The World of Mathematics

Four volumes, edited by James Newman, published by Simon and Schuster, New York, 1956.

James Newman was an extraordinary man. He was a lawyer and, during WW2, was Chief Intelligence Officer at the US Embassy in London. After the war, among other things, he became a member of the board of editors for Scientific American.

The format of the four volumes is:

  • a topic, such as “The Mathematics of Infinity”
  • a commentary by James Newman
  • a selection of essays on the topic by the mathematicians: Edmund Halley; Jacob Bernoulli; Sir Ronald Fisher; Sir Arthur Eddington; Bertrand Russell; Charles Sanders Peirce.

It is not a light read. It does not skate over a topic. If you read Hans Hahn’s essay on Infinity, you come away with a good understanding of Cantor’s proof of an infinite number of infinities.

Republished by Dover Publications:

ISBN-13: 978-0486411538

ISBN-13: 978-0486411507

ISBN-13: 978-0486411514

ISBN-13: 978-0486411521

GeoGebra Dynamic Mathematics Software


“GeoGebra is dynamic mathematics software for all levels of education that brings together geometry, algebra, spreadsheets, graphing, statistics and calculus”.

Open source. Works online, on the desktop, and as an app.

This software is useful for creating your own objects to achieve a better understanding of mathematical concepts.

Example: Coordinate Geometry


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Calculus for Beginners and Artists: Prof. Daniel Kleitman, MIT

Professor Daniel Kleitman, Emeritus Professor of Applied Mathematics at MIT

Calculus for Beginners and Artists

From Chapter 1 What is Calculus and Why do we Study it? “Calculus is the study of how things change. It provides a framework for modeling systems in which there is change, and a way to deduce the predictions of such models…It provides a way for us to construct relatively simple quantitative models of change, and to deduce their consequences.”

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The Open University: MathsChoices

The Open University: distance learning in the UK

Faculty of Science, Technology, Engineering & Mathematics

MathsChoices: the choices available to study Mathematics by distance learning.

To understand much about modern science requires a reasonable level of mathematics. Without some appreciation of the mathematics, the explanations are incomprehensible. The difficulty for many of us is that we dropped sciences and mathematics because they were too hard to understand at the speed required to complete a curriculum. I don’t doubt that, given enough time and good materials, an educated person could eventually understand enough. But if that time were more time than required to complete a curriculum, then it is probably a non-starter.

How to improve your mathematics

MIT: Big Picture of Calculus

MIT Open Courseware

Big Picture of Calculus

“Calculus is about change. One function tells how quickly another function is changing. Professor Strang of MIT shows how calculus applies to ordinary life situations.”

Follow the links to find textbook and study guide.

Calculus is required to find any properties of an orbit, for example where an object will be at a given time, or how fast it is travelling at a given position.