# [[ read online ]] Elements of Mathematics: From euclid to Gödel Author John Stillwell – Andy-palmer.co.uk

this book provides an advanced discussion about elementary mathematics Primarily, the author has tried to partition math into two buckets elementary vs advanced Secondly, uncovers known and hidden linkages connecting different branches of math Third, every chapter ends with a historic overview.Pretty solid and comprehensive on all three counts Great read for anyone trying to do a full review of all their math education and gain a lot of new insights as well. As someone who has taken many advanced calculus and introductory probability courses many years ago, I found the coverage of these and related subjects and of Euclid s Elements quite good In several cases, particularly infinite series, the book clarified some mysteries I never did understand as a student.On the negative side, I fault the book format, i.e., being an image of pages and not a digital Kindle, made reading very difficult at times In particular figures were often discussed on one or rwo pages prior Plus the author s use of notation sometimes assumed the reader was reading the book in one or two sittings not the case for me. This is a great introduction to central issues in core areas of elementary mathematics, and the ties that connect them Stillwell doesn t dumb things down while eminently readable, this book gets into the weeds of formalism and proof quite quickly There is content of value even for people with advanced mathematical background in particular, I found Stillwell s musing on the division between elementary and advanced mathematics quite illuminating Especially appreciated are the remarks on historical and philosophical matters that Stillwell uses to contextualize otherwise highly abstract areas in mathematics. Like all books from Stillwell, it is a well structured and written book with a treasure trove of things I teach a course teaching math from a historical perspective now for the 8th time which has a similar scope a panoramic view over many different topics in math I had used an other book from Stillwell mathematics and its history before for that class The elements would be even better suited Every chapter finishes with a section on philosophical remarks and a section with historical remarks Part of the book goes further than any other book for a general audience examples are reverse mathematics or the Koenig infinity lemma The book will definitely enrich any course with a broader scope. 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 Integers To Propositional Logic, Stillwell Delves Into Arithmetic, Computation, Algebra, Geometry, Calculus, Combinatorics, Probability, And Logic He Discusses How Each Area Ties Into Advanced Topics To Build Mathematics As A Whole Through A Rich Collection Of Basic Principles, Vivid Examples, And Interesting Problems, Stillwell Demonstrates That Elementary Mathematics Becomes Advanced With The Intervention Of Infinity Infinity Has Been Observed Throughout Mathematical History, But The Recent Development Of Reverse Mathematics Confirms That Infinity Is Essential For Proving Well Known Theorems, And Helps To Determine The Nature, Contours, And Borders Of Elementary Mathematics Elements Of Mathematics Gives Readers, From High School Students To Professional Mathematicians, The Highlights Of Elementary Mathematics And Glimpses Of The Parts Of Math Beyond Its Boundaries