Yair Shapira

Quantum Mechanics and Algorithms:
An Algebraic-Geometric Perspective

DETAILS
EXPLANATIONS

This book presents quantum mechanics from an algebraic-geometric perspective, emphasizing the mathematical foundations of the subject through three core disciplines:

  1. Linear Algebra
  2. Calculus
  3. Geometry

Rather than treating quantum mechanics primarily as a physical theory, the author develops the subject through mathematical structures, allowing physical concepts to emerge naturally from geometric and algebraic principles.

Major topics covered include:

The book is intended for readers interested in the intersection of:

TABLE OF CONTENTS

A complete official table of contents was not available in the publisher metadata currently indexed online. However, based on the publisher's summary, the book is organized approximately around the following themes:

  1. Introduction to Quantum Mechanics
  2. Linear Algebra, Calculus, and Geometry Foundations
  3. Algebraic-Geometric Formulation of Quantum Theory
  4. Quantum States and Observables
  5. Entropy and Entanglement Entropy
  6. Angular Momentum
  7. Spin and Polarization
  8. Energy Operators and Symmetry
  9. Quantum Algorithms
  10. Quantum Fast Fourier Transform (QFFT)
  11. Shor's Factoring Algorithm
  12. Quantum Cryptography Applications
  13. Algebraic Treatment of Feynman Diagrams
  14. Programming Quantum Algorithms
  15. Computational Examples and Implementations
ABOUT THE AUTHOR

Yair Shapira received his B.Sc. and M.Sc. in Mathematics from the Hebrew University of Jerusalem and earned a Doctor of Science degree in Applied Mathematics from the Technion – Israel Institute of Technology. He has conducted research at the Technion and at Los Alamos National Laboratory, focusing on numerical algorithms and multigrid methods. He is also the author of several books in mathematical physics and scientific computing.


Yair Shapira — Technion – Israel Institute of Technology, Israel.

Classical and Quantum Mechanics With Lie Algebras (Second Edition)

DETAILS
EXPLANATIONS

This book presents an original approach to learning physics through the language of algebra and geometry, with particular emphasis on Lie algebras as a unifying framework connecting classical mechanics, quantum mechanics, and relativity. The author aims to minimize reliance on advanced mathematical analysis while maintaining mathematical rigor.

A central idea of the book is that many physical theories can be understood naturally through algebraic structures. Starting from Newtonian mechanics, the exposition gradually develops the mathematical tools required to understand modern quantum mechanics and relativistic physics. The only assumed prerequisites are elementary calculus and linear algebra, which are reviewed in a self-contained appendix.

The second edition includes substantial revisions and expansions, especially in the sections on quantum mechanics and symmetry. New material has been added on:

Each chapter contains extensive exercises with solutions, designed to introduce new concepts progressively and reinforce understanding through problem solving.

TABLE OF CONTENTS

A complete official chapter-by-chapter table of contents has not yet been publicly released. However, according to the publisher's description, the book develops the following major topics in sequence:

Part I. Mathematical Foundations

Part II. Classical Mechanics

Part III. Relativity

Part IV. Quantum Mechanics

Part V. Advanced Topics

Part VI. Modern Methods

Appendices

KEY TOPICS COVERED

This book is particularly valuable for students and researchers who want to understand how algebraic structures unify diverse areas of theoretical physics and provide a bridge between classical and quantum descriptions of nature.


Constantin Andrei

Machine Learning Tutorials in Pure Mathematics and Theoretical Physics

DETAILS
EXPLANATIONS

This book aims to introduce machine learning methods within the contexts of pure mathematics and theoretical physics, illustrating how modern AI techniques can be applied to mathematical structures and physical theories.

Based on the currently available publisher records, the book is intended as a tutorial-oriented treatment rather than a specialized research monograph. It is expected to demonstrate how machine learning techniques can assist with:

The work appears to target readers interested in the growing interaction between:

TABLE OF CONTENTS

The complete Table of Contents has not yet been publicly released. Available catalog records currently provide only bibliographic information and do not include chapter titles or a detailed contents list.

Based on the title and publisher description, the book is expected to contain tutorial material related to:

  1. Introduction to Machine Learning
  2. Mathematical Foundations of Learning Algorithms
  3. Neural Networks and Deep Learning
  4. Applications in Pure Mathematics
  5. Symbolic Computation and AI
  6. Machine Learning in Theoretical Physics
  7. Scientific Computing and Data Analysis
  8. Research Case Studies and Computational Experiments

However, these topics should be regarded as inferred themes rather than an official table of contents, since no publisher-issued chapter list is currently available.