Orlando Luongo — Associate Professor of Theoretical Physics at the University of Camerino, Italy,
and head of the Cosmology and Theoretical Physics Group.

Fundamental Interactions:
A Roadmap to Classical and Quantum Field Theories

DETAILS
EXPLANATIONS

This book provides a modern and accessible introduction to the fundamental interactions of nature, bridging classical field theory, relativistic quantum mechanics, and quantum field theory. The presentation combines rigorous mathematical derivations with intuitive physical explanations and is designed to support active learning through numerous exercises and discussion problems.

The material is organized into three broad parts:

  1. Classical Field Theory
  2. Quantum Field Theory
  3. Fundamental Interactions

The text is intended primarily for advanced undergraduate and beginning graduate students who already possess a background in classical mechanics, special relativity, and introductory quantum mechanics. It serves as a bridge from standard undergraduate physics to modern quantum field theory and particle physics.

TABLE OF CONTENTS
  1. The Language of Symmetries
  2. Special Relativity
  3. Relativistic Field Theory
  4. Relativistic Quantum Mechanics
  5. Generalities about Classical and Quantum Scattering
  6. Quantum Field Theory
  7. Quantum Field Theory in Action Beyond Its Foundations
  8. Quasiparticles
  9. Electromagnetism
  10. Gravity
  11. Weak Interactions
  12. Strong Interactions
  13. Index
KEY TOPICS COVERED

This book is particularly valuable for readers seeking a single-volume roadmap from classical relativistic physics to modern quantum field theory and the theory of fundamental interactions.


David E. Rowe (historian of mathematics and professor emeritus at the University of Mainz, Germany)

Bernhard Riemann:
His Life and Wondrous Mathematical Legacy

DETAILS
EXPLANATIONS

This book is the first comprehensive scholarly biography devoted to the life and work of the great German mathematician Bernhard Riemann. It combines a detailed account of his personal life with extensive analyses of his mathematical achievements and their lasting influence on modern mathematics and physics.

The narrative follows Riemann's development from his early years through his brief but extraordinarily productive career. Special attention is given to the mathematicians and scientists who shaped his thinking, including Carl Friedrich Gauss, Peter Gustav Lejeune Dirichlet, Carl Gustav Jacob Jacobi, and physicist Wilhelm Eduard Weber.

Drawing on family correspondence and archival sources, the author explores Riemann's health struggles, financial difficulties, intellectual interests, and relationships with colleagues and family members. The book also examines the posthumous publication of his papers and the role played by his widow Elise as well as mathematicians Richard Dedekind and Heinrich Weber in preserving his legacy.

The mathematical chapters discuss Riemann's groundbreaking contributions to:

TABLE OF CONTENTS

Preface

Introduction

Part I — Riemann's Life

Chapter 1. Riemann's Formative Years, 1826–1847

Chapter 2. Years of Adventure, 1848–1853

Chapter 3. Years of Struggle, 1854–1858

Chapter 4. Triumph and Tragedy, 1859–1866

Part II — Riemann's Works

Chapter 5. Riemann's Doctoral Dissertation

Chapter 6. Riemann's Habilitation Texts

Chapter 7. Elliptic and Abelian Functions

Chapter 8. Zeta-Function and Paris Paper

Chapter 9. Mathematical Physics

Chapter 10. Gaussian Influences

Part III — Riemann's Legacy

Chapter 11. Riemann's Pupils and Followers

Chapter 12. Editing Riemann's Collected Works

SIGNIFICANCE OF THE BOOK

The book is noteworthy because it combines historical biography with detailed mathematical exposition. It not only reconstructs Riemann's life but also explains how his ideas transformed modern mathematics, influencing fields such as Riemannian geometry, analytic number theory, topology, and mathematical physics. It is written for historians of science, mathematicians, graduate students, and readers interested in the development of nineteenth-century mathematics.


Edited by Bharath Sriraman

Handbook of Visual, Experimental and Computational Mathematics:
Bridges through Data

DETAILS
EXPLANATIONS

This handbook explores the interaction between visual mathematics, experimental mathematics, and computational mathematics, emphasizing the central role of data in modern mathematical discovery and communication. It shows how advances in computing power, algorithms, visualization techniques, and data analysis have transformed both pure and applied mathematics.

