Author: Norman L. Johnson

Geometry of Derivation, Volume III: Classification of Skewfield Flocks

• Publisher: CRC Press / Routledge
• Publication Date: June 30, 2026
• Format: Hardcover
• Pages: 360
• Language: English
• ISBN-13: 9781041290889

Details

This book is the third volume in the Geometry of Derivation research series and focuses on the classification theory of skewfield flocks in combinatorial and incidence geometry. It studies the relationship between:

• derivable nets,
• translation planes,
• semifields,
• skewfields,
• hyperbolic and conical flocks,
• non-commutative algebraic structures.

The work develops advanced geometric methods for finite and infinite cases and systematically studies flocks over non-commutative division rings.

The book is intended mainly for:

• researchers in finite geometry,
• graduate students in incidence geometry,
• specialists in combinatorics and algebraic geometry.

Explanation / Description

According to the publisher description, the book:

“establishes the techniques, examples, and future directions of the specifics of flock theory over skewfields.”

Major themes include:

• classification of skewfield flocks,
• translation planes over non-commutative skewfields,
• generalized hyperbolic quadrics,
• generalized quadratic cones,
• semifield extensions,
• automorphism groups,
• isomorphism problems,
• Baer flocks and spread theory.

The volume emphasizes a geometric treatment of non-commutative algebra and extends the theory developed in:

1. Geometry of Derivations with Applications (Vol. I, 2023)
2. Geometry of Derivation, Volume II: Theory of Skewfield Flocks (2026).

Table of Contents

Part 1: The Classification of Flocks

1. The Classes of Flocks
2. General Theorems of Flocks
3. The Isomorphism Questions

Part 2: Multiple Replacement−Redux

4. Extension of Division Rings
5. Automorphism Groups of Division Rings
6. The Theorem of Andre’
7. Dickson Nearfield Planes
8. Ostrom’s Theorem

Part 3: Simultaneous Flock Spreads

9. Simultaneous Spreads of Type 2

Part 4: Semifields over Division Rings

10. Twisted T-Copies
11. General Skewfield Lifts to Semifields
12. Central Extensions of Degree 3, 4
13. Central Cyclic Extensions

Part 5: Lifting Skewfields – Degree n

14. General Lifting

Part 6: Kantor-Pentilla and CJV σ–Flokki

15. Transform and CJV-Methods
16. Choices of Representation

Part 7: JPW-Hyperbolic Flocks

17. Idea of “Left-Inversion”

Part 8: Non-Linear Hyperbolic Flocks

18. Adjoining Inner Derivation Functions
19. Resolved Conical Flocks
20. The Isomorphism Questions
21. The Hyperbolic Isomorphism Question

Part 9: The Baer Flocks

22. Draxl's Theorem
23. Transposed Baer Flocks

Part 10: Anti-Isomorphic Flocks

24. The Hyperbolic Flock Square

Part 11: Elation Group Double Covers

25. The Three Spreads of a Double Cover
26. Skew-Desarguesian Spreads
27. Right Skew-Desarguesian Spreads

Part 12: Strings

28. Strings of Quasifibrations and Spreads
29. Corresponding Right “Flocks”

Part 13: Switch and Imposter Switch

30. Derivation of Flock Spreads

Part 14: Baer Groups over Skewfields

31. Point-Baer Subplanes of Planes
32. Baer Collineations in Translation Planes
33. Derived Spreads and Baer Groups
34. Deficiency One Flocks of Order $p^4$
35. $t_o$-Interchange-Hyperbolic Spreads
36. $t_o$-Interchange-Conical Spreads
37. Left Inversing “Minus One”
38. Deficiency One
39. Hyperbolic Skew-Desarguesian Flocks

Part 15: Three Line Problem

40. Do Three Components Define a Pseudo-Regulus?
41. Three Component-Three Point Construction

Part 16: The Flocks and Spreads

42. Anti-Isomorphic Flocks
43. Constructions-Generalized Lifted
44. 1-A Conical Spreads
45. Flocks from Lifted Types
46. The Open Types and New Directions

*

Author: Norman L. Johnson

Geometry of Derivation, Volume II: Theory of Skewfield Flocks

• Publisher: CRC Press / Taylor & Francis
• Publication Date: June 26, 2026
• Format: Hardcover
• Pages: 340
• Language: English
• ISBN-13: 9781041290940

Details

This volume is an advanced research monograph in combinatorial geometry, especially the theory of:

• skewfield flocks,
• derivable nets,
• translation planes,
• semifields,
• non-commutative incidence geometry.

