[About the product]

ーThe solution of equations embodies the essence of mathematical thinking-

Regarding algebraic solutions of algebraic equations, it is known from Abel's and Galois' theories that algebraic solutions to general quadratic to quartic algebraic equations exist. To date, famous mathematicians such as Euler, Galois, and Lagrange have found various ways to derive this algebraic solution. In this book, we divide algebraic solutions into five major types and explain in detail the algebraic solutions within each category. This is a book that can be enjoyed not only by students in the Faculty of Science, but also by researchers, engineers, and math enthusiasts.



[Contents]

1. Introduction

2. Numbers and Their Definition

3. Various algebraic solutions algebrac equations of 2nd to 4th degree

4. Summary of Solutions for Algebraic Equations of the 2nd to 4th Degree

5．Lagrange-type Expression between Every Root of Algebraic Equations and Linear Sum of Their ALL Roots,and Solutions by Abel of General Algebraic Equations of the 2nd to 4th Degree and of General Algebraic Equations of the 5fh Degree

6. Solutions by Galois of Algebraic Equations of 2nd to 4th Degree

7. Solutions of General Quintic Equations

8. Numerical Analysis of Algebraic Equations

9. Summary of Solutions of Algebraic Equations

10. References and Citations

11. Postscript

12. Indices



[Comments from the Editor]

Although reading this book requires a certain level of mathematical ability, the various solutions are carefully explained using mathematical formulas, making it as enjoyable as listening to a lecture right in front of your eyes. It's fine to think of mathematics as a useful tool, but it's also fun to appreciate the trajectory of thought behind it. Please take a look.



[Author Profile]

Takahisa Furuichi

1965 Graduated from Yokohama National University, Faculty of Engineering, Department of Mechanical Engineering

After working as a researcher at the Japan Automobile Research Institute and as a small and medium-sized enterprise consultant (while completing a doctoral course in mechanical engineering at a graduate school in the Department of Technology and Ecology) at an American university.



the current

Professor Emeritus of EARIST University (Philippines), Professor Emeritus of Samar Science and Technology University (SCST), Doctor of Science (Sc.D.), Doctor of Education Honorary Degree (Pd.D.(hc)); Doctor of Engineering (Ph.D.)