{"product_id":"another-sort-of-mathematics-selected-proofs-necessary-to-finally-acquire-an-education-in-mathematics","title":"Another Sort of Mathematics: Selected Proofs Necessary to Finally Acquire an Education in Mathematics by Jacob Tawney","description":"\u003cp\u003eYears ago, James V. Schall wrote \u003cem\u003eAnother Sort of Learning\u003c\/em\u003e, a book listing those things you \u003ci\u003eshould\u003c\/i\u003e read but probably were never \u003ci\u003erequired\u003c\/i\u003e to read. It is not a curriculum, except maybe one \"for life.\" This book you have in your hands is something of a mathematical tribute to Schall's basic idea and is aptly titled \u003cem\u003eAnother Sort of Mathematics. \u003c\/em\u003eLike Schall's book, it is not a curriculum. It is, however, a list of some things from mathematics you should experience but probably were never required to experience. The theorems and proofs in this book represent, in a small way, some of the best that has been said within the discipline of mathematics.\u003c\/p\u003e\n\u003cp\u003eThere is something unique in the human soul that can only be satisfied by wondering about mathematics. And that means, regardless of your background, this book is for you. Reclaim your mathematical inheritance. Embrace the mathematician within you. Choose to wonder.\u003c\/p\u003e\n\u003ctable border=\"0\" align=\"center\" cellpadding=\"2\" cellspacing=\"2\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eIntroduction\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003eix\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003ePart I\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eThe Nature of Mathematics\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 1\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eWhy Mathematics Is Worth Knowing\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e3\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 2\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eWhat Is Mathematics?\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e15\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 3\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eThe Quest for a Better Mathematics Curriculum\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e27\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 4\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eWarm-Up: A Mysterious Fact About the Angles in a Triangle\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e35\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003ePart II\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eTen Proofs Everyone Ought to Know\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 1\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eWhich Regular Polygons Tile the Plane?\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e45\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 2\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eThe Platonic Solids\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e57\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 3\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eThe Pythagorean Theorem\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e71\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 4\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eThe Existence of Irrational Numbers\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e83\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 5\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eIrrational Decimals\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e89\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 7\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eHow Many Prime Numbers Are There?\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e103\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 8\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eThe Fundamental Theorem of Arithmetic\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e113\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 9\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eHow Many Irrational Numbers Are There?\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e119\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 10\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eThe Seven Bridges of Konigsberg\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e137\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003ePart III\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eTen Theorems Worth Knowing, Though the Proofs are Difficult\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 1\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eIs an Irrational Number\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e149\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 2\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eThe Area of a Circle\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e157\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 3\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eThe Independence of the Parallel Postulate\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e163\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 4\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eImpossible Constructions\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e173\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 5\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eA Formula for the Fibonacci Numbers\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e183\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 6\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eThe Fundamental Theorem of