available from June 2023
FORMAT: Hardback ISBN: 9781009322171
FORMAT: Paperback ISBN: 9781009322157
LENGTH: 125 pagesDIMENSIONS: 216 x 140 mm
General Linear Model methods are the most widely used in data analysis in applied empirical research. Still, there exists no compact text that can be used in statistics courses and as a guide in data analysis. This volume fills this void by introducing the General Linear Model (GLM), whose basic concept is that an observed variable can be explained from weighted independent variables plus an additive error term that reflects imperfections of the model and measurement error. It also covers multivariate regression, analysis of variance, analysis under consideration of covariates, variable selection methods, symmetric regression, and the recently developed methods of recursive partitioning and direction dependence analysis. Each method is formally derived and embedded in the GLM, and characteristics of these methods are highlighted. Real-world data examples illustrate the application of each of these methods, and it is shown how results can be interpreted.
Introduces the General Linear Model as the basis of many other methods
Illustrates other methods of correlation, regression, and analysis of variance
Accessible to multiple audiences including students, researchers, and practitioners
'This book provides a thorough overview of regression analysis and the analysis of variance and covariance, foundational research methods in social and behavioral sciences. Dr. von Eye and Wiedermann, the authors, have decades of experience training graduate students on these methods and conducting research. Each chapter has a specific learning objective and methodically progresses toward more complex subjects. In addition, the latest methodological developments in causal inference and computationally intensive approaches are well integrated, which should greatly interest any social and behavioral scientists who want to stay abreast of the current state-of-the-art methods. This advanced graduate-level textbook is well-organized, up-to-date, and in-depth while still being understandable, with data examples and key takeaways. As someone involved in training graduate students in social and behavioral sciences, I am excited to use and recommend this book.' Eun-Young Mun, University of North Texas, USA
1. The general linear model
2. OLS parameter estimation
3. Regression analysis
4. Analysis of variance (ANOVA).
available from August 2023
FORMAT: HardbackISBN: 9781009260596
Projective geometry is the geometry of vision, and this book introduces students to this beautiful subject from an analytic perspective, emphasising its close relationship with linear algebra and the central role of symmetry. Starting with elementary and familiar geometry over real numbers, readers will soon build upon that knowledge via geometric pathways and journey on to deep and interesting corners of the subject. Through a projective approach to geometry, readers will discover connections between seemingly distant (and ancient) results in Euclidean geometry. By mixing recent results from the past 100 years with the history of the field, this text is one of the most comprehensive surveys of the subject and an invaluable reference for undergraduate and beginning graduate students learning classic geometry, as well as young researchers in computer graphics. Students will also appreciate the worked examples and diagrams throughout.
Covers a wide range of material in a coherent narrative, including remarkable results in projective geometry that are often excluded from other texts, making this one of the most comprehensive texts on the subject
Starts with elementary material on familiar geometry over real numbers, and builds upon that knowledge via geometric pathways to deep and interesting corners of the subject
Builds the material without delving into axiomatic and logical foundations or studying geometry over arbitrary fields
Emphasises the visual beauty of projective geometry, inspiring readers to dive further into geometry
Preface
Part I. The Real Projective Plane:
1. Fundamental aspects of the real projective plane
2. Collineations
3. Polarities and conics
4. Cross-ratio
5. The group of the conic
6. Involution
7. Affine plane geometry viewed projectively
8. Euclidean plane geometry viewed projectively
9. Transformation geometry: Klein's point of view
10. The power of projective thinking
11. From perspective to projective
12. Remarks on the history of projective geometry
Part II. Two Real Projective 3-Space:
13. Fundamental aspects of real projective space
14. Triangles and tetrahedra
15. Reguli and quadrics
16. Line geometry
17. Projections
18. A glance at inversive geometry
Part III. Higher Dimensions:
19. Generalising to higher dimensions
20. The Klein quadric and Veronese surface
Appendix: Group actions
References
Index.
Copyright 2024
Hardback
ISBN 9781032481128
160 Pages
August 28, 2023 by Chapman & Hall
Aspects of Integration: Novel Approaches to the Riemann and Lebesgue Integrals is comprised of two parts. The first part is devoted to the Riemann integral, and provides not only a novel approach, but also includes several neat examples that are rarely found in other treatments of Riemann integration. Historical remarks trace the development of integration from the method of exhaustion of Eudoxus and Archimedes, used to evaluate areas related to circles and parabolas, to Riemannfs careful definition of the definite integral, which is a powerful expansion of the method of exhaustion and makes it clear what a definite integral really is.
The second part follows the approach of Riesz and Nagy in which the Lebesgue integral is developed without the need for any measure theory. Our approach is novel in part because it uses integrals of continuous functions rather than integrals of step functions as its starting point. This is natural because Riemann integrals of continuous functions occur much more frequently than do integrals of step functions as a precursor to Lebesgue integration. In addition, the approach used here is natural because step functions play no role in the novel development of the Riemann integral in the first part of the book. Our presentation of the Riesz-Nagy approach is significantly more accessible, especially in its discussion of the two key lemmas upon which the approach critically depends, and is more concise than other treatments.
