Christoph Borgers's Books

An Introduction to Modeling Neuronal Dynamics

By: Christoph Börgers

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An Introduction to Modeling Neuronal Dynamics

By: Christoph Börgers

This book is intended as a text for a one-semester course on Mathematical and Computational Neuroscience for upper-level undergraduate and beginning graduate students of mathematics, the natural sciences, engineering, or computer science. An undergraduate introduction to differential equations is more than enough mathematical background. Only a slim, high school-level background in physics is assumed, and none in biology. Topics include models of individual nerve cells and their dynamics, models of networks of neurons coupled by synapses and gap junctions, origins and functions of population rhythms in neuronal networks, and models of synaptic plasticity. An extensive online collection of Matlab programs generating the figures accompanies the book.

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Page Count

445

Publisher

Springer

Published Date

ISBN 10

3319511718

ISBN 13

9783319511719

Introduction to Numerical Linear Algebra

By: Christoph Börgers

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Introduction to Numerical Linear Algebra

By: Christoph Börgers

This textbook on numerical methods for linear algebra problems presents detailed explanations that beginning students can read on their own, allowing instructors to go beyond lecturing and making it suitable for a “flipped” classroom. The author covers several topics not commonly addressed in related introductory books, including diffusion, a toy model of computed tomography, global positioning systems, the use of eigenvalues in analyzing stability of equilibria, and multigrid methods. A detailed derivation and careful motivation of the QR method for eigenvalues starting from power iteration is also included, as is a discussion of the use of the SVD for grading. Introduction to Numerical Linear Algebra is appropriate for undergraduate and beginning graduate students in mathematics and related fields. It assumes that the reader has taken a course on linear algebra but reviews background as needed. It is intended as a textbook for a one-semester course on numerical linear algebra and provides background and tools for a range of application areas, including data science.

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Page Count

358

Publisher

SIAM

Published Date

ISBN 10

1611976928

ISBN 13

9781611976922

Computational Radiology and Imaging

Therapy and Diagnostics

By: Christoph Börgers,Frank Natterer

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Computational Radiology and Imaging

Therapy and Diagnostics

By: Christoph Börgers,Frank Natterer

The articles collected in this volume are based on lectures given at the IMA Workshop, Computational Radiology and Imaging: Therapy and Diagnostics, March 17-21, 1997. Introductory articles by the editors have been added. The focus is on inverse problems involving electromagnetic radiation and particle beams, with applications to X-ray tomography, nuclear medicine, near infrared imaging, microwave imaging, electron microscopy, and radiation therapy planning. Mathematical and computational tools and models which play important roles in this volume include the X-ray transform and other integral transforms, the linear Boltzmann equation and, for near infrared imaging, its diffusion approximation, iterative methods for large linear and non linear least squares problems, iterative methods for linear feasibility problems, and optimization methods. The volume is intended not only for mathematical scientists and engineers working on these and related problems, but also for non specialists. It contains much introductory expository material, and a large number of references. Many unsolved computational and mathematical problems of substantial practical importance are pointed out.

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Page Count

314

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387987991

ISBN 13

9780387987996

Mathematics of Social Choice

Voting, Compensation, and Division

By: Christoph Borgers

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Mathematics of Social Choice

Voting, Compensation, and Division

By: Christoph Borgers

An accessible exposition of social choices such as selecting a winning competitor, or dividing up resources.

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Page Count

232

Publisher

SIAM

Published Date

ISBN 10

0898716950

ISBN 13

9780898716955

An Introduction to Modeling Neuronal Dynamics

By: Christoph Börgers

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An Introduction to Modeling Neuronal Dynamics

By: Christoph Börgers

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445

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Springer

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ISBN 10

3319511718

ISBN 13

9783319511719

Mathematics of Social Choice

Voting, Compensation, and Division

By: Christoph Borgers

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Mathematics of Social Choice

Voting, Compensation, and Division

By: Christoph Borgers

Mathematics of Social Choice is a fun and accessible book that looks at the choices made by groups of people with different preferences, needs, and interests. Divided into three parts, the text first examines voting methods for selecting or ranking candidates. A brief second part addresses compensation problems wherein an indivisible item must be assigned to one of several people who are equally entitled to ownership of the item, with monetary compensation paid to the others. The third part discusses the problem of sharing a divisible resource among several people. Mathematics of Social Choice can be used by undergraduates studying mathematics and students whose only mathematical background is elementary algebra. More advanced material can be skipped without any loss of continuity. The book can also serve as an easy introduction to topics such as the Gibbard-Satterthwaite theorem, Arrow's theorem, and fair division for readers with more mathematical background.

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Page Count

233

Publisher

SIAM

Published Date

ISBN 10

0898717620

ISBN 13

9780898717624

Computational Radiology and Imaging

Therapy and Diagnostics

By: Christoph Börgers,Frank Natterer

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Computational Radiology and Imaging

Therapy and Diagnostics

By: Christoph Börgers,Frank Natterer

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Solve jigsaw puzzle

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Page Count

314

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387987991

ISBN 13

9780387987996

Book's by Christoph Borgers

An Introduction to Modeling Neuronal Dynamics

An Introduction to Modeling Neuronal Dynamics

Introduction to Numerical Linear Algebra

Introduction to Numerical Linear Algebra

Computational Radiology and Imaging

Computational Radiology and Imaging

Mathematics of Social Choice

Mathematics of Social Choice

An Introduction to Modeling Neuronal Dynamics

An Introduction to Modeling Neuronal Dynamics

Mathematics of Social Choice

Mathematics of Social Choice

Computational Radiology and Imaging

Computational Radiology and Imaging

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