It is the second volume in the Geometry of Derivation series and develops the foundations and structural theory of flocks over skewfields.

The book particularly studies:

• hyperbolic and conical flocks,
• spread constructions,
• quasifibrations,
• semifield planes,
• isomorphism questions,
• non-commutative algebraic geometry,
• derivation theory for affine planes.

Explanation / Description

Publisher descriptions explain that the book:

“is concerned mainly with the theory of flocks over skewfields.”

The text begins by analyzing conditions required to extend:

• flocks of hyperbolic quadrics,
• flocks of quadratic cones,

leading to a revised theory of derivation for affine planes containing derivable nets.

A central feature is the construction of four types of $(i,j)$-determinants used to determine existence conditions for spreads. The book also introduces the:

• left unwrapping principle,
• left/right flock spreads,
• generic and non-generic flocks,
• skewfield lifting methods.

The author emphasizes geometric treatments of:

• non-commutative algebra,
• finite and infinite translation planes,
• incidence structures over skewfields.

The volume continues:

1. Geometry of Derivations with Applications (Vol. I)
2. and precedes Geometry of Derivation, Volume III: Classification of Skewfield Flocks.

Table of Contents

Part 1: When Quasifibrations become Spreads

1. Quasifibrations
2. Unwrapping
3. Twisted Extensions
4. Semifield Planes from Cyclic Algebras
5. Proper Quasifibrations of Dimension 2

Part 2: Skewfield Flocks – A Window

6. The Main Points and Ideas

Part 3: Foundations of Flock Theory

7. Building the Foundation
8. Generic and Non-Generic Flocks

Part 4: Framework for Flock Theory

9. Setting up Flock and Spread Connections

Part 5: Left A Flocks and Spreads

10. Left A-Hyperbolic Flocks
11. Left A-Conical Flocks; 1st and 2nd Main Theorems
12. The Lower Left Form Theory
13. The 1st General Theorem of Flocks over Skewfields

Part 6: Right A** Flocks and Spreads

14. A Hyperbolic Flocks
15. Right A Hyperbolic 1st and 2nd Main Theorems
16. A Right Conical Flocks
17. The Right Upper Form Theory
18. Four “Easy” Problems

Part 7: The Kaleidoscope of Derivable Nets

19. The Conical and Hyperbolic Isomorphism Questions

Part 8: Apps of the Kaleidoscope

20. Resolution and Return-Flock Spreads
21. A Class of Linear 1 Cc Conical Flocks

Part 9: Double Covers

22. The Left Generic Elation Double Nets

Part 10: The Group of Conical Flock Spreads

23. Why Semifields?
24. Omnibus Theorem

Part 11: Quaternion Division Ring Variations

25. 1-A Left Conical Spreads
26. Why Unwrapping?

Part 12: Left Pseudo-Regulus-Inducing Homology Groups and Transposition**

27. Inversing-Right Hyperbolic Spreads

Author: Dhirgham T. Murran

Perspective as Geometry and Design

Publisher: CRC Press / Taylor & Francis
Format: Hardcover
Language: English
Pages: 168
Publication Date: August 2026 (pre-release listings)

DETAILS

The book focuses on the geometry and mathematical foundations of perspective drawing. It is intended for:

• Architects
• Engineers
• Industrial designers
• Interior designers
• Artists and illustrators
• Visual-effects creators
• Students and educators

According to the publisher descriptions, the book introduces both classical and original methods for constructing:

• One-point perspective
• Two-point perspective
• Three-point perspective
• Bird’s-eye and worm’s-eye views
• Vector-based perspective systems

It also includes:

• Camera tilt integration
• Methods for distant vanishing points
• Mechanical construction methods without vanishing points
• Excel/vector equation implementations for 3D projection

EXPLANATION (Summary of the Book)

The author argues that perspective drawing should not be treated only as an artistic technique, but as a rigorous geometric system.

The book is divided into two major parts:

Part 1 — One- and Two-Point Perspective

This section explains:

• Fundamental perspective geometry
• Alternative construction methods
• How to work when vanishing points are outside the drawing area
• Miniature-construction techniques that avoid large drafting layouts

Three of the methods reportedly avoid the traditional “station point” approach used in most perspective manuals.

Part 2 — Three-Point Perspective

This section introduces:

• Original methods for three-point construction
• Height-determination systems
• Camera tilt geometry
• Extreme-angle perspective solutions

The author emphasizes simplified geometric procedures instead of older complex systems involving tilted plans and overlapping elevations.

