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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.
Document from the Internet Archive. (Opens as external PDF)
Details page in the Internet Archive. (Opens external website)
“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.”
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
Click here to read Precalculus Prerequistes a.k.a. ‘Chapter 0’
Click here to read Precalculus, version 3
This website provides an unbelievable amount of knowledge about algebra, including calculus and the required knowledge to master it.
If you’re interested, I suggest starting with the Prerequisites a.k.a. ‘Chapter 0’ and then going to Precalculus.
Click here to read Mathematics Made Difficult, by Carl E. Linderholm
A book of complicated proofs for simple math problems.
Understated; can break your brain.
Click here to read “Book of Proof”, by Richard Hammack
This website provides an unbelievable amount of knowledge about algebra, including calculus and the required knowledge to master it.
You can visit the website in order to learn more and to
“The Industrial Revolution and its consequences have been a disaster for the human race. They have greatly increased the life-expectancy of those of us who live in “advanced” countries, but
they have destabilized society, have made life unfulfilling, have subjected human beings to indignities, have led to widespread psychological suffering (in the Third World to physical suffering as well) and have inflicted severe damage on the natural world. The continued development of technology will worsen the situation. It will certainly subject human beings to greater indignities and inflict greater damage on the natural world, it will probably lead to greater social disruption and psychological suffering, and it may lead to increased physical suffering even in “advanced” countries.”
According to the University of Davis, “[this] essay first appeared appeared in The New York Times and The Washington Post on Sept 19, 1995. It was published under the pseudonym FC, for Freedom Club. “
You can read the book in the following links.
Read from the UC Davis website (PDF) https://web.cs.ucdavis.edu/~rogaway/classes/188/materials/Industrial%20Society%20and%20Its%20Future.pdf
Read from The Washington Post (site) https://www.washingtonpost.com/wp-srv/national/longterm/unabomber/manifesto.text.htm
