Offers an accessible introduction to combinatorics, infused with Solomon
Golomb’s insights and illuminating examples
Features a conversational style that suits the classroom or independent study
Includes numerous exercises, examples, and solutions that will serve as a
valuable resource for instructors
This textbook offers an accessible introduction to combinatorics, infused with Solomon Golomb’
s insights and illustrative examples. Core concepts in combinatorics are presented with an
engaging narrative that suits undergraduate study at any level. Featuring early coverage of the
Principle of Inclusion-Exclusion and a unified treatment of permutations later on, the structure
emphasizes the cohesive development of ideas. Combined with the conversational style, this
approach is especially well suited to independent study. Falling naturally into three parts, the
book begins with a flexible Chapter Zero that can be used to cover essential background
topics, or as a standalone problem-solving course. The following three chapters cover core
topics in combinatorics, such as combinations, generating functions, and permutations. The
final three chapters present additional topics, such as Fibonacci numbers, finite groups, and
combinatorial structures. Numerous illuminating examples are included throughout, along with
exercises of all levels. Three appendices include additional exercises, examples, and solutions
to a selection of problems. Solomon Golomb’s Course on Undergraduate Combinatorics is ideal
for introducing mathematics students to combinatorics at any stage in their program. There are
no formal prerequisites, but readers will benefit from mathematical curiosity and a willingness
to engage in the book’s many entertaining challenges
Due 2021-06-11
1st ed. 2021, VIII, 464 p.
Hardcover
ISBN 978-3-030-72227-2
Product category : Undergraduate textbook
Mathematics : Combinatorics
Qualitative and Quantitative Studies with Pre-Service Teachers
Interviews regarding epistemological beliefs
Measuring mathematical critical thinking
Epistemological beliefs and critical thinking in pre-service teacher education
Certainty of knowledge
Inductive and deductive justification of knowledge
Epistemological beliefs?i.e. beliefs on the nature of knowledge, its limits, sources, and
justification?play an important role both in everyday life and in learning processes. This book
comprises several studies dealing with such beliefs in the domain of mathematics; amongst
others a qualitative interview study, and quantitative studies for which a new questionnaire has
been developed. In this new instrument, belief position (e.g. “mathematical knowledge is
certain” vs. “uncertain”) and belief argumentation (the way those positions are justified) are
differentiated. Additionally, a test for mathematical critical thinking has been designed. The
results show significant correlations between sophisticated belief argumentations and high
scores in the critical thinking test, but no correlations regarding belief positions.
Due 2021-06-30
1st ed. 2021, XII, 146 p. 12 illus.
Softcover
ISBN 978-3-658-33538-0
Product category : Monograph
Series : Freiburger Empirische Forschung in der Mathematikdidaktik
Mathematics : Mathematics (general)
Develops the foundations, principles, theory, and methods of hypothesis testing
Offers a greatly expanded treatment of multiple hypothesis testing in Volume
I, as well as an introduction to the principle of monotonicity and the problem of testing moment inequalities
Features over 100 new problems, bringing the total to approximately 900 problems across both volumes.
Testing Statistical Hypotheses, 4th Edition updates and expands upon the classic graduate text,
now a two-volume set. The first volume covers finite-sample theory, while the second volume
discusses large-sample theory. A definitive resource for graduate students and researchers
alike, this work grows to include new topics of current relevance. New additions include an
expanded treatment of multiple hypothesis testing, a new section on extensions of the Central
Limit Theorem, coverage of high-dimensional testing, expanded discussions of permutation and
randomization tests, coverage of testing moment inequalities, and many new problems
throughout the text.
Due 2021-07-03
4th ed. 2021, Approx. 440 p.
Hardcover
ISBN 978-3-030-70577-0
Product category : Graduate/advanced undergraduate textbook
Series : Springer Texts in Statistics
Statistics : Statistical Theory and Methods
Develops the foundations, principles, theory, and methods of hypothesistesting
Offers a greatly expanded treatment of multiple hypothesis testing in Volume
I, as well as an introduction to the principle of monotonicity and the problem
of testing moment inequalities
Features over 100 new problems, bringing the total to approximately 900
problems across both volumes.
Testing Statistical Hypotheses, 4th Edition updates and expands upon the classic graduate text,
now a two-volume set. The first volume covers finite-sample theory, while the second volume
discusses large-sample theory. A definitive resource for graduate students and researchers
alike, this work grows to include new topics of current relevance. New additions include an
expanded treatment of multiple hypothesis testing, a new section on extensions of the Central
Limit Theorem, coverage of high-dimensional testing, expanded discussions of permutation and
randomization tests, coverage of testing moment inequalities, and many new problems
throughout the text.
Due 2021-07-03
4th ed. 2021, Approx. 440 p.
