Explore Author's Collection.
01
Title
Recollected material taught at UNC Charlotte, and material newly researched, and my CDs with flute music.
Classics in Graphic Theory
This book is a tour through the classics in graph theory, including
Eulerian and Hamiltonian graphs, trees, many algorithms, graph coloring, planar graphs, celebrated problems about cubic graphs and more. The book contains detailed proofs and many solved problems and colored figures.
It recollects both material taught at UNC Charlotte, and material newly researched.
Number Theory and Modern Algerbra
This book is a our through topics from number theory and modern algebra, including the Chinese remainder theorem, quadratic reciprocity and geometric construction of the regular 17, 257 and even the 65 537-gon, Galo is theory, and more. The book contains detailed proofs and many numerical examples with computer code.
My Invitation to Mathematical Problems
My Invitation to Mathematical Problems: Computation, Solutions, Proof, and Insights” is an engaging mathematical book that offers a unique approach to the world of mathematics. Dr. Franz Rothe invites readers to explore a wide range of mathematical problems, guiding them through computations, providing solutions, and offering valuable insights into the underlying concepts. The book is designed to inspire and challenge both novice and experienced mathematicians, making it a compelling resource for those who want to delve deeper into the beauty of mathematical problem-solving
Recalling Past Life
This booklet originated from personal notes the author had shared with relatives and classmates several years ago, predating major crises like floods, pandemics, and war. In retirement, the author’s revived interest in literature led to the thoughtful compilation of these writings. The booklet includes an English translation that has been improved and extended. Additionally, there is an audio version in the original German, accompanied by flute music. The author expresses sincere thanks to all those who contributed to this project
Old and New Topics in Geometry, Volume 1
This first volume explores the fundamentals of geometry, starting with Hilbert’s axioms from the “Foundations of Geometry.” It covers logic, axioms, incidence geometries, and dimensions in affine and projective geometry. The text investigates axioms of order, congruence, measurement, and completeness, with a unique focus on circles. It also delves into the independence of the parallel axiom and introduces the uniformity theorem for classifying Hilbert planes. The volume concludes with a simplified examination of Euclidean geometry, featuring Thales’ theorem, Euclid’s theorems, and key principles like the Pythagorean theorem and trigonometry.
Old and New Topics in Geometry, Volume 2
This extensive work draws upon a decade of experience teaching “Fundamentals of Geometry.” The first volume covers Hilbert’s axioms and essential Euclidean, projective, and neutral geometry topics, featuring numerous exercises with solutions and computer-generated drawings.
The second volume delves into advanced Euclidean geometry, offering a comprehensive exploration of hyperbolic geometry using Poincaré and Klein disk models. It also explains Hilbert’s axiomatic approach, with a final section providing a brief course on Gauss’ differential geometry and the pseudo-sphere concept.