TABLE OF CONTENTS

The most complete TOC currently available online is:

1. Elements of Perspective Drawing
2. Perspective Structure
3. Perspective Methods
4. Applications
5. Far Objects and Miniatures
6. Perspective Vector Equations
7. Fundamentals of Three-Point Perspective
8. Three-Point Perspective Methods
9. Advanced Applications
10. Vector Equations with the Tilt Angle
11. Mechanical Method
    
    

Author: Erik Wallace

Linear Algebra by Example: An Active Approach

Publisher: CRC Press / Taylor & Francis
Language: English
Format: Hardcover
Pages: 440
Publication Date: August 2026

DETAILS

This textbook is designed as a modern, activity-based introduction to linear algebra for undergraduate students in:

• Mathematics
• Engineering
• Computer Science
• Physics and related sciences

The book emphasizes:

• Symmetry
• Transformations
• Mathematical structure

rather than rote matrix computation alone. It is built for:

• active-learning classrooms,
• flexible course pacing,
• and self-study.

Key educational features include:

• Modular chapter organization
• Dependency flowcharts at the beginning of chapters
• Gradual introduction to proofs
• Classroom-tested activities
• Integrated SageMath and Python explorations
• AI-assisted learning prompts
• Real-world applications such as:
  • ray tracing,
  • molecular symmetry,
  • structural engineering

EXPLANATION (What the Book Is About)

Unlike many traditional linear algebra textbooks that begin heavily with matrix operations and abstract proofs, this book uses an example-driven and exploratory approach.

The author aims to help students:

• build intuition first,
• understand geometric meaning,
• and gradually develop formal mathematical reasoning.

The structure is intentionally flexible:

• instructors can skip or rearrange sections,
• students with different backgrounds can progress at different speeds,
• and proofs are introduced through guided examples instead of dense formalism.

The pedagogical style resembles:

• inquiry-based learning,
• active learning,
• and computational exploration.

Programming tools like Python and SageMath are integrated to help students visualize and experiment with:

• vector spaces,
• transformations,
• eigenvalues,
• orthogonality,
• and applications.

TABLE OF CONTENTS

A complete official TOC is not yet publicly available online, but publisher previews indicate the book covers topics such as:

1. Systems of Linear Equations
2. Matrices and Matrix Operations
3. Vector Geometry
4. Vector Spaces
5. Linear Transformations
6. Determinants
7. Eigenvalues and Eigenvectors
8. Orthogonality
9. Inner Product Spaces
10. Applications in Science and Engineering
11. Computational Linear Algebra with Python/SageMath
12. Advanced Explorations and Projects
    
    
    

    Authors: Reinaldo B. Arellano-Valle & Marc G. Genton

    Multivariate Statistics Beyond Normality

    Publisher: CRC Press / Chapman & Hall
    Language: English
    Format: Hardcover
    Pages: 400
    Publication Date: September 11, 2026

    ---

    DETAILS

    This book is an advanced statistics textbook and research-oriented reference focused on multivariate statistical distributions beyond the classical normal (Gaussian) framework.

    It covers:

    • multivariate normal theory,
    • spherical and elliptical distributions,
    • skew-normal and skew-elliptical models,
    • weighted and selection distributions,
    • Bayesian and frequentist applications.

    The authors are internationally known researchers in:

    • multivariate analysis,
    • skew distributions,
    • elliptical distributions,
    • and robust statistical modeling.

    Key Features

    According to publisher descriptions, the book includes:

    • over 100 illustrative examples,
    • about 150 exercises,
    • 40 open research problems,
    • unified treatment of singular and nonsingular cases,
    • color-coded learning highlights,
    • modern theoretical developments,
    • practical data-analysis applications beyond normality.

    ---

    EXPLANATION (What the Book Is About)

    Traditional multivariate statistics often assumes data follow the multivariate normal distribution:

    $X \sim N_p(\mu,\Sigma)$

    However, many real-world datasets exhibit:

    • skewness,
    • heavy tails,
    • asymmetry,
    • outliers,
    • non-elliptical behavior.

    This book studies statistical models that generalize normal theory to handle such phenomena.

    The progression of the book reportedly moves from:

    1. classical multivariate distributions,
    2. symmetry concepts,
    3. elliptical distributions,
    4. skew-normal theory,
    5. unified skew-elliptical families,
    6. practical statistical applications.

    The text is designed for:

    • graduate students,
    • statisticians,
    • data scientists,
    • quantitative researchers,
    • and researchers in probability theory.