Algebra\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e191\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 7\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eEuler's Identity\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e199\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 8\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eThe Prime Number Theorem\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e207\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 9\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eFermat's Last Theorem\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e217\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 10\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eGodel's Incompleteness Theorems\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e225\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003ePart IV\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eTen Unsolved Problems Worth Knowing\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 1\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eThe Perfect Brick\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e243\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 2\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eThe Napkin Folding Problem\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e251\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 3\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eThe Twin Prime Conjecture\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e259\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 4\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eThe Goldbach Conjecture\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e265\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 5\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eThe Quest for a Formula That Generates Prime Numbers\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e271\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 6\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eAre There Any Odd Perfect Numbers?\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e277\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 7\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eThe Collatz Conjecture\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e283\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 8\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eThe 196-Algorithm\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e289\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 9\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eIs n + e a Rational Number? How About nx e?\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e295\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003eChapter 10\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eA Question About Friends and Strangers\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e301\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eEpilogue\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e309\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eIndex of Theorems and Lemmas\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e311\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eIndex of Unsolved Problems\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e313\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e \u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\"\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" colspan=\"1\"\u003e\u003cstrong\u003eIndex\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd class=\"textWhiteBG\" align=\"right\"\u003e315\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/tbody\u003e\n\u003c\/table\u003e\n\u003cp\u003e \u003c\/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003cspan\u003eThis book is a joyful reclaiming of the liberal art of mathematics. With wit, reverence, and luminous clarity, Tawney invites us to encounter math not merely as a subject to master but as a soul-shaping journey into wonder, beauty, and truth.\u003c\/span\u003e\u003cb\u003e--Christopher Perrin, founder, Classical Academic Press\u003c\/b\u003e\u003c\/p\u003e\n\u003cp\u003eCan mathematics be a super habit--a way of seeing that is, at once, illuminative of the here and now and transcendent? Jake Tawney says yes, and he offers compelling proof. Wise, witty, and practical, his contrary vision of mathematics frees his readers to experience what most of us miss. Our academies need this book. We all need to see what Tawney sees: that mathematics is true, good, and beautiful.\u003cb\u003e--\u003c\/b\u003e\u003cb\u003eAndrew J. Zwerneman, president, Cana Academy\u003c\/b\u003e\u003c\/p\u003e\n\u003cp\u003eIt is exceedingly rare for a math book to be compelling to mathematicians and non-mathematicians alike, but\u003cspan\u003e \u003c\/span\u003e\u003ci\u003eAnother Sort of Mathematics\u003c\/i\u003e\u003cspan\u003e \u003c\/span\u003eis just that. The problems and proofs are fascinating, the prose is lucid to readers of all mathematical backgrounds, and the stories, images, and analogies that accompany the math add a much-needed human dimension to the subject. Tawney's book challenges the division between \"math-people\" and \"non-math-people,\" bringing new light to ancient wisdom and making \"math-people\" of us all.\u003cb\u003e--\u003c\/b\u003e\u003cb\u003eJon Gregg, Professor of Education, Hillsdale College\u003c\/b\u003e\u003c\/p\u003e\n\u003cp\u003e\"If there is something in math--or life--you want, make it happen (but be willing to deal with the consequences!).\" Well, Tawney has made it happen, and the result is this stunning exposition. Tawney pulls readers into the awe of mathematics as a profound human endeavor--a celebration of curiosity and the soul's search for truth, beauty, and goodness. The consequences? A gift for us all.