Alexander J. Hahn's Books

Basic Calculus of Planetary Orbits and Interplanetary Flight

The Missions of the Voyagers, Cassini, and Juno

By: Alexander J. Hahn

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Basic Calculus of Planetary Orbits and Interplanetary Flight

The Missions of the Voyagers, Cassini, and Juno

By: Alexander J. Hahn

Intended for a one- or two-semester course, this text applies basic, one-variable calculus to analyze the motion both of planets in their orbits as well as interplanetary spacecraft in their trajectories. The remarkable spacecraft missions to the inner and outermost reaches of our solar system have been one of the greatest success stories of modern human history. Much of the underlying mathematical story is presented alongside the astonishing images and extensive data that NASA’s Voyager, NEAR-Shoemaker, Cassini, and Juno missions have sent back to us. First and second year college students in mathematics, engineering, or science, and those seeking an enriching independent study, will experience the mathematical language and methods of single variable calculus within their application to relevant conceptual and strategic aspects of the navigation of a spacecraft. The reader is expected to have taken one or two semesters of the basic calculus of derivatives, integrals, and the role that limits play. Additional prerequisites include knowledge of coordinate plane geometry, basic trigonometry, functions and graphs, including trig, inverse, exponential, and log functions. The discussions begin with the rich history of humanity’s efforts to understand the universe from the Greeks, to Newton and the Scientific Revolution, to Hubble and galaxies, to NASA and the space missions. The calculus of polar functions that plays a central mathematical role is presented in a self-contained way in complete detail. Each of the six chapters is followed by an extensive problem set that deals with and also expands on the concerns of the chapter. The instructor has the flexibility to engage them with greater or lesser intensity. “I have been an aerospace engineer for 39 years and honestly, it would be hard for me to overstate how valuable I believe this book will be to numerous scientific and engineering disciplines and in particular to the future of aerospace engineering ... This book is perfectly crafted to motivate, educate, and prepare the scientists and engineers who wish to reach for the sky and beyond.” —Dr. Mario Zoccoli, Aerospace Engineer, NASA and Lockheed Martin

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387

Publisher

Springer Nature

Published Date

ISBN 10

3030248682

ISBN 13

9783030248680

The Classical Groups and K-Theory

By: Alexander J. Hahn,O.Timothy O'Meara

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The Classical Groups and K-Theory

By: Alexander J. Hahn,O.Timothy O'Meara

It is a great satisfaction for a mathematician to witness the growth and expansion of a theory in which he has taken some part during its early years. When H. Weyl coined the words "classical groups", foremost in his mind were their connections with invariant theory, which his famous book helped to revive. Although his approach in that book was deliberately algebraic, his interest in these groups directly derived from his pioneering study of the special case in which the scalars are real or complex numbers, where for the first time he injected Topology into Lie theory. But ever since the definition of Lie groups, the analogy between simple classical groups over finite fields and simple classical groups over IR or C had been observed, even if the concept of "simplicity" was not quite the same in both cases. With the discovery of the exceptional simple complex Lie algebras by Killing and E. Cartan, it was natural to look for corresponding groups over finite fields, and already around 1900 this was done by Dickson for the exceptional Lie algebras G and E • However, a deep reason for this 2 6 parallelism was missing, and it is only Chevalley who, in 1955 and 1961, discovered that to each complex simple Lie algebra corresponds, by a uniform process, a group scheme (fj over the ring Z of integers, from which, for any field K, could be derived a group (fj(K).

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589

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662131528

ISBN 13

9783662131527

Calculus in Context

Background, Basics, and Applications

By: Alexander J. Hahn

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Calculus in Context

Background, Basics, and Applications

By: Alexander J. Hahn

A new approach to teaching calculus that uses historical examples and draws on applications from science and engineering. Breaking the mold of existing calculus textbooks, Calculus in Context draws students into the subject in two new ways. Part I develops the mathematical preliminaries (including geometry, trigonometry, algebra, and coordinate geometry) within the historical frame of the ancient Greeks and the heliocentric revolution in astronomy. Part II starts with comprehensive and modern treatments of the fundamentals of both differential and integral calculus, then turns to a wide-ranging discussion of applications. Students will learn that core ideas of calculus are central to concepts such as acceleration, force, momentum, torque, inertia, and the properties of lenses. Classroom-tested at Notre Dame University, this textbook is suitable for students of wide-ranging backgrounds because it engages its subject at several levels and offers ample and flexible problem set options for instructors. Parts I and II are both supplemented by expansive Problems and Projects segments. Topics covered in the book include: • the basics of geometry, trigonometry, algebra, and coordinate geometry and the historical, scientific agenda that drove their development • a brief, introductory calculus from the works of Newton and Leibniz • a modern development of the essentials of differential and integral calculus • the analysis of specific, relatable applications, such as the arc of the George Washington Bridge; the dome of the Pantheon; the optics of a telescope; the dynamics of a bullet; the geometry of the pseudosphere; the motion of a planet in orbit; and the momentum of an object in free fall. Calculus in Context is a compelling exploration—for students and instructors alike—of a discipline that is both rich in conceptual beauty and broad in its applied relevance.

