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Author: James E. Duane
Publisher: Educational Technology
ISBN: 9780877780434
Category : Education
Languages : en
Pages : 448
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Book Description
Author: James E. Duane
Publisher: Educational Technology
ISBN: 9780877780434
Category : Education
Languages : en
Pages : 448
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Book Description
Author: Richard S. Millman
Publisher: Springer Science & Business Media
ISBN: 9780387974125
Category : Mathematics
Languages : en
Pages : 394
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Book Description
Geometry: A Metric Approach with Models, imparts a real feeling for Euclidean and non-Euclidean (in particular, hyperbolic) geometry. Intended as a rigorous first course, the book introduces and develops the various axioms slowly, and then, in a departure from other texts, continually illustrates the major definitions and axioms with two or three models, enabling the reader to picture the idea more clearly. The second edition has been expanded to include a selection of expository exercises. Additionally, the authors have designed software with computational problems to accompany the text. This software may be obtained from George Parker.
Author: Rhonda Douglas Brown
Publisher: Springer
ISBN: 3319764098
Category : Psychology
Languages : en
Pages : 155
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Book Description
This book examines the neuroscience of mathematical cognitive development from infancy into emerging adulthood, addressing both biological and environmental influences on brain development and plasticity. It begins by presenting major theoretical frameworks for designing and interpreting neuroscience studies of mathematical cognitive development, including developmental evolutionary theory, developmental systems approaches, and the triple-code model of numerical processing. The book includes chapters that discuss findings from studies using neuroscience research methods to examine numerical and visuospatial cognition, calculation, and mathematical difficulties and exceptionalities. It concludes with a review of mathematical intervention programs and recommendations for future neuroscience research on mathematical cognitive development. Featured neuroscience research methods include: Functional Magnetic Resonance Imaging (fMRI). Diffusion Tensor Imaging (DTI). Event Related Potentials (ERP). Transcranial Magnetic Stimulation (TMS). Neuroscience of Mathematical Cognitive Development is an essential resource for researchers, clinicians and related professionals, and graduate students in child and school psychology, neuroscience, educational psychology, neuropsychology, and mathematics education.
Author: Gisbert Wüstholz
Publisher: Princeton University Press
ISBN: 0691193770
Category : Mathematics
Languages : en
Pages : 186
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Book Description
Arithmetic and Geometry presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures—which were delivered in celebration of the tenth anniversary of the annual summer workshops in Alpbach, Austria—provide an introduction to high-level research on three topics: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings height and L-functions. The book consists of notes, written by young researchers, on three sets of lectures or minicourses given at Alpbach. The first course, taught by Peter Scholze, contains his recent results dealing with the local Langlands conjecture. The fundamental question is whether for a given datum there exists a so-called local Shimura variety. In some cases, they exist in the category of rigid analytic spaces; in others, one has to use Scholze's perfectoid spaces. The second course, taught by Umberto Zannier, addresses the famous Pell equation—not in the classical setting but rather with the so-called polynomial Pell equation, where the integers are replaced by polynomials in one variable with complex coefficients, which leads to the study of hyperelliptic continued fractions and generalized Jacobians. The third course, taught by Shou-Wu Zhang, originates in the Chowla–Selberg formula, which was taken up by Gross and Zagier to relate values of the L-function for elliptic curves with the height of Heegner points on the curves. Zhang, X. Yuan, and Wei Zhang prove the Gross–Zagier formula on Shimura curves and verify the Colmez conjecture on average.
Author: Volker Schmidt
Publisher: Springer
ISBN: 3319100645
Category : Mathematics
Languages : en
Pages : 484
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Book Description
This volume is an attempt to provide a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, with special emphasis placed on fundamental classes of models and algorithms as well as on their applications, e.g. in materials science, biology and genetics. This book has a strong focus on simulations and includes extensive codes in Matlab and R which are widely used in the mathematical community. It can be seen as a continuation of the recent volume 2068 of Lecture Notes in Mathematics, where other issues of stochastic geometry, spatial statistics and random fields were considered with a focus on asymptotic methods.