Hardcover
ISBN 978-3-030-70577-0
Product category : Graduate/advanced undergraduate textbook
Series : Springer Texts in Statistics
Statistics : Statistical Theory and Methods
Presents the latest research on model order reduction of complex dynamical
systems
Features contributions from leading researchers and users of model order
reduction techniques
Offers an ideal resource for graduate students and researchers in all areas of
model reduction, as well as those working in applied mathematics and
theoretical informatics
This contributed volume presents some of the latest research related to model order reduction
of complex dynamical systems with a focus on time-dependent problems. Chapters are written
by leading researchers and users of model order reduction techniques and are based on
presentations given at the 2019 edition of the workshop series Model Reduction of Complex
Dynamical Systems ? MODRED, held at the University of Graz in Austria. The topics considered
can be divided into five categories: system-theoretic methods, such as balanced truncation,
Hankel norm approximation, and reduced-basis methods; data-driven methods, including
Loewner matrix and pencil-based approaches, dynamic mode decomposition, and kernel-based
methods; surrogate modeling for design and optimization, with special emphasis on control
and data assimilation; model reduction methods in applications, such as control and network
systems, computational electromagnetics, structural mechanics, and fluid dynamics; and model
order reduction software packages and benchmarks. This volume will be an ideal resource for
graduate students and researchers in all areas of model reduction, as well as those working in
applied mathematics and theoretical informatics
Due 2021-07-30
1st ed. 2021, X, 395 p. 24 illus.
Hardcover
ISBN 978-3-030-72982-0
Product category : Contributed volume
Series : International Series of Numerical Mathematics
Mathematics : Numerical Analysis
Pages: 274
ISBN: 978-1-80061-027-9 (hardcover)
Based on ideas first published in Geometry of Time-Spaces: Non-commutative Algebraic Geometry Applied to Quantum Theory (World Scientific, 2011), Olav Arnfinn Laudal proposes a Toy Model as a Theory of Everything, starting with the notion of the Big Bang in Cosmology, modelled as the non-commutative deformation of a thick point. From this point, the author shows how to extract reasonable models for both General Relativity and Quantum Theory. This book concludes that the universe turns out to be the 6-dimensional Hilbert scheme of pairs of points in affine 3-space. With this in place, one may develop within the model much of the physics known to the reader. In particular, this theory is applicable to the concept of Dark Matter and its effects on our visual universe.
Hence, Mathematical Models in Science proves the dependency of deformation theory in Mathematical Physics and summarises the development of physical applications of pure mathematics developed in the twentieth century.
Introduction
Dynamics
Non-commutative Algebraic Geometry
The Dirac Derivation and Dynamical Structures
Time-space and Space-times
Entropy
Cosmology, Cosmos and Cosmological Time
The Universe as a Versal Base Space
Worked out Formulas
Summing up the Model
Particles, Fields and Probabilities
Interactions
Comparing the Toy Model with the Standard Model
End Words
Bibliography
This book is of value to researchers in most fields of mathematics and theoretical physics and will be an excellent starting point for a PhD or Post Doc in these fields. Will act as a base for research seminars in mathematical physics and non-commutative algebraic geometry.
Series on Knots and Everything
Pages: 200
ISBN: 978-981-123-386-9 (hardcover)
Cosmology, the study of the universe, arouses a great deal of public interest, with serious articles both in the scientific press and in major newspapers, with many of the theories and concepts (e.g. the "big bang" and "black holes") discussed, often in great depth.
Accordingly the book is divided into three parts:
Part 1: The whole story presented as far as possible for a nontechnical reader
Part 2: The same story, told again but for a reader with some technical knowledge
Part 3: Appendices with full technical details of several of the important topics covered.
Part 1 is readable (and understandable) by anyone with a nodding acquaintance with the basic language of cosmology: events, lights paths, galaxies, black holes and so on. It covers the whole story of the book in a way as untechnical as possible given the scope of the topics covered.
Part 2 covers the same ground again but with enough technical details to satisfy a reader with basic knowledge of mathematics and/or physics.
Part 3 consists of appendices which are referred to in the other parts and which also contain the highly technical material omitted from Section 2.
Part 1:
From the Greeks to Einstein
Einstein, Relativity, Model Building and de Sitter
The Biggest Blunder, the Standard Model, Dark Matter, Quasars
Part 2:
Sciama's Principle
The Rotation Curve
Quasars
Spiral Structure
Observations
Cosmology
Part 3:
Appendix A: Introduction to Relativity
Appendix B: De Sitter Space
Appendix C: Quasars: Technical Material
Appendix D: Local Stellar Velocities
Appendix E: Optical Distortion in the Hubble Ultra-Deep Field
Appendix F: Gamma Ray Bursts
Graduates in science or mathematics, general readership with interest in cosmology and the universe, advanced textbook suitable for postgraduate course.
Pages: 1700
ISBN: 978-981-123-701-0 (hardcover)
The book is devoted to the subject of quantum field theory. It is divided into two volumes. The first volume can serve as a textbook on main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation.
The second edition is extended by additional material, mostly concerning the impact of noncommutative geometry on theories beyond the standard model of particle physics, especially the possible role of torsion in the context of the dark matter problem. Furthermore, the text includes a discussion of the Randall-Sundrum model and the Seiberg-Witten equations.
Volume 1:
Clasical Relativistic Field Theory: Kinematical Aspects
Classical Relativistic Field Theory: Dynamical Aspects
Relativistic Quantum Field Theory: Operator Methods
Nonrelativistic Quantum Mechanics: Functional Integral Methods
Relativistic Quantum Field Theory: Functional Integral Methods
Quantum Field Theory at Nonzero Temperature
Volume 2:
Symmetries and Canonical Formalism
Gauge Symmetries and Constrained Systems
Weyl Quantization
Anomalies in Quantum Field Theory
Noncommutative Geometry
Quantum Groups
Noncommutative Geometry and Quantum Groups
Advanced undergraduate and graduate students, researchers in particle physics, theoretical physics, and mathematical physics.