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707

Publisher

JHU Press

Published Date

ISBN 10

142142231X

ISBN 13

9781421422312

Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups

By: Alexander J. Hahn

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Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups

By: Alexander J. Hahn

Quadratic Algebras, Clifford Algebras, and Arithmetic Forms introduces mathematicians to the large and dynamic area of algebras and forms over commutative rings. The book begins very elementary and progresses gradually in its degree of difficulty. Topics include the connection between quadratic algebras, Clifford algebras and quadratic forms, Brauer groups, the matrix theory of Clifford algebras over fields, Witt groups of quadratic and symmetric bilinear forms. Some of the new results included by the author concern the representation of Clifford algebras, the structure of Arf algebra in the free case, connections between the group of isomorphic classes of finitely generated projectives of rank one and arithmetic results about the quadratic Witt group.

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296

Publisher

Springer Science & Business Media

Published Date

ISBN 10

146846311X

ISBN 13

9781468463118

Quantitative Risk Management

Concepts, Techniques and Tools - Revised Edition

By: Alexander J. McNeil,Rüdiger Frey,Paul Embrechts

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Quantitative Risk Management

Concepts, Techniques and Tools - Revised Edition

By: Alexander J. McNeil,Rüdiger Frey,Paul Embrechts

This book provides the most comprehensive treatment of the theoretical concepts and modelling techniques of quantitative risk management. Whether you are a financial risk analyst, actuary, regulator or student of quantitative finance, Quantitative Risk Management gives you the practical tools you need to solve real-world problems. Describing the latest advances in the field, Quantitative Risk Management covers the methods for market, credit and operational risk modelling. It places standard industry approaches on a more formal footing and explores key concepts such as loss distributions, risk measures and risk aggregation and allocation principles. The book's methodology draws on diverse quantitative disciplines, from mathematical finance and statistics to econometrics and actuarial mathematics. A primary theme throughout is the need to satisfactorily address extreme outcomes and the dependence of key risk drivers. Proven in the classroom, the book also covers advanced topics like credit derivatives. Fully revised and expanded to reflect developments in the field since the financial crisis Features shorter chapters to facilitate teaching and learning Provides enhanced coverage of Solvency II and insurance risk management and extended treatment of credit risk, including counterparty credit risk and CDO pricing Includes a new chapter on market risk and new material on risk measures and risk aggregation

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Page Count

721

Publisher

Princeton University Press

Published Date

ISBN 10

1400866286

ISBN 13

9781400866281

Dictionary of the Old Testament: Pentateuch

A Compendium Of Contemporary Biblical Scholarship

By: T DESMOND ALEXANDER,DAVID W BAKER

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Dictionary of the Old Testament: Pentateuch

A Compendium Of Contemporary Biblical Scholarship

By: T DESMOND ALEXANDER,DAVID W BAKER

The Dictionary of the Old Testament: Pentateuch' is the first in a four-volume series covering the text of the Old Testament. Following in the tradition of the four award-winning IVP dictionaries focused on the New Testament and its background, this encyclopedic work is characterized by close attention to the text of the Old Testament and the ongoing conversation of contemporary scholarship. In exploring the major themes and issues of the Pentateuch, it informs and challenges its readers with authoritative overviews, detailed examinations and new insights from the world of the ancient Near East. The 'Dictionary of the Old Testament: Pentateuch' is designed to be your first stop in the study and research of the Pentateuch, on which the rest of the Bible is built.

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1521

Publisher

Inter-Varsity Press

Published Date

ISBN 10

1789740282

ISBN 13

9781789740288

Multiple Sclerosis and Related Disorders

Diagnosis, Medical Management, and Rehabilitation

By: Alexander Rae-Grant, MD,Alexander Rae-Grant,Robert Fox, MD,Francois Bethoux, MD

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Multiple Sclerosis and Related Disorders

Diagnosis, Medical Management, and Rehabilitation

By: Alexander Rae-Grant, MD,Alexander Rae-Grant,Robert Fox, MD,Francois Bethoux, MD

Special populations, societal and family issues, and related disorders that are often mistaken for MS are also covered. Dedicated chapters on neuromyelitis optica and acute disseminated encephalomyelitis incorporate newer diagnostic criteria. Because comorbidities often make the management of MS-related disability more complex, the book addresses these comorbidities as part of a comprehensive management plan. To enhance the clinical utility, critical-to-know information and management pearls are boxed for quick reference and most chapters include lists of "Key Points" for clinicians, and for patients and families. Illustrations, tables, graphs, assessment scales, and up-to-date MRI imaging inform the text throughout. The treatment chapters include specific recommendations where available and highlight areas of controversy.

