Developed from a course on the history of mathematics, the book is aimed at school teachers of mathematics who need to learn more about mathematics than its history, and in a way they can communicate to middle and high school students. The author hopes to overcome, through these teachers using this book, math phobia among these students.
Developed from a course on the history of mathematics, the book is aimed at school teachers of mathematics who need to learn more about mathematics than its history, and in a way they can communicate to middle and high school students. The author hopes to overcome, through these teachers using this book, math phobia among these students.
Dr. J. S. Chahal is a professor of mathematics at Brigham Young University. He earned a PhD from Johns Hopkins University. After spending a couple of years at the University of Wisconsin as a postdoc, he joined Brigham Young University as an assistant professor and has been there ever since. He specializes in and has published several papers in number theory. For hobbies, he likes to travel and hike. His books, Fundamentals of Linear Algebra, and Algebraic Number Theory, are also published by CRC Press.
Inhaltsangabe
I Arithmetic 1 What is a Number? 1.1 Various Numerals to Represent 2 Arithmetic in Different Bases 3 Arithmetic in Euclid's Elements 4 Gauss-Advent of Modern Number Theory 4.1 Number Theory of Gauss 4.2 Cryptography 4.3 Complex Numbers 4.4 Application of Number Theory - Construction of Septadecagon 4.5 How Did Gauss Do It? 4.6 Equations over Finite Fields* 4.7 Law of Quadratic Reciprocity* 4.8 Cubic Equations* 4.9 Riemann Hypothesis* 5 Numbers beyond Rationals 5.1 Arithmetic of Rational Numbers 5.2 Real Numbers II Geometry 6 Basic Geometry 7 Greece: Beginning of Theoretical Mathematics 8 Euclid: The Founder of Pure Mathematics 8.1 Some Comments on Euclid's Proof 9 Famous Problems from Greek Geometry III Contributions of Some Prominent Mathematicians 10 Fibonacci's Time and Legacy 10.1 Liber Abaci 10.2 Liber Quadratorum 10.3 Equivalent Formulations of the Problems 11 Solution of the Cubic 11.1 Introduction 11.2 History 12 Leibniz, Newton, and Calculus 12.1 Differential Calculus 12.2 Integral Calculus 12.3 Proof of FTC 12.4 Application of FTC 13 Euler and Modern Mathematics 13.1 Algebraic Number Theory 13.2 Analytical Number Theory 13.3 Euler's Discovery of e¿i + 1 = 0 13.4 Graph Theory and Topology 13.5 Traveling Salesman Problem 13.6 Planar Graphs 13.7 Euler-Poincaré Characteristic 13.8 Euler Characteristic Formula 14 Non-European Roots of Mathematics 15 Mathematics of the 20th Century* 15.1 Hilbert's 23 Problems 1 Riemann Hypothesis 2 Poincaré Conjecture 3 Birch & Swinnerton-Dyer (B&S-D) Conjecture 15.2 Fermat's Last Theorem 15.3 Miscellaneous
I Arithmetic 1 What is a Number? 1.1 Various Numerals to Represent 2 Arithmetic in Different Bases 3 Arithmetic in Euclid's Elements 4 Gauss-Advent of Modern Number Theory 4.1 Number Theory of Gauss 4.2 Cryptography 4.3 Complex Numbers 4.4 Application of Number Theory - Construction of Septadecagon 4.5 How Did Gauss Do It? 4.6 Equations over Finite Fields* 4.7 Law of Quadratic Reciprocity* 4.8 Cubic Equations* 4.9 Riemann Hypothesis* 5 Numbers beyond Rationals 5.1 Arithmetic of Rational Numbers 5.2 Real Numbers II Geometry 6 Basic Geometry 7 Greece: Beginning of Theoretical Mathematics 8 Euclid: The Founder of Pure Mathematics 8.1 Some Comments on Euclid's Proof 9 Famous Problems from Greek Geometry III Contributions of Some Prominent Mathematicians 10 Fibonacci's Time and Legacy 10.1 Liber Abaci 10.2 Liber Quadratorum 10.3 Equivalent Formulations of the Problems 11 Solution of the Cubic 11.1 Introduction 11.2 History 12 Leibniz, Newton, and Calculus 12.1 Differential Calculus 12.2 Integral Calculus 12.3 Proof of FTC 12.4 Application of FTC 13 Euler and Modern Mathematics 13.1 Algebraic Number Theory 13.2 Analytical Number Theory 13.3 Euler's Discovery of e¿i + 1 = 0 13.4 Graph Theory and Topology 13.5 Traveling Salesman Problem 13.6 Planar Graphs 13.7 Euler-Poincaré Characteristic 13.8 Euler Characteristic Formula 14 Non-European Roots of Mathematics 15 Mathematics of the 20th Century* 15.1 Hilbert's 23 Problems 1 Riemann Hypothesis 2 Poincaré Conjecture 3 Birch & Swinnerton-Dyer (B&S-D) Conjecture 15.2 Fermat's Last Theorem 15.3 Miscellaneous
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