Gilbert Helmberg's Books

Introduction to Spectral Theory in Hilbert Space

North-Holland Series in Applied Mathematics and Mechanics

By: Gilbert Helmberg

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Introduction to Spectral Theory in Hilbert Space

North-Holland Series in Applied Mathematics and Mechanics

By: Gilbert Helmberg

North-Holland Series in Applied Mathematics and Mechanics, Volume 6: Introduction to Spectral Theory in Hilbert Space focuses on the mechanics, principles, and approaches involved in spectral theory in Hilbert space. The publication first elaborates on the concept and specific geometry of Hilbert space and bounded linear operators. Discussions focus on projection and adjoint operators, bilinear forms, bounded linear mappings, isomorphisms, orthogonal subspaces, base, subspaces, finite dimensional Euclidean space, and normed linear spaces. The text then takes a look at the general theory of linear operators and spectral analysis of compact linear operators, including spectral decomposition of a compact selfadjoint operator, weakly convergent sequences, spectrum of a compact linear operator, and eigenvalues of a linear operator. The manuscript ponders on the spectral analysis of bounded linear operators and unbounded selfadjoint operators. Topics include spectral decomposition of an unbounded selfadjoint operator and bounded normal operator, functions of a unitary operator, step functions of a bounded selfadjoint operator, polynomials in a bounded operator, and order relation for bounded selfadjoint operators. The publication is a valuable source of data for mathematicians and researchers interested in spectral theory in Hilbert space.

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Page Count

362

Publisher

Elsevier

Published Date

ISBN 10

1483164179

ISBN 13

9781483164175

Getting Acquainted with Fractals

By: Gilbert Helmberg

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Getting Acquainted with Fractals

By: Gilbert Helmberg

The first instance of pre-computer fractals was noted by the French mathematician Gaston Julia. He wondered what a complex polynomial function would look like, such as the ones named after him (in the form of z2 + c, where c is a complex constant with real and imaginary parts). The idea behind this formula is that one takes the x and y coordinates of a point z, and plug them into z in the form of x + i*y, where i is the square root of -1, square this number, and then add c, a constant. Then plug the resulting pair of real and imaginary numbers back into z, run the operation again, and keep doing that until the result is greater than some number. The number of times you have to run the equations to get out of an 'orbit' not specified here can be assigned a colour and then the pixel (x,y) gets turned that colour, unless those coordinates can't get out of their orbit, in which case they are made black. Later it was Benoit Mandelbrot who used computers to produce fractals. A basic property of fractals is that they contain a large degree of self similarity, i.e., they usually contain little copies within the original, and these copies also have infinite detail. That means the more you zoom in on a fractal, the more detail you get, and this keeps going on forever and ever. The well-written book 'Getting acquainted with fractals' by Gilbert Helmberg provides a mathematically oriented introduction to fractals, with a focus upon three types of fractals: fractals of curves, attractors for iterative function systems in the plane, and Julia sets. The presentation is on an undergraduate level, with an ample presentation of the corresponding mathematical background, e.g., linear algebra, calculus, algebra, geometry, topology, measure theory and complex analysis. The book contains over 170 color illustrations.

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Page Count

189

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110206617

ISBN 13

9783110206616

Getting Acquainted with Fractals

By: Gilbert Helmberg

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Getting Acquainted with Fractals

By: Gilbert Helmberg

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189

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110206617

ISBN 13

9783110206616

Introduction to Spectral Theory in Hilbert Space

North-Holland Series in Applied Mathematics and Mechanics

By: Gilbert Helmberg

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Introduction to Spectral Theory in Hilbert Space

North-Holland Series in Applied Mathematics and Mechanics

By: Gilbert Helmberg

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362

Publisher

Elsevier

Published Date

ISBN 10

1483164179

ISBN 13

9781483164175

Human Incompetence

Confessions of a Psychologist

By: Thomas F. Gilbert

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Human Incompetence

Confessions of a Psychologist

By: Thomas F. Gilbert

Thomas Gilbert (1927-1995) was a psychologist who is often referred to as the founder of the field of performance technology, also known as Human Performance Technology (HPT). He never completed this autobiography. Clearly, he was still on a journey of discovery with numerous unfinished manuscripts in draft awaiting final revision and publication. Tom's own words introduce his story best. "...I had studied all there was to be known about human learning and that field was a complete mess. I felt I was going to have to do with it what Descartes had done with philosophy, start all over from scratch...Just before going my own way to reconstruct all of psychology...I sat down with [B.F.] Skinner's first book, "The Behavior of Organisms". This was about 1955, and I was a young assistant professor at the University of Georgia. I've never been the same since." While going through a number of storage boxes several years ago, Marilyn Gilbert, Tom's wife of twenty-seven years, found his unfinished autobiography. This book is that work, untouched, which provides intriguing insight into a man who has been referred to as one of the top three most brilliant American psychologists of the twentieth century."--publisher description.

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Page Count

259

Published Date

ISBN 10

0937100218

ISBN 13

9780937100219

Book's by Gilbert Helmberg

Introduction to Spectral Theory in Hilbert Space

Introduction to Spectral Theory in Hilbert Space

Getting Acquainted with Fractals

Getting Acquainted with Fractals

Getting Acquainted with Fractals

Getting Acquainted with Fractals

Introduction to Spectral Theory in Hilbert Space

Introduction to Spectral Theory in Hilbert Space

Human Incompetence

Human Incompetence

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