about the book
MATHEMATICAL MILESTONES
NATURE, SCIENCE, BUSINESS, COMPUTERS
AND ARTIFICIAL INTELLIGENCE
MATHEMATICAL MILESTONES
NATURE, SCIENCE, BUSINESS, COMPUTERS
AND ARTIFICIAL INTELLIGENCE
The book, Mathematical Milestones, Professor Clement Falbo, PhD, shares many of the interesting historical anecdotes about mathematics. When Archimedes invented calculus in 250 BCE, like the first snows of winter, it didn’t stick, when it was reinvented in the 17th century, it did stick because of its necessity in burgeoning world-wide industrial activity. This time, Rene Descartes (1630), Pierre De Fermat (1635), Bonaventura Cavalieri (1635), Isaac Newton, and Gottfried Leibnitz (1660) and (1670) were given credit. In Falbo’s book we see how new inventions, discoveries and applications in science, engineering, and economics contributed to and benefited from mathematical growth. This book allows reader to engage in the exciting axiom-and-theorem narrative that develops complex numbers, matrices, vectors, and quaternions, all in historical contexts. Professor Falbo provides us with food for thought by hypothesizing that modern mathematics was born when Abstract Algebra was invented, and Non-Euclidean Geometry was discovered in the 1800’s.
-Professor Jean Chan, Mathematics Department, Sonoma State University
Anyone who reads this book will discover interesting new information and fresh perspectives on well- known ideas. The brief calculus chapter by Professor Falbo is exciting and vibrant and even has a proof of the fundamental theorem. A unique feature of this book is the way Clem traces the history of Game Theory and Operations Research from Jiuzhan Suanshu (300 BCE) in China to Seki Kawa (1683 CE) in Japan to Gauss and Jordan in Germany in the 19th Century all the way to Von Neumann, Morgenstern, and Dantzig in the 20th Century. His Chapters on matrix applications and operations research provide a readily accessible introduction to the powerful Simplex Algorithm.
We can see where artificial intelligence originated from the sections of the book that explore logic and game theory. The chapter “A Crisis in Mathematics” in the books last section, describes how Kurt Godel, in 1931 destroyed mathematicians’ dreams of having a discipline that was both comprehensive and consistent.
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about the book
FIRST YEAR CALCULUS AN INQUIRY-BASED LEARNING APPROACH
FIRST YEAR CALCULUS AN INQUIRY-BASED LEARNING APPROACH
“We own the Calculus.” This was a sentiment proclaimed by students who took calculus at the University of Texas as it was taught by Professor R. L. Moore.
This book captures the method which facilitates the teaching of students through Inquiry-Based Learning (IBL). It is based on notes taken by the author as a student of Dr. Moore at the University of Texas, Austin, in 1955. It includes Dr. Moore’s collection of seminal “problems that teach” — designed to stimulate creativity and encourage student presentations of their solutions in the classroom.
The intention of IBL is to minimize or even eliminate lectures by the instructor and to maximize student participation in the learning process. In the classes taught this way, the students take charge and compete to show their classmates how they solved the problems. The great American mathematician Paul Halmos, says: “The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic or Texas Method.” Through the last five or so decades, it has evolved into what is now known as IBL and is being promoted, not only at Texas but through regular classes, summer projects, and workshops at several U. S. Colleges and universities, such as California Polytechnic at San Luis Obispo, University of Nebraska, U.S. Naval Academy, University of Chicago, and other places.
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