Learning – Deathvision

Mathematics is, in short, the study of patterns.

Natural numbers go from one to one, following each other in an ordered pattern, that can be arranged by units, tens, hundreds, as in 532 being just 5 hundreds, 3 tens and 2 units.

Starting from this definition, and with the deliberate mistake of going too fast, you can also group them by pairs, or select specific sets of numbers, like the group of all pair numbers, 2, 4, 6, 8… or, the set of numbers called x such that x is part of the integers and x divided by 2 is also an integer; even further {x|x∈Z,x/2∈Z}.

Reading about math will give you the knowledge to read codes and find meaning in mathematical concepts and notation like the one presented above and many such cases found throughout life.

What Is Mathematics? An Elementary Approach to Ideas and Methods, by Richard Courant, Herbert Robbins

Document from the Internet Archive. (Opens as external PDF)

Details page in the Internet Archive. (Opens external website)

Abstract

“For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person.

Today, unfortunately, the traditional place of mathematics in education is in grave danger.

The teaching and learning of mathematics [have] degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence.

This new edition of Richard Courant’s and Herbert Robbins’s classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.

Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving.

With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.

Brought up to date with a new chapter by Ian Stewart, What is Mathematics?, Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat’s Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved. Formal mathematics is like spelling and grammar–a matter of the correct application of local rules. Meaningful mathematics is like journalism–it tells an interesting story. But unlike some journalism, the story has to be true.

The best mathematics is like literature–it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature–it opens a window onto the world of mathematics for anyone interested to view.”

Document from the Internet Archive.

Details page in the Internet Archive.

Stitz-Zeager Open Source Mathematics

Visit Stitz Zeager Open Source Mathematics to access all material discussed in this post.

Link updated February 2026.

Stitz-Zeager offers free, open-source precalculus, algebra, and trigonometry materials designed for both students and educators.

Their Precalculus (3rd Corrected Edition), along with companion volumes like College Algebra and College Trigonometry, are available as free downloadable PDFs. (Click here to download Stitz-Zeager Precalculus, 3rd Corrected Edition free eBook.)

Democratizing education is important and making basic concepts in mathematics as accessible and approachable as possible is a major challenge that is being presented with better solutions every day.

Knowledge as a shared resource is a philosophy that ensures constant evolution and actualization of ideas and practices remains within reach of everyone.

Visit Stitz Zeager Open Source Mathematics.

Download the book on Prerequisites, “Chapter 0”, to be reviewed before reading Precalculus. https://www.stitz-zeager.com/ch_0_links.pdf

Read Precalculus. https://www.stitz-zeager.com/szprecalculus07042013.pdf