Core reading recommendations

From Cognito
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The books here are intellectually engaging and enriching, but do not require you to work through a lot of details while reading them, so you can read them without paper and pencil.

Unless otherwise stated, books are generally accessible to reasonably academically talented high school students with an interest in the relevant subjects, and also to highly precocious middle school students. However, we would recommend reading a few sample chapters of the books (generally available for free download) to see if the difficulty level is suitable before you buy the book.

Mathematics

Book Author ISBN and purchase links Why we're recommending it
Mathematics: A Very Short Introduction Timothy Gowers ISBN 978-0192853615, Amazon purchase ??
The Mathematical Experience Philip J. Davis, Reuben Hersh ISBN 978-0395929681, Amazon purchase The book provides excellent insight into the kind of work that mathematicians do, without requiring the readers to grasp a lot of mathematics.

Statistics and applications to data analysis

Book Author ISBN and purchase links Difficulty level Why we're recommending it
The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century David Salsburg ISBN 978-0805071344 Provides a historical overview of the important developments in statistics and the statistical way of thinking.
Naked Statistics: Stripping the Dread from the Data Charles Wheelan ISBN 978-0393347777 (paperback), Amazon link Explores statistics concepts through a number of simple real-world examples.
The Signal and the Noise: Why So Many Predictions Fail-but Some Don't Nate Silver ISBN 978-0141975658 (paperback), Amazon paperback, Amazon Kindle Explores ideas from statistics and data analysis with the specific goal of understanding the art and science of predicting the future.

Economics