My Invitation to Mathematical Problems: Computations, Solutions, Proofs and Insights

by Franz Rothe

It turned out to be a challenge to write a book like this one, keeping about the same level of difficulty through the entire text. In the end, here is a text which poses somewhat increasing difficulty, as one turns its pages. The topics come from a variety of fields of mathematics and even physics,  

and much impact is given to computation with mathematica. Some basic important theorem which are used in mathematics again and again are stated without proof. The intention is not to give any textbook. Instead, it is my hope to keep alive the interest of a broader group of young and older readers, who are not mainly concerned to dig themselves into a single field of speciality. Too, the reader will realize that I was not able to solve all problems. The intention is to show a somewhat realistic and honest picture of the working mathematician. This intention implies not to hide all awkward looking explicit calculations, and even more important, not to hide all failures. 

In the end the main purpose of the book is to sharpen the mathematical abilities of the reader, and my own ones, too, -while keeping an equilibrium of entertainment and challenge.

233 pages, Kindle Edition

Published May 28, 2024

Reviews

[Michael Doane · Rating 5 out of 5]

I just dropped a review for My Invitation to Mathematical Problems: Computations, Solutions, Proofs and Insights, and it’s a fascinating and refreshingly honest exploration of mathematics that blends problem-solving, computation, theory, and intellectual curiosity. Franz Rothe presents mathematics not as a rigid, polished discipline, but as a dynamic, human process filled with challenge, discovery, and even occasional failures, exactly the kind of authenticity that makes this book stand out.

What I particularly appreciate is the steady increase in difficulty as the reader progresses, paired with a diverse selection of topics that span multiple areas of mathematics and even physics. Thehttps://www.goodreads.com/review/new/...# integration of Mathematica computations adds an extra layer of depth and makes the learning experience more hands-on. Rothe’s willingness to show unfinished attempts, awkward calculations, and the reality of trial-and-error gives the reader valuable insight into how real mathematicians think and work.

More than anything, this book succeeds in sharpening problem-solving skills while maintaining a strong balance between entertainment and challenge. It’s a rewarding and intellectually stimulating read for anyone who enjoys diving into mathematical thinking, whether young learners, lifelong students, or professionals who simply love the craft.

[Eleanor Pilcher · Rating 5 out of 5]

My Invitation to Mathematical Problems is a rare and refreshing exploration of mathematics that combines rigor, honesty, and intellectual curiosity. Franz Rothe’s text challenges readers with a carefully calibrated progression of problems, covering multiple areas of mathematics and even physics, while remaining accessible to both students and lifelong learners.

What makes this book stand out is the author’s candid approach. Rothe doesn’t hide the awkward calculations or unsolved problems, offering a genuine glimpse into the working mind of a mathematician. This honesty makes the book not only educational but inspiring, it encourages readers to embrace the process of problem-solving, celebrate small victories, and persist through challenges.

The blend of computation, theoretical insight, and Mathematica applications makes it ideal for readers eager to sharpen their skills while enjoying a balance of challenge and entertainment. A stimulating resource for anyone who loves mathematics and intellectual exploration.