Presents novel approaches designed to be more accessible than classical presentations.
A welcome alternative approach to the Riemann integral in undergraduate analysis courses.
Makes the Lebesgue integral accessible to upper division undergraduate students.
How completion of the Riemann integral leads to the Lebesgue integral.
Contains a number of historical insights.
Gives added perspective to researchers and postgraduates interested in the Riemann and Lebesgue integrals.
I. A Novel Approach to Riemann Integration. 1. Preliminaries. 1.1. Sums of Powers of Positive Integers. 1.2. Bernstein Polynomials. 2. The Riemann Integral. 2.1. Method of Exhaustion. 2.2. Integral of a Continuous Function. 2.3. Foundational Theorems of Integral Calculus. 2.4. Integration by Substitution. 3. Extension to Higher Dimensions. 3.1. Method of Exhaustion. 3.2. Bernstein Polynomials in 2 Dimensions. 3.3. Integral of a Continuous Function. 4. Extension to the Lebesgue Integral. 4.1. Convergence and Cauchy Sequences. 4.2. Completion of the Rational Numbers. 4.3. Completion of C in the 1-norm. II. Lebesgue Integration. 5. Riesz-Nagy Approach. 5.1. Null Sets and Sets of Measure Zero. 5.2. Lemmas A and B. 5.3. The Class C1. 5.4. The Class C2. 5.5. Convergence Theorems. 5.6. Completeness. 5.7. The C2-Integral is the Lebesgue Integral. 6. Comparing Integrals. 6.1. Properly Integrable Functions. 6.2. Characterization of the Riemann Integral. 6.3. Riemann vs. Lebesgue Integrals. 6.4. The Novel Approach. A. Dinis Lemma. B. Semicontinuity. C. Completion of a Normed Linear Space. Bibliography. Index.
Copyright 2023
Hardback
ISBN 9780367183738
168 Pages 8 Color & 7 B/W Illustrations
August 2, 2023 by Chapman & Hall
This book provides a general framework for learning sparse graphical models with conditional independence tests. It includes complete treatments for Gaussian, Poisson, multinomial, and mixed data; unified treatments for covariate adjustments, data integration, and network comparison; unified treatments for missing data and heterogeneous data; efficient methods for joint estimation of multiple graphical models; effective methods of high-dimensional variable selection; and effective methods of high-dimensional inference. The methods possess an embarrassingly parallel structure in performing conditional independence tests, and the computation can be significantly accelerated by running in parallel on a multi-core computer or a parallel architecture. This book is intended to serve researchers and scientists interested in high-dimensional statistics, and graduate students in broad data science disciplines.
A general framework for learning sparse graphical models with conditional independence tests
Complete treatments for different types of data, Gaussian, Poisson, multinomial, and mixed data
Unified treatments for data integration, network comparison, and covariate adjustment
Unified treatments for missing data and heterogeneous data
Efficient methods for joint estimation of multiple graphical models
Effective methods of high-dimensional variable selection
Effective methods of high-dimensional inference
1. Introduction to Sparse Graphical Models 2. Gaussian Graphical Models 3. Gaussian Graphical Modeling with Missing Data 4. Gaussian Graphical Modeling for Heterogeneous Data 5. Poisson Graphical Models 6. Mixed Graphical Models 7. Joint Estimation of Multiple Graphical Models 8. Nonlinear and Non-Gaussian Graphical Models 9. High-Dimensional Inference with the Aid of Sparse Graphical Modeling 10. Appendix
Copyright 2024
Hardback
ISBN 9781032398525
550 Pages 145 Color & 55 B/W Illustrations
August 21, 2023 by Chapman & Hall
This book, for a first undergraduate course in Discrete Mathematics, systematically exploits the relationship between discrete mathematics and computer programming. Unlike most discrete mathematics texts focusing on one of the other, the book explores the rich and important connection between these two disciplines and shows how each discipline reinforces and enhances the other.
The mathematics in the book is self-contained, requiring only a good background in precalculus and some mathematical maturity. New mathematical topics are introduced as needed.
The coding language used is VBA Excel. The language is easy to learn, has intuitive commands, and the reader can develop interesting programs from the outset. Additionally, the spreadsheet platform in Excel makes for convenient and transparent data input and output and provides a powerful venue for complex data manipulation. Manipulating data is greatly simpli?ed using spreadsheet features and visualizing the data can make programming and debugging easier.
The VBA language is seamlessly integrated into the spreadsheet environment with no other resources required. Furthermore, as some of the modules in the book show, intricate patterns, graphs, and animation in the form of moving cells is possible.
Introduces coding in VBA Excel assuming no previous coding experience.
Develops programs in Linear Analysis, Logic, Combinatorics, Probability, and Number Theory.
Contains over 90 fully tested and debugged programs. The code for these is as well as the exercises is available on the author's website.
Contains numerous examples that gradually introduce the reader to coding techniques.
Includes programs that solve systems of linear equations, linear programming problems, combinatorial problems, Venn diagram problems and programs that produce truth tables from logic statements and logic statements from switching and gate circuits, encrypt and decrypt messages and simulate probability experiments.