithmetic: Exposition of the System by Gottlob Frege is a seminal work that aims to establish arithmetic and mathematical analysis as logical systems derived from pure logic. Published in 1893, it represents a cornerstone in the history of mathematical and philosophical thought. Frege’s primary objective was to substantiate logicism, the view that truths of arithmetic are not irreducibly mathematical, synthetic a priori, or empirical, but are instead expressions of logical truths. The book lays out three core tasks: defining logical propositions and rules of inference, and deriving arithmetic's fundamental truths from these logical principles. While Frege’s meticulous approach to these tasks helped establish mathematical logic as a discipline, his work ultimately failed to achieve its purpose, as the set theory underpinning his system proved inconsistent, a flaw brought to his attention by Bertrand Russell.

Despite its failure as Frege envisioned it, the work remains profoundly influential. Frege’s exploration of logical truth and inference pioneered formal logic, including propositional calculus, quantification theory, and set theory. His philosophy of language, embedded within the system’s semantics, offers a deep and nuanced understanding of meaning that continues to resonate within analytical philosophy. Moreover, Frege’s precise and rigorous standards of reasoning surpass many subsequent works, including the more widely adopted Principia Mathematica. Although his logicism is untenable in its original form, Frege’s ideas remain a vital resource for understanding the intersection of logic, mathematics, and language, making his Grundgesetze a crucial study for philosophers, logicians, and historians. This translation of key sections emphasizes its ongoing relevance to modern philosophical inquiries into meaning and language.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.

Barnabas Bernard Hughes

Jordanus de Nemore, de Numeris Datis

$23.95

Jordanus de Nemore's De Numeris Datis stands as a groundbreaking text, marking the advent of advanced algebra in Western Europe. Written in the 13th century, the work assumes mastery of basic algebra and progresses to develop a systematic approach to quadratic, simultaneous, and proportional equations, many of which had not been previously articulated in European mathematics. By providing sophisticated techniques for numerical analysis, Jordanus not only addressed the needs of his contemporary mathematical community but also laid a foundational stone for the algebraic advancements that followed. The text bridges a gap between the classical mathematical traditions of the Greeks and the revolutionary algebraic methods emerging in the medieval Islamic world, showcasing Jordanus’s role as an intellectual conduit in a period of vibrant cross-cultural exchange.

Despite scant biographical information about Jordanus himself, his contributions resonate through the depth and structure of his work. De Numeris Datis combines theoretical rigor with practical application, offering propositions and methods that are both abstract and directly applicable to real-world problems. The text's influence is underscored by its enduring presence in medieval and Renaissance scholarship, with numerous surviving manuscripts and commentaries attesting to its relevance. By formalizing algebraic analysis in a way that prefigures later works like Viète's Introduction to the Analytical Art, Jordanus elevated algebra from a computational tool to a discipline of logical inquiry, cementing his legacy as one of the seminal figures in the history of mathematics.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1981.

Cover image for Jordanus de Nemore, de Numeris Datis, isbn: 9780520321687

Stanton A. Glantz

Mathematics for Biomedical Applications

$95.00

Mathematics for Biomedical Applications bridges the gap between introductory calculus and advanced mathematical techniques, offering a practical framework for biomedical students and professionals. Originating from a course developed in Stanford University's Cardiology Division, this text equips readers with the tools to model, analyze, and solve real-world biomedical problems using applied mathematics. The author prioritizes a pragmatic approach, ensuring that even a traditionally skeptical audience finds value in the mathematical concepts presented.

The book begins by formulating biomedical problems into differential equations, gradually building to solutions using direct methods and advanced techniques like the Laplace transform and Fourier analysis. It integrates these mathematical tools into biological contexts, such as signal processing, to demonstrate their relevance. The inclusion of numerical methods and guidance for interpreting algorithms provides a stepping stone for readers to delve into more specialized texts or computational tools. Supplementary appendices review calculus basics, properties of complex numbers, and key integral tables, making this a comprehensive yet accessible resource for students aiming to integrate mathematical rigor into their biomedical expertise.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1979.