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Page Count

344

Publisher

Demos Medical Publishing

Published Date

ISBN 10

1936287757

ISBN 13

9781936287758

Mathematical Excursions to the World's Great Buildings

By: Alexander J. Hahn

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Mathematical Excursions to the World's Great Buildings

By: Alexander J. Hahn

How mathematics helped build the world's most important buildings from early Egypt to the present From the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular buildings. Beautifully illustrated, the book explores the milestones in elementary mathematics that enliven the understanding of these buildings and combines this with an in-depth look at their aesthetics, history, and structure. Whether using trigonometry and vectors to explain why Gothic arches are structurally superior to Roman arches, or showing how simple ruler and compass constructions can produce sophisticated architectural details, Alexander Hahn describes the points at which elementary mathematics and architecture intersect. Beginning in prehistoric times, Hahn proceeds to guide readers through the Greek, Roman, Islamic, Romanesque, Gothic, Renaissance, and modern styles. He explores the unique features of the Pantheon, the Hagia Sophia, the Great Mosque of Cordoba, the Duomo in Florence, Palladio's villas, and Saint Peter's Basilica, as well as the U.S. Capitol Building. Hahn celebrates the forms and structures of architecture made possible by mathematical achievements from Greek geometry, the Hindu-Arabic number system, two- and three-dimensional coordinate geometry, and calculus. Along the way, Hahn introduces groundbreaking architects, including Brunelleschi, Alberti, da Vinci, Bramante, Michelangelo, della Porta, Wren, Gaudí, Saarinen, Utzon, and Gehry. Rich in detail, this book takes readers on an expedition around the globe, providing a deeper understanding of the mathematical forces at play in the world's most elegant buildings.

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336

Publisher

Princeton University Press

Published Date

ISBN 10

1400841992

ISBN 13

9781400841998

Learning Basic Calculus

From Archimedes to Newton to Its Role in Science

By: Alexander Hahn

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Learning Basic Calculus

From Archimedes to Newton to Its Role in Science

By: Alexander Hahn

This introductory calculus text was developed by the author through his teaching of an honors calculus course at Notre Dame. The book develops calculus, as well as the necessary trigonometry and analytic geometry, from witin the relevant historical context, and yet it is not a textbook in the history of mathematics as such. The notation is modern, and the material is selected to cover the basics of the subject. Special emphasis is placed on pedagogy throughout. Whhile emphasizing the broad applications of the subject, emphasis is placed on the mathematical content of the subject.

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Page Count

572

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387946063

ISBN 13

9780387946061

Basic Calculus of Planetary Orbits and Interplanetary Flight

The Missions of the Voyagers, Cassini, and Juno

By: Alexander J. Hahn

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Basic Calculus of Planetary Orbits and Interplanetary Flight

The Missions of the Voyagers, Cassini, and Juno

By: Alexander J. Hahn

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Solve jigsaw puzzle

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Page Count

387

Publisher

Springer Nature

Published Date

ISBN 10

3030248682

ISBN 13

9783030248680

Mathematical Excursions to the World's Great Buildings

By: Alexander Hahn

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Mathematical Excursions to the World's Great Buildings

By: Alexander Hahn

Describes the mathematics behind the design of famous buildings, including the Parthenon, the Sydney Opera House, and the Bilbao Guggenheim.

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Page Count

344

Publisher

Princeton University Press

Published Date

ISBN 10

0691145202

ISBN 13

9780691145204

Book's by Alexander J. Hahn

Basic Calculus of Planetary Orbits and Interplanetary Flight

Basic Calculus of Planetary Orbits and Interplanetary Flight

The Classical Groups and K-Theory

The Classical Groups and K-Theory

Calculus in Context

Calculus in Context

Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups

Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups

Quantitative Risk Management

Quantitative Risk Management

Dictionary of the Old Testament: Pentateuch

Dictionary of the Old Testament: Pentateuch

Multiple Sclerosis and Related Disorders

Multiple Sclerosis and Related Disorders

Mathematical Excursions to the World's Great Buildings

Mathematical Excursions to the World's Great Buildings

Learning Basic Calculus

Learning Basic Calculus

Basic Calculus of Planetary Orbits and Interplanetary Flight

Basic Calculus of Planetary Orbits and Interplanetary Flight

Mathematical Excursions to the World's Great Buildings

Mathematical Excursions to the World's Great Buildings

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