    A major contribution of the book is its unified framework for skew distributions, especially:

    $SUN_{p,q}(\xi,\Omega,\Delta,\gamma,\Gamma)$

    which refers to the Unified Skew-Normal (SUN) family discussed extensively in modern multivariate theory.

    The book also reportedly includes unpublished material related to elliptical distributions from the first author's PhD research.

    ---

    TABLE OF CONTENTS

    A detailed TOC available from retailer listings is:

    1. Preface
    2. Multivariate Distributions
    3. Some Notions of Multivariate Symmetry
    4. The Multivariate Normal Distribution
    5. Multivariate Spherical and Elliptical Distributions
    6. The Multivariate Skew-Normal Distribution
    7. The Multivariate Unified Skew-Normal Distribution
    8. The Multivariate Unified Skew-t Distribution
    9. Multivariate Unified Skew-Elliptical Distributions
    10. Weighted and Selection Multivariate Distributions
    11. Data Applications Beyond Normality
    12. Appendix: Linear Algebra
    13. Index

    ---

    Academic Level and Intended Audience

    This is likely suitable for:

    • advanced undergraduate mathematics/statistics students,
    • graduate-level statistics courses,
    • researchers in multivariate analysis,
    • Bayesian statistics researchers,
    • quantitative finance and machine learning researchers.

    The mathematical level appears to include:

    • linear algebra,
    • matrix calculus,
    • probability theory,
    • distribution theory,
    • statistical inference
      
      
      
      

      Authors: Hisham Sati and Urs Schreiber

      Geometric Orbifold Cohomology

      Publisher: CRC Press / Chapman & Hall
      Publication Date: September 2026
      Format: Hardcover
      Pages: 344
      Language: English

      ---

      DETAILS

      This is an advanced research monograph in:

      • algebraic topology,
      • differential geometry,
      • higher category theory,
      • mathematical physics,
      • and quantum field/string theory.

      The book develops a modern theory of orbifold cohomology using:

      • higher topos theory,
      • nonabelian cohomology,
      • differential cohomology,
      • and cohesive homotopy theory.

      Its main physical motivations include:

      • topological phases of quantum materials,
      • topological insulators,
      • M-brane charges in M-theory,
      • and quantum gravity.

      A central theme is that generalized cohomology theories on orbifolds can describe physical charges and topological quantum structures.

      The book reportedly bridges:

      • classical equivariant topology
        and
      • modern higher-geometric methods.

      ---

      EXPLANATION (What the Book Is About)

      The classical notion of cohomology studies global geometric/topological structure of spaces.

      For example:

      $H^n(X;\mathbb{Z})$

      But modern physics often requires:

      • singular spaces,
      • orbifolds,
      • gauge fields,
      • higher symmetries,
      • and twisted geometric structures.

      This book develops a generalized framework for these settings.

      A key conceptual object is the orbifold:

      • a space locally modeled by quotient symmetries.

      Symbolically:

      $X/G$

      where a group $G$ acts on a space $X$.

      The authors extend ordinary cohomology into:

      • twisted,
      • nonabelian,
      • differential,
      • and equivariant versions.

      The framework uses modern tools such as:

      • higher stacks,
      • ∞-groupoids,
      • cohesive ∞-toposes,
      • modal operators,
      • and synthetic differential geometry.

      The book especially emphasizes:

      • geometric singularities,
      • orbifold K-theory,
      • twisted cohomotopy,
      • and applications to condensed matter and string theory.

      One highlighted application is:

      • classification of topological phases in quantum materials.

      The mathematical level is highly advanced and intended mainly for:

      • graduate students,
      • researchers,
      • mathematical physicists,
      • and advanced algebraic topologists.

      ---

      TABLE OF CONTENTS

      A complete official TOC is not yet publicly available, but available descriptions and draft references indicate the book contains material on:

      1. Foundations of Orbifold Cohomology
      2. Topological Groupoids and Stacks
      3. Twisted Nonabelian Orbifold Cohomology
      4. Orbifold K-Theory
      5. Cohesive Higher Topos Theory
      6. Global Equivariant Homotopy Theory
      7. Synthetic Orbifold Geometry
      8. Higher Orbifold Cartan Geometry
      9. Differential Cohomology
      10. Tangentially Twisted Cohomology
      11. J-Twisted Orbifold Cohomotopy
      12. Applications to M-Theory and Quantum Materials
      13. Topological Insulators and Topological Phases
      14. Proper Equivariant Homotopy Types
      15. Modal Operators in Higher Geometry