The volume demonstrates how computational experiments and visualizations can lead to new mathematical insights, conjectures, proofs, and applications. It covers topics ranging from theoretical mathematics to real-world applications in epidemiology, climate science, ecology, information theory, music, social sciences, machine learning, and sports analytics.

The handbook is intended for:

A distinctive feature of the book is its emphasis on data as a bridge connecting theory, computation, experimentation, and visualization. The contributors illustrate how mathematical ideas can be explored and communicated through computational tools and graphical representations.

TABLE OF CONTENTS

The complete table of contents has not yet been publicly released, but currently announced chapters include:

  1. Introduction to Experimental Mathematics
  2. Computational Aspects of Totally Disconnected Locally Compact Groups
  3. Experimental Mathematics and the Post-secondary Visualization Toolbox: Mathematics, History, and the Visual
  4. Data-Informed Modeling of the Formation, Persistence, and Evolution of Social Norms and Conventions
  5. Visualization of Convergence Behavior of a Generalized Newton Method and Levenberg–Marquardt Algorithm
  6. Working Out Counterexamples in Convex Geometry
  7. Computational Mathematics and Music: Optimising Frequency Modulation
  8. Instance Space Analysis for Visualization of Algorithmic Trust
  9. Computational Convex Analysis
MAJOR THEMES COVERED
ABOUT THE EDITOR

Bharath Sriraman is Professor of Mathematics at the University of Montana. His research spans mathematics, creativity, cognition, philosophy of mathematics, and mathematics education. He has edited numerous major reference works, including the Handbook of the Mathematics of the Arts and Sciences and the Handbook of the History and Philosophy of Mathematical Practice.

This handbook is expected to become a major reference source for researchers interested in the growing role of computation, experimentation, and visualization in contemporary mathematics.

Yisong Yang — Professor of Mathematics at New York University,
known for research in mathematical physics, partial differential equations, and applied mathematics.

Lectures on Mathematical Statistics

DETAILS
  • Title: Lectures on Mathematical Statistics
  • Author: Yisong Yang
  • Publisher: Springer Nature Switzerland AG
  • ISBN: 9783032273772
  • Format: Hardcover
  • Language: English
  • Publication Date: July 22, 2026
  • Pages: Approximately 255–256 pages
  • Subject Areas: Mathematical Statistics, Probability Theory, Statistical Inference, Bayesian Statistics, Regression Analysis, Logistic Regression.
EXPLANATIONS

This book presents a concise yet rigorous introduction to the foundations of mathematical statistics. It integrates probability theory with modern statistical inference, leading the reader from fundamental sampling concepts through estimation, hypothesis testing, Bayesian methods, and regression analysis.

The author emphasizes mathematical clarity and conceptual understanding rather than a purely formula-driven approach. Major theorems are carefully proved or justified, and each lecture contains examples and exercises designed to reinforce theoretical ideas.

The text is organized as 15 lectures, each intended for one or two class sessions. This structure makes the book suitable for:

  • Advanced undergraduate students
  • Beginning graduate students
  • Researchers needing a refresher in statistical inference
  • Practitioners seeking a mathematically rigorous treatment of statistics.

A key feature of the book is its unified treatment of classical and Bayesian inference, together with both parametric and nonparametric methods. The exposition aims to bridge the gap between elementary probability courses and more advanced statistical theory.

TABLE OF CONTENTS

Chapter 1. Basic Facts, Concepts, and Ideas

  • Foundations of statistical reasoning
  • Basic probability concepts
  • Statistical models and inference.

Chapter 2. Sampling Theory

  • Random sampling
  • Sampling distributions
  • Statistical populations and samples.

Chapter 3. Confidence Intervals

  • Estimation methods
  • Construction and interpretation of confidence intervals.

Chapter 4. Confidence Intervals for Variance

  • Variance estimation
  • Chi-square methods and interval construction.