Author: John W. Ogle
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 224
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Book Description
Author: S. Bandopadhyay
Publisher: CRC Press
ISBN: 1482283891
Category : Technology & Engineering
Languages : en
Pages : 537
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Book Description
The purpose of the 10th US North American Mine Ventilation Symposium in Anchorage 2004 was to bring together practitioners involved in the planning and operation of underground ventilation systems, to provide a forum for debate and exchange of ideas, and to share information on the advances which have been made and consider problems
Author: André Hoffmann
Publisher: Hoffmann
ISBN: 3340000468
Category : Medical
Languages : en
Pages : 200
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Book Description
André Hoffmann, innovator, researcher and developer, pioneer in the field of optical technologies (photonics), systematically researched the tooth colour and its origin with highest precision (see publication in 2000). This book shows an excerpt of this systematic original research at human teeth and dental shade guides with high-precision measuring systems and high-precision positioning system in vitro. Due to his basic scientific research, he was able to quantify and isolate manifold factors influencing the colour of teeth. These include, for example, the light or measuring light and the type of light (illuminant) and illumination and colour temperature, the optical beam path of the light or the measuring geometry, the observation angle (2°, 10°), the size of the measuring surface, and measuring opening, the gloss, the liquid content (with scientific evidence of the relationship between liquid content and tooth colour), effect of drying, moisture and rehydration, the correlation between the liquid content and the gloss effect, the subjectivity of visual subjective shade matching, crown curvature, type of system (spectrophotometer, tristimulus colorimeter), measuring mode (contact or non-contact), system-object-relation, positioning, repeatability or reproducibility, lens shift, displacement between sample and measuring surface and further intra- and interindividual factors. In addition, subjective-visual determinations and objectified measurements were examined in subjective-objective comparisons using colour coordinates comparisons. All these influencing factors are investigated on moist, drying, drier (various specific dehydration and rehydration states) and dry teeth based on the brightness (L*), on colour measurement values, such as a*, b* (CIELAB), C*, h, (CIELCH), ΔE, on the metamerism index, on spectral values and curves, tabs of dental shade guides and on tooth colour spaces ... As part of this exploration, phenomena (e.g. changes and breaks in behaviour as well as highly individual developments in colour values, paradoxes between the values of subjective determination using shade guides and the values of objective measurements) were identified and insights into the very complex colour dynamics through dehydration and rehydration were shown (up to more than >8 days). The development of the individual colour measurement values was based on the liquid flow through the tooth and its tissues, in particular during drying and rehydration, and gave information about dynamics and the temporal extent of these processes. On the basis of this data, Hoffmann had developed several methods for research and practice, suggestions for feasible innovations, such as monitoring of dental treatment to protect against pulp damage based on drying, and reconstructing the colour of naturally moist teeth on those that have already dried, the identification of the living and the dead, human and animals via the "dental fingerprint" and a novel method of measuring the time of death for forensic medicine. He also described a time limit of drying up to which relatively natural, suitable colour values and shade matching results can be obtained and after which no colour determination should be carried out; and he established the rehydration time after the end of the drying or dental treatment, which must be waited in order to regain a natural tooth colour and to get correct values and results again. His findings also show that teeth are able to store information on, for example, the condition (liquid content, colour values) and the time within the drying and liquid re-absorption chronology. The author articulates a "dental chronometer" ("tooth clock"), "dental data store" ("tooth data store") and a "dental memory" ("tooth memory") and believes that significant progress in this field may include and could be achieved via a neural network for colour measurement apparatus. A book for anyone interested in the natural sciences.
Author: Moreno Andreatta
Publisher: CRC Press
ISBN: 1040156703
Category : Mathematics
Languages : en
Pages : 130
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Book Description
This book introduces path-breaking applications of concepts from mathematical topology to music-theory topics including harmony, chord progressions, rhythm, and music classification. Contributions address topics of voice leading, Tonnetze (maps of notes and chords), and automatic music classification. Focusing on some geometrical and topological aspects of the representation and formalisation of musical structures and processes, the book covers topological features of voice-leading geometries in the most recent advances in this mathematical approach to representing how chords are connected through the motion of voices, leading to analytically useful simplified models of high-dimensional spaces; It generalizes the idea of a Tonnetz, a geometrical map of tones or chords, and shows how topological aspects of these maps can correspond to many concepts from music theory. The resulting framework embeds the chord maps of neo-Riemannian theory in continuous spaces that relate chords of different sizes and includes extensions of this approach to rhythm theory. It further introduces an application of topology to automatic music classification, drawing upon both static topological representations and time-series evolution, showing how static and dynamic features of music interact as features of musical style. This volume will be a key resource for academics, researchers, and advanced students of music, music analyses, music composition, mathematical music theory, computational musicology, and music informatics. It was originally published as a special issue of the Journal of Mathematics and Music.
Author: National Information Center for Special Education Materials
Publisher:
ISBN:
Category : Children with disabilities
Languages : en
Pages : 1108
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Book Description