Stanton A. Glantz

Mathematics for Biomedical Applications

$49.95

Mathematics for Biomedical Applications bridges the gap between introductory calculus and advanced mathematical techniques, offering a practical framework for biomedical students and professionals. Originating from a course developed in Stanford University's Cardiology Division, this text equips readers with the tools to model, analyze, and solve real-world biomedical problems using applied mathematics. The author prioritizes a pragmatic approach, ensuring that even a traditionally skeptical audience finds value in the mathematical concepts presented.

The book begins by formulating biomedical problems into differential equations, gradually building to solutions using direct methods and advanced techniques like the Laplace transform and Fourier analysis. It integrates these mathematical tools into biological contexts, such as signal processing, to demonstrate their relevance. The inclusion of numerical methods and guidance for interpreting algorithms provides a stepping stone for readers to delve into more specialized texts or computational tools. Supplementary appendices review calculus basics, properties of complex numbers, and key integral tables, making this a comprehensive yet accessible resource for students aiming to integrate mathematical rigor into their biomedical expertise.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1979.

Barnabas Bernard Hughes

Jordanus de Nemore, de Numeris Datis

$95.00

Jordanus de Nemore's De Numeris Datis stands as a groundbreaking text, marking the advent of advanced algebra in Western Europe. Written in the 13th century, the work assumes mastery of basic algebra and progresses to develop a systematic approach to quadratic, simultaneous, and proportional equations, many of which had not been previously articulated in European mathematics. By providing sophisticated techniques for numerical analysis, Jordanus not only addressed the needs of his contemporary mathematical community but also laid a foundational stone for the algebraic advancements that followed. The text bridges a gap between the classical mathematical traditions of the Greeks and the revolutionary algebraic methods emerging in the medieval Islamic world, showcasing Jordanus’s role as an intellectual conduit in a period of vibrant cross-cultural exchange.

Despite scant biographical information about Jordanus himself, his contributions resonate through the depth and structure of his work. De Numeris Datis combines theoretical rigor with practical application, offering propositions and methods that are both abstract and directly applicable to real-world problems. The text's influence is underscored by its enduring presence in medieval and Renaissance scholarship, with numerous surviving manuscripts and commentaries attesting to its relevance. By formalizing algebraic analysis in a way that prefigures later works like Viète's Introduction to the Analytical Art, Jordanus elevated algebra from a computational tool to a discipline of logical inquiry, cementing his legacy as one of the seminal figures in the history of mathematics.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1981.

Barnabas Bernard Hughes

Jordanus de Nemore, de Numeris Datis

$39.95

Jordanus de Nemore's De Numeris Datis stands as a groundbreaking text, marking the advent of advanced algebra in Western Europe. Written in the 13th century, the work assumes mastery of basic algebra and progresses to develop a systematic approach to quadratic, simultaneous, and proportional equations, many of which had not been previously articulated in European mathematics. By providing sophisticated techniques for numerical analysis, Jordanus not only addressed the needs of his contemporary mathematical community but also laid a foundational stone for the algebraic advancements that followed. The text bridges a gap between the classical mathematical traditions of the Greeks and the revolutionary algebraic methods emerging in the medieval Islamic world, showcasing Jordanus’s role as an intellectual conduit in a period of vibrant cross-cultural exchange.

Despite scant biographical information about Jordanus himself, his contributions resonate through the depth and structure of his work. De Numeris Datis combines theoretical rigor with practical application, offering propositions and methods that are both abstract and directly applicable to real-world problems. The text's influence is underscored by its enduring presence in medieval and Renaissance scholarship, with numerous surviving manuscripts and commentaries attesting to its relevance. By formalizing algebraic analysis in a way that prefigures later works like Viète's Introduction to the Analytical Art, Jordanus elevated algebra from a computational tool to a discipline of logical inquiry, cementing his legacy as one of the seminal figures in the history of mathematics.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1981.