Foundations of Measurement offers the most coherently organized treatment of the topics and issues central to measurement. Much of the research involved has been scattered over several decades and a multitude of journals--available in many instances only to specialties. With the publication of Volumes two and three of this important work, Foundations of Measurement is the most comprehensive presentation in the area of measurement.

Foundations of Measurement, Vol. 2: Geometrical, Threshold and Probabilistic Representations

Business & Money

Patrick Suppes

David H. Krantz

R. Duncan Luce

Amos Tversky

Economics

Academic Press

Sets, Numbers, and Systems - Book 2 (Singer Mathematics Program)

Bruce Meserve

Phyllis Sears

Random House]

In modern mathematics, both the theory of proof and the derivation of theorems from axioms bear an unquestioned importance. The necessary skills behind these methods, however, are frequently underdeveloped. This book counters that neglect with a rigorous introduction that is simple enough in presentation and context to permit relatively easy comprehension. It comprises the sentential theory of inference, inference with universal quantifiers, and applications of the theory of inference developed to the elementary theory of commutative groups. Throughout the book, the authors emphasize the pervasive and important problem of translating English sentences into logical or mathematical symbolism. Their clear and coherent style of writing ensures that this work may be used by students in a wide range of ages and abilities.

First Course in Mathematical Logic (Dover Books on Mathematics)

Science & Math

Shirley Hill

Mathematics

Dover Publications

All of the sciences — physical, biological, and social — have a need for quantitative measurement. This influential series, Foundations of Measurement, established the formal foundations for measurement, justifying the assignment of numbers to objects in terms of their structural correspondence. Volume I introduces the distinct mathematical results that serve to formulate numerical representations of qualitative structures. Volume II extends the subject in the direction of geometrical, threshold, and probabilistic representations, and Volume III examines representation as expressed in axiomatization and invariance.

Foundations of Measurement Volume I: Additive and Polynomial Representations (Volume 1) (Dover Books on Mathematics)

Experiments, Instruments & Measurement

All of the sciences―physical, biological, and social―have a need for quantitative measurement. This influential series, Foundations of Measurement, established the formal foundations for measurement, justifying the assignment of numbers to objects in terms of their structural correspondence. Volume I introduces the distinct mathematical results that serve to formulate numerical representations of qualitative structures. Volume II extends the subject in the direction of geometrical, threshold, and probabilistic representations, and Volume III examines representation as expressed in axiomatization and invariance.

Foundations of Measurement Volume II: Geometrical, Threshold, and Probabilistic Representations (Dover Books on Mathematics)

All of the sciences — physical, biological, and social — have a need for quantitative measurement. This influential series, Foundations of Measurement, established the formal basis for measurement, justifying the assignment of numbers to objects in terms of their structural correspondence. Volume I introduces the distinct mathematical results that serve to formulate numerical representations of qualitative structures. Volume II extends the subject in the direction of geometrical, threshold, and probabilistic representations, and Volume III examines representation as expressed in axiomatization and invariance.

Foundations of Measurement Volume III: Representation, Axiomatization, and Invariance (Volume 3) (Dover Books on Mathematics)

One of the most pressingproblems of mathematics over the last hundred years has been the question: What is a number? One of the most impressive answers has been the axiomatic development of set theory. The question raised is: "Exactly what assumptions, beyond those of elementary logic, are required as a basis for modern mathematics?" Answering this question by means of the Zermelo-Fraenkel system, Professor Suppes' coverage is the best treatment of axiomatic set theory for the mathematics student on the upper undergraduate or graduate level. The opening chapter covers the basic paradoxes and the history of set theory and provides a motivation for the study. The second and third chapters cover the basic definitions and axioms and the theory of relations and functions. Beginning with the fourth chapter, equipollence, finite sets and cardinal numbers are dealt with. Chapter five continues the development with finite ordinals and denumerable sets. Chapter six, on rational numbers and real numbers, has been arranged so that it can be omitted without loss of continuity. In chapter seven, transfinite induction and ordinal arithmetic are introduced and the system of axioms is revised. The final chapter deals with the axiom of choice. Throughout, emphasis is on axioms and theorems; proofs are informal. Exercises supplement the text. Much coverage is given to intuitive ideas as well as to comparative development of other systems of set theory. Although a degree of mathematical sophistication is necessary, especially for the final two chapters, no previous work in mathematical logic or set theory is required. For the student of mathematics, set theory is necessary for the proper understanding of the foundations of mathematics. Professor Suppes in Axiomatic Set Theory provides a very clear and well-developed approach. For those with more than a classroom interest in set theory, the historical references and the coverage of the rationale behind the axioms will provide a strong background to the major developments in the field. 1960 edition.

Axiomatic Set Theory (Dover Books on Mathematics)

The series of workbooks, Key to Geometry, gives students an opportunity to discover the relationships of geometry through experience with the tools fundamental to the creation of geometry: the compass and straightedge. Key to Geometry is presented in a careful sequence to be followed with very little intervention by the teacher. Even the answer book is intended to be used for self-checking by the student. These are the answers and notes for Book 7 of the Key to Geometry Series. Format: PaperbackPublisher: Key Curriculum Press

Key to Geometry: Answers and Notes, Book 7

Peter Rasmussen

George Gearhart

Newton Hawley

Key Curriculum Press

The series of workbooks, Key to Geometry, gives students an opportunity to discover the relationships of geometry through experience with the tools fundamental to the creation of geometry: the compass and straightedge. Key to Geometry is presented in a careful sequence to be followed with very little intervention by the teacher. Even the answer book is intended to be used for self-checking by the student. These are the answers and notes for Book 8 of the Key to Geometry Series. Format: PaperbackPublisher: Key Curriculum Press

Key to Geometry: Answers and Notes, Book 8

McGraw=Hill

First Course in Mathematical Logic (A Blaisdell book in the pure and applied sciences)

Blaisdell Pub. Co.

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Books by Patrick Suppes