CurvedLand is an applet for showing what the world would look like with different geometry. It is named CurvedLand in tribute to the science fiction novel, Flatland, by Edwin Abbott, which describes the adventures of a two-dimensional being who is visited by a stranger from the third dimension.

One of the central ideas of Einstein's theory of relativity is that space and time curve in response to the matter and energy within them. A curved space is one that doesn't obey the usual laws of Euclidean geometry: the angles of a triangle don't generally add up to 180 degrees, the circumference of a circle isn't pi times the diameter, parallel lines can either converge towards each other or move apart, and so on.

Since the geometry we observe is very close to Euclidean, however, it is hard for most of us to picture what this difference would mean physically. If you draw a circle and a diameter, how could the ratio be anything other than pi? To answer this question, imagine that as you move around in space the shapes of objects appear to distort. This is what happens in curved space. If you draw a circle around yourself and then start walking around it to pace out the circumference, it will look to you like you are walking along a constantly changing ellipse.

CurvedLand illustrates this distortion as it would appear in a two-dimensional curved space. The structure is similar to a mapping program. You can place objects of different shapes in different places in the world and then move around the space to see what they look like from different perspectives.

Foundations of Computation is a free textbook for a one-semester course in theoretical computer science. It has been used for several years in a course at Hobart and William Smith Colleges. The course has no prerequisites other than introductory computer programming. The first half of the course covers material on logic, sets, and functions that would often be taught in a course in discrete mathematics. The second part covers material on automata, formal languages, and grammar that would ordinarily be encountered in an upper level course in theoretical computer science.

This book is directed mainly towards beginning programmers, although it might also be useful for experienced programmers who want to learn something about Java. It is certainly not meant to provide complete coverage of the Java language.

Help! I’m completely new to coding and I need to learn R and RStudio! What do I do?

If you’re asking yourself this question, then you’ve come to the right place! Start with the “Introduction for students” section.

Are you an instructor hoping to use this book in your courses? We recommend reading the “Introduction for students” section first. Then, read the “Introduction for instructors” section for more information on how to teach with this book.
Are you looking to connect with and contribute to ModernDive? Then, read the “Connect and contribute” section for information on how.
Are you curious about the publishing of this book? Then, read the “About this book” section for more information on the open-source technology, in particular R Markdown and the bookdown package.

This record and link is to the website for the book: Statistical Inference via Data Science: A ModernDive into R and the Tidyverse!