Paul J. Sally (Jr.)'s Books

Fundamentals of Mathematical Analysis

By: Paul J. Sally (Jr.)

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Fundamentals of Mathematical Analysis

By: Paul J. Sally (Jr.)

This is a textbook for a course in Honors Analysis (for freshman/sophomore undergraduates) or Real Analysis (for junior/senior undergraduates) or Analysis-I (beginning graduates). It is intended for students who completed a course in ``AP Calculus'', possibly followed by a routine course in multivariable calculus and a computational course in linear algebra. There are three features that distinguish this book from many other books of a similar nature and which are important for the use of this book as a text. The first, and most important, feature is the collection of exercises. These are spread throughout the chapters and should be regarded as an essential component of the student's learning. Some of these exercises comprise a routine follow-up to the material, while others challenge the student's understanding more deeply. The second feature is the set of independent projects presented at the end of each chapter. These projects supplement the content studied in their respective chapters. They can be used to expand the student's knowledge and understanding or as an opportunity to conduct a seminar in Inquiry Based Learning in which the students present the material to their class. The third really important feature is a series of challenge problems that increase in impossibility as the chapters progress.

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Page Count

379

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821891413

ISBN 13

9780821891414

Tools of the Trade

Introduction to Advanced Mathematics

By: Paul J. Sally (Jr.)

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Tools of the Trade

Introduction to Advanced Mathematics

By: Paul J. Sally (Jr.)

This book provides a transition from the formula-full aspects of the beginning study of college level mathematics to the rich and creative world of more advanced topics. It is designed to assist the student in mastering the techniques of analysis and proof that are required to do mathematics." "Along with the standard material such as linear algebra, construction of the real numbers via Cauchy sequences, metric spaces and complete metric spaces, there are three projects at the end of each chapter that form an integral part of the text. These projects include a detailed discussion of topics such as group theory, convergence of infinite series, decimal expansions of real numbers, point set topology and topological groups. They are carefully designed to guide the student through the subject matter. Together with numerous exercises included in the book, these projects may be used as part of the regular classroom presentation, as self-study projects for students, or for Inquiry Based Learning activities presented by the students."--BOOK JACKET.

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Page Count

210

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821846345

ISBN 13

9780821846346

Integers, Fractions, and Arithmetic

A Guide for Teachers

By: Judith D. Sally,Paul J. Sally (Jr.)

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Integers, Fractions, and Arithmetic

A Guide for Teachers

By: Judith D. Sally,Paul J. Sally (Jr.)

A co-publication of the AMS and the Mathematical Sciences Research Institute. This book, which consists of twelve interactive seminars, is a comprehensive and careful study of the fundamental topics of K–8 arithmetic. The guide aims to help teachers understand the mathematical foundations of number theory in order to strengthen and enrich their mathematics classes. Five seminars are dedicated to fractions and decimals because of their importance in the classroom curriculum. The standard topics are covered in detail, but are arranged in an order that is slightly different from the usual one. Multiplication is treated first, and with that in hand, common denominators and equivalent fractions are more readily understood and are available for use when discussing addition. The book is intended for the professional development of teachers. It is appropriate for teacher education programs as well as for enrichment programs such as Mathematical Circles for Teachers. There are numerous activities in each seminar that teachers can bring into their classrooms. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.--Publisher website.

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Page Count

226

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082188798X

ISBN 13

9780821887981

Number, Shape, & Symmetry

An Introduction to Number Theory, Geometry, and Group Theory

By: Diane L. Herrmann,Paul J. Sally Jr.

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Number, Shape, & Symmetry

An Introduction to Number Theory, Geometry, and Group Theory

By: Diane L. Herrmann,Paul J. Sally Jr.

Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors' successful work with undergraduate students at the University of Chicago, seventh

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Page Count

444

Publisher

CRC Press

Published Date

ISBN 10

1466554657

ISBN 13

9781466554658

Geometry

A Guide for Teachers

By: Judith D. Sally,Paul J. Sally (Jr.)

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Geometry

A Guide for Teachers

By: Judith D. Sally,Paul J. Sally (Jr.)

This geometry book is written foremost for future and current middle school teachers, but is also designed for elementary and high school teachers. The book consists of ten seminars covering in a rigorous way the fundamental topics in school geometry, including all of the significant topics in high school geometry. The seminars are crafted to clarify and enhance understanding of the subject. Concepts in plane and solid geometry are carefully explained, and activities that teachers can use in their classrooms are emphasized. The book draws on the pictorial nature of geometry since that is what attracts students at every level to the subject. The book should give teachers a firm foundation on which to base their instruction in the elementary and middle grades. In addition, it should help teachers give their students a solid basis for the geometry that they will study in high school. The book is also intended to be a source for problems in geometry for enrichment programs such as Math Circles and Young Scholars. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI). Publisher's note.