Chapter 5. Nonparametric Inference

  • Distribution-free methods
  • Rank-based procedures.

Chapter 6. Hoeffding's Inequality and Related Topics

  • Concentration inequalities
  • Applications in statistical theory.

Chapter 7. Methods of Parametric Inference

  • Maximum likelihood estimation
  • Classical inferential techniques.

Chapter 8. Asymptotic Normality and Fisher Information

  • Large-sample theory
  • Information measures
  • Efficiency of estimators.

Chapter 9. Hypothesis Testing: Concepts, Formalism, and Methods

  • Neyman–Pearson framework
  • Test statistics
  • Type I and Type II errors.

Chapter 10. Hypothesis Testing Involving Two Populations

  • Two-sample tests
  • Comparative inference methods.

Chapter 11. Bayes' Method of Estimation

  • Bayesian inference
  • Prior and posterior distributions
  • Bayesian estimators.

Chapter 12. Regression and Correlation

  • Linear regression
  • Correlation coefficients
  • Statistical relationships.

Chapter 13. Bivariate Normal Regression and Correlation Analysis

  • Bivariate normal distributions
  • Correlation structure
  • Regression modeling.

Chapter 14. Logistic Regression and Applications

  • Binary-response models
  • Logistic regression theory
  • Practical applications.

Chapter 15. Brief Overview of Some Further Topics of Interest

  • Selected advanced topics
  • Directions for further study.
MATHEMATICAL TOPICS COVERED
  • Probability Theory
  • Sampling Theory
  • Statistical Inference
  • Confidence Intervals
  • Hypothesis Testing
  • Parametric Statistics
  • Nonparametric Statistics
  • Bayesian Statistics
  • Fisher Information
  • Asymptotic Theory
  • Regression Analysis
  • Correlation Analysis
  • Logistic Regression
  • Mathematical Foundations of Data Science and Machine Learning.

This book is particularly suitable for readers seeking a mathematically rigorous one-semester course text that connects probability theory with modern statistical inference in a clear lecture-based format.


Edited by János Pach and Géza Tóth.

New Probes into Discrete and Convex Geometry

DETAILS
EXPLANATIONS

This volume originated from the 2023 special semester on Discrete Geometry and Convexity held at the Erdős Center of the Alfréd Rényi Institute in Budapest. It brings together 17 invited survey articles written by leading experts in the field.

The book surveys some of the most active areas of modern discrete and convex geometry, including:

Rather than being a textbook, the volume serves as a research survey collection, offering accessible introductions to current research frontiers while highlighting important open problems and recent breakthroughs. It is aimed at graduate students, researchers, and specialists interested in geometry, combinatorics, topology, and theoretical computer science.

TABLE OF CONTENTS

Chapter 1. Efficient Triangulations of Manifolds

Chapter 2. Short Path and Short Chain Problems in the Plane

Chapter 3. On Separability in Discrete Geometry

Chapter 4. The Brascamp–Lieb Inequality in Convex Geometry and in the Theory of Algorithms

Chapter 5. Chromatic Topological Data Analysis

Chapter 6. Free Sets in Planar Graphs: History and Applications

Chapter 7. Lattice and Non-lattice Piercing of Axis-Parallel Rectangles

Chapter 8. Why Do Adjacent Crossings Matter?

Chapter 9. Helly-Type Problems in Convexity Spaces

Chapter 10. Centroids and Equilibrium Points of Convex Bodies

Chapter 11. Using the KKM Theorem

Chapter 12. New Combinatorial Challenges and Variations Arising from Tverberg’s Theorem

Chapter 13. Helly-Type Problems from a Topological Perspective

Chapter 14. No-Dimensional Tverberg-Type Problems

Chapter 15. On Flotation, Stability and Related Questions: A Survey

Chapter 16. A Survey of Zarankiewicz Problems in Geometry

Chapter 17. Coloring Geometric Hypergraphs: A Survey

KEY MATHEMATICAL TOPICS

This volume provides an excellent overview of the state of the art in discrete and convex geometry and serves as a valuable reference for researchers seeking both broad surveys and open problems in the field.