Visual maths book

Question

Background

Even when complex maths get abstract, usually there are helpful visual models. John Wheeler said he couldn't understand some functions without a picture of them. It is in this sense I use the word visual, but not only restricted to functions.

What I mean by concrete

This video is a very good example of what I mean by visual maths.

Typing visual mathematics book google returns a list but I don't know if any would be good.

Also Euler's elements is being rather pleasant.

Question

Is there any book with this kind of approach to maths?

Answer 1

First, two definitions:

Concrete thinking is literal thinking that is focused on the physical world.

Abstract thinking is the ability to think about objects, principles, and ideas that are not physically present.

https://www.goodtherapy.org/blog/psychpedia/concrete-thinking

**

Better you than me to understand what "you" need.

Have you delved into Schaum´s collection?

Category: Science & Math

https://www.mhprofessional.com/catalogsearch/result/index/?cat=49&q=schaum

Category: Engineering & Architecture

https://www.mhprofessional.com/catalogsearch/result/index/?cat=39&q=schaum

Engineering books deal with "natural way of thinking and are related to everyday stuff".

Maybe one in thermodynamics? Or fluid dynamics?

Or https://www.amazon.com/Unofficial-IEEE-Brainbuster-Gamebook-Technically/dp/0780304233

Or https://books.google.pt/books/about/Trigonometric_Delights.html?id=Znnedp6kmRgC&redir_esc=y

Answer 2

You might have a look at Hutz, Am Experimental Introduction to Number Theory. It says,

"This book presents material suitable for an undergraduate course in elementary number theory from a computational perspective. It seeks to not only introduce students to the standard topics in elementary number theory, such as prime factorization and modular arithmetic, but also to develop their ability to formulate and test precise conjectures from experimental data. Each topic is motivated by a question to be answered, followed by some experimental data, and, finally, the statement and proof of a theorem. There are numerous opportunities throughout the chapters and exercises for the students to engage in (guided) open-ended exploration. At the end of a course using this book, the students will understand how mathematics is developed from asking questions to gathering data to formulating and proving theorems.

"The mathematical prerequisites for this book are few. Early chapters contain topics such as integer divisibility, modular arithmetic, and applications to cryptography, while later chapters contain more specialized topics, such as Diophantine approximation, number theory of dynamical systems, and number theory with polynomials. Students of all levels will be drawn in by the patterns and relationships of number theory uncovered through data driven exploration."

Also, Weissman, An Illustrated Theory of Numbers. It says,

"An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history.

"Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights, and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers.

"Data visualizations introduce the reader to open questions and cutting-edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition.

"Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject."