This book has been growing over the years out of several resources. Firstly, the courses in number theory and modern algebra I had occasionally been teaching at UNC Charlotte. Secondly, my interest to invent mathematical problems for competitions, and invent and pose problems for individual work with gifted students. After being forced to retire about two years ago because of health reasons, I did continue to occupy myself with these topics, and I learned more substantially from the work of Gauss on quadratic reciprocity and on the construction of Fermat polygons. Too, I did take up numerical computation with the computer language of Dr. Racket, which is based on Lisp and freely available on the internet.

Number Theory and Modern Algebra Notes: A Personal Approach

Science & Math

Rothe, Franz

Mathematics

iUniverse

Recalling Past Life: About Days Forgotten, Dreams Dreamt, Books Read, and Some Flute Music

This booklet is grown from careless, partly lost notes that had been sent to relatives and classmates several years ago. It dates back to an era before the flood and pandemic and war struck worse than ever. Retired because of my poor eyesight, my interest in literature had awakened, and the exchange seemed worthwhile once more. Thus this little booklet has still been gathered. &#65279;This English translation has been corrected and slightly extended. The older German version is available as an audio-book, together with some flute music. My heartfelt thanks go to everyone involved.

Biographies & Memoirs

Urlink Print & Media, LLC

This booklet is grown from careless, partly lost notes that had been sent to relatives and classmates several years ago. It dates back to an era before the flood and pandemic and war struck worse than ever. Retired because of my poor eyesight, my interest in literature had awakened, and the exchange seemed worthwhile once more. Thus this little booklet has still been gathered. This English translation has been corrected and slightly extended. The older German version is available as an audio-book, together with some flute music. My heartfelt thanks go to everyone involved.

For a regular 17-gon, the formulas above give the x-coordinate of the first vertex in the upper half plane.The first formula goes back to Gauss. The second formula is obtained by a more elementary method, see pages 175 to 180 in this book. This method uses only the trigonometric addition theorem and some clever guesses. 
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.

Number Theory and Modern Algebra: A Personal Approach

Education & Teaching

Schools & Teaching

Word Art Publishing

Recalling Past Life

Scriptor House

Old and New Topics in Geometry: Volume II: Advanced Euclidean and Hyperbolic Geometry

Politics & Social Sciences

Philosophy

Litprime Solutions

Old and New Topics in Geometry: Volume I: Projective, Neutral and Basic Euclidean Geometry

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Books by Rothe, Franz