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Page Count

215

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821853627

ISBN 13

9780821853627

Admissible Invariant Distributions on Reductive $p$-adic Groups

By: Harish-Chandra,Stephen DeBacker,Paul J. Sally (Jr.)

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Admissible Invariant Distributions on Reductive $p$-adic Groups

By: Harish-Chandra,Stephen DeBacker,Paul J. Sally (Jr.)

The main purpose of Harish-Chandra's lectures was to show that the character of an irreducible admissible representation of a connected reductive p-adic group G is represented by a locally summable function on G.A key ingredient in this proof is the study of the Fourier transforms of distributions on g, the Lie algebra of G. In particular, Harish-Chandra shows that if the support of a G-invariant distribution on g is compactly generated, then its Fourier transform has an asymptotic expansion about any semisimple point of g."--Jacket.

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Page Count

113

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821820257

ISBN 13

9780821820254

Integer-valued Polynomials

By: Paul-Jean Cahen,Jean-Luc Chabert

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Integer-valued Polynomials

By: Paul-Jean Cahen,Jean-Luc Chabert

Integer-valued polynomials on the ring of integers have been known for a long time and have been used in calculus. Polya and Ostrowski generalized this notion to rings of integers of number fields. More generally still, one may consider a domain $D$ and the polynomials (with coefficients in its quotient field) mapping $D$ into itself. They form a $D$-algebra - that is, a $D$-module with a ring structure. Appearing in a very natural fashion, this ring possesses quite a rich structure, and the very numerous questions it raises allow a thorough exploration of commutative algebra. Here is the first book devoted entirely to this topic. This book features: thorough reviews of many published works; self-contained text with complete proofs; and numerous exercises.

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Page Count

345

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821803883

ISBN 13

9780821803882

Consequences of the Axiom of Choice

By: Paul Howard,Jean E. Rubin

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Consequences of the Axiom of Choice

By: Paul Howard,Jean E. Rubin

This book, Consequences of the Axiom of Choice, is a comprehensive listing of statements that have been proved in the last 100 years using the axiom of choice. Each consequence, also referred to as a form of the axiom of choice, is assigned a number. Part I is a listing of the forms by number. In this part each form is given together with a listing of all statements known to be equivalent to it (equivalent in set theory without the axiom of choice). In Part II the forms are arranged by topic. In Part III we describe the models of set theory which are used to show non-implications between forms. Part IV, the notes section, contains definitions, summaries of important sub-areas and proofs that are not readily available elsewhere. Part V gives references for the relationships between forms and Part VI is the bibliography. Part VII is contained on the floppy disk which is enclosed in the book. It contains a table with form numbers as row and column headings. The entry in the table in row $n$, column $k$ gives the status of the implication ``form $n$ implies form $k$''. Software for easily extracting information from the table is also provided. Features: complete summary of all the work done in the last 100 years on statements that are weaker than the axiom of choice software provided gives complete, convenient access to information about relationships between the various consequences of the axiom of choice and about the models of set theory descriptions of more than 100 models used in the study of the axiom of choice an extensive bibliography About the software: Tables 1 and 2 are accessible on the PC-compatible software included with the book. In addition, the program maketex.c in the software package will create TeX files containing copies of Table 1 and Table 2 which may then be printed. (Tables 1 and 2 are also available at the authors' Web sites: http://www.math.purdue.edu/$\sim$jer/ or http://www.emunix.emich.edu/$\sim$phoward/.) Detailed instructions for setting up and using the software are included in the book's Introduction, and technical support is available directly from the authors.

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Page Count

442

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821809776

ISBN 13

9780821809778

TriMathlon

A Workout Beyond the School Curriculum

By: Judith Sally,Paul Sally

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TriMathlon

A Workout Beyond the School Curriculum

By: Judith Sally,Paul Sally

Swim, Run, and Bike your way to math success! Judith and Paul Sally, accomplished mathematicians and experienced teachers, offer a challenging athletic workout to the minds of their young readers through exercises in areas of number theory and geometry that extend beyond the realm of basic mathematics in the school curriculum. The activities in the

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Page Count

265

Publisher

CRC Press

Published Date

ISBN 10

1439870055

ISBN 13

9781439870051

Book's by Paul J. Sally (Jr.)

Fundamentals of Mathematical Analysis

Fundamentals of Mathematical Analysis

Tools of the Trade

Tools of the Trade

Integers, Fractions, and Arithmetic

Integers, Fractions, and Arithmetic

Number, Shape, & Symmetry

Number, Shape, & Symmetry

Geometry

Geometry

Admissible Invariant Distributions on Reductive $p$-adic Groups

Admissible Invariant Distributions on Reductive $p$-adic Groups

Integer-valued Polynomials

Integer-valued Polynomials

Consequences of the Axiom of Choice

Consequences of the Axiom of Choice

TriMathlon

TriMathlon

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