Elements of Mathematics
by John C. Stillwell · first published 2016
100% recommend
Why HN recommends it
Surveys elementary and advanced mathematics from Euclid to Gödel, showing how topics like groups and classical problems connect; a more understanding alternative to purely technical texts for post-high-school readers.
Summarised by Claude from recommending comments
Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary." Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits. From Gaussian
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Seems similar to John Stillwell's classic Elements of Mathematics: From Euclid to Gödel - https://press.princeton.edu/books/hardcover/9780691171685/el... It has one chapter each for Arithmetic, Computation, Algebra, Geometry, Calculus, Combinatorics, Probability, Logic.…
on “Six Math Essentials” ↗You might find the couple of books that i mention in my other comments here useful; Concepts of Modern Mathematics by Ian Stewart - https://store.doverpublications.com/products/9780486284248 Elements of Mathematics: From Euclid to Gödel by John Stillwell - https://press.princeton.edu/books/hardcover/9780691171685/el... Both of them give a nice tour of various domains within modern mathematics and their inter-relationships…
on “Six Math Essentials” ↗…Mathematics by Jeremy Kun is wide ranging and appropriate if there is also interest in programming. Nature and Growth of Modern Mathematics by Edna Kramer is a wonderful book if history is a passion as well. Elements of Mathematics by John Stillwell is a broad overview of subjects. It has a crisp mathematical feel to it. Vector Calculus, Linear Algebra, and Differential Forms by John & Barbara Hubbard is a beautiful introduction…
on “Ask HN: Recommend a maths book for a teenager?” ↗…worth the money. 2) Mathematics: Its Content, Methods and Meaning by Aleksandrov, Kolmogorov et al. - Absolutely brilliant overview of Basic Mathematics. Published by Dover and hence very affordable. 3) Elements of Mathematics: From Euclid to Gödel by John Stillwell - Written as sort of an update to the great Felix Klein's Elementary Mathematics from an Advanced Standpoint books. The Topics are particularly well chosen given…
on “Basic Math Textbook: The Napkin Project” ↗The revised Stuart edition nothing is changed except Stewart has added a preface, and a 37 page chapter "Recent Developments". John Stillwell also has a good survey book "Elements of Mathematics From Euclid to Gödel"
on “A View of Mathematics (2005) [pdf]” ↗…intuitions and scenarios to solve mathematical problems. Pask - Magnificent Principia. Tour of newtons principia that includes both newtons geometric language and modern vector calculus version. Stillwell - Elements of Mathematics. Discusses some important classical problems in the history of mathematics taken from 8 subjects: arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, logic. Wow! Yandell…
on “Classic Mathematics Books for Lifelong Learners” ↗The book "Elements of Mathematics: From Euclid to Gödel" by Stillwell does this in terms of identifying what is considered advanced in a survey of elementary math topics and showing how they fit together or don't, like how Groups drop…
on “The Map of Mathematics [video]” ↗…in exploring all later material. Technical Mathematics with Calculus by Calter is a single volume that covers stuff up through calculus in a, well, technical manner. For a more understanding way, try Elements of Mathematics by Stillwell. If you get past Calculus, I recommend Vector Calculus, Linear Algebra, and Differential Forms by Hubbard. It gives an amazingly clear viewpoint on the higher level analysis and algebra…
on “Ask HN: How to self-learn math?” ↗…this; "Dover Publications" might be a good one since they publish a lot of classics particularly if you position this as a modern update to the Engel book. For example; John Stillwell positioned his Elements of Mathematics: From Euclid to Gödel as a sort of modern update to Felix Klein's Elementary Mathematics from an Advanced Standpoint. From the preface; This book grew from an article I wrote in 2008 for the centenary…
on “Online Book: Exploring Mathematics with Python” ↗