\u003cb\u003e--\u003c\/b\u003e\u003cb\u003eJames Tanton, MAA (Mathematician-at-Large)\u003c\/b\u003e\u003c\/p\u003e\n\u003cp\u003e\u003ci\u003eAnother Sort of Mathematics\u003c\/i\u003e\u003cspan\u003e \u003c\/span\u003eis a singular sort of book about math. Many books plumb the wondrous depths of mathematics, but are esoteric. Other books are more accessible but fail to present mathematics in a way that makes readers rightly marvel at it. Tawney has gifted us with a book that is both accessible and soul-stirring. Read the book, apprehend mathematics as it truly is, and be awestruck.\u003cb\u003e--\u003c\/b\u003e\u003cb\u003eAlbert Cheng, University of Arkansas\u003c\/b\u003e\u003c\/p\u003e\n\u003cp\u003eA wonderfully curated and sharply focused book that summons the wonders and pleasures of mathematics from its glorious heights to each of our longing souls. Tawney's delight in mathematics and his absolute mastery in teaching it are laid bare in every page.\u003cb\u003e--\u003c\/b\u003e\u003cb\u003eSatyan L. Devadoss, Fletcher Jones Professor of Applied Mathematics, University of San Diego\u003c\/b\u003e\u003c\/p\u003e\n\u003cp\u003eMathematics thrives on play, wonder, and the pursuit of truth. Too often, math education is gamified or forced to tie in real-world contexts, overshadowing its intrinsic beauty. This book invites all readers to rediscover the power of mathematics through proof--a cornerstone that fosters curiosity and deeper understanding. By embracing proof, we are invited to honor mathematics as a joyful exploration, reminding us that its greatest rewards come not just from answers or procedures, but from the journey of discovery.\u003cb\u003e--\u003c\/b\u003e\u003cb\u003eChris Bolognese, Presidential Award in Excellence in Math and Science Teaching, McElroy Master Chair in Math, Columbus Academy\u003c\/b\u003e\u003c\/p\u003e\n\u003cp\u003e\u003ci\u003eAnother Sort of Mathematics\u003c\/i\u003e\u003cspan\u003e \u003c\/span\u003eis a gift for both those who love mathematics and those who do not (yet). Through his excellent use of narrative, images, and argument, Tawney's book promises to arouse wonder, give delight, and deepen understanding of central tenets of modern mathematics. His book should also contribute to the important efforts underway to fully integrate modern mathematics into today's classical liberal arts curriculum.\u003cb\u003e--\u003c\/b\u003e\u003cb\u003eAndrew Seeley, president, Boethius Institute for the Advancement of Liberal Education\u003c\/b\u003e\u003c\/p\u003e\n\u003cp\u003eAt last, in a single volume we find an antidote to the flat, uninspiring mathematics education to which most of us have been subjected. In accessible and amusing prose, Jake Tawney entices his readers to reconsider mathematics as an invitation to wonder. Whether one has a natural love of math or a persistent aversion to it, this book offers a chance to delight in its mystery, beauty, and meaning.\u003cb\u003e--\u003c\/b\u003e\u003cb\u003eElisabeth Sullivan, executive director, Institute for Catholic Liberal Education\u003c\/b\u003e\u003c\/p\u003e\n\u003cp\u003eJake Tawney's prose is pure joy. This book is a must read in the art of being fully human. For the first time I have been truly invited into the wonder and awe of mathematics and experienced the span of its truth, goodness, and beauty.\u003cb\u003e--\u003c\/b\u003e\u003cb\u003eDan Scoggin, co-founder, Great Hearts\u003c\/b\u003e\u003c\/p\u003e\n\u003cp\u003eBecause of the state of mathematical education, many readers probably just thought nothing could be more tedious, but that couldn't be more wrong. The proofs and theorems are delightful, surprising, elegant, and clearly explained. The math is, in fact, interesting in itself. As Tawney reminds us often, it is up to us whether we recognize that fact: \"We must choose to find mathematics interesting.\"\u003cb\u003e--The Federalist\u003c\/b\u003e\u003c\/p\u003e\n\u003cp\u003eTawney's metaphysics are unapologetically Platonic. This is an excellent position from which to begin to recover the possibility of real learning, as the machinery of fake expertise and empty credentials crumbles around us.\u003cb\u003e--\u003ci\u003eFirst Things\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e\n\u003cp\u003e \u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eJ. Jacob (\"Jake\") Tawney\u003c\/strong\u003e has been enamored by mathematics for as long as he can remember, from kindergarten to calculus. But he truly fell in love with it during his sophomore year at Denison University during a course on mathematical proofs. After completing an undergraduate degree in mathematics and computer science from Denison, he continued his studies at The Ohio State University. There he earned a master's degree in mathematics, submitting a thesis on the mathematics of juggling. During his time in Ohio, Tawney taught at Upper Arlington High School and the Pontifical College Josephinum, including courses in Euclid and the philosophy of mathematics. In 2014 he relocated his family to Phoenix, Arizona, to join Great Hearts Academies, where he currently serves as the chief academic officer.\u003c\/p\u003e\n\u003cp\u003eJake is the proud husband of Christina and the proud father of eight children, all of whom have something unique in their souls that can only be satisfied by wondering about mathematics.\u003c\/p\u003e\n\u003cp\u003e \u003c\/p\u003e","brand":"IPS","offers":[{"title":"Default Title","offer_id":45753065373882,"sku":"9781641774444","price":34.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0444\/2213\/5968\/files\/imageloader_4c3b00eb-6d82-4cbe-b9cd-6a8884f88cad.jpg?v=1775320959","url":"https:\/\/naturenurture.shop\/products\/another-sort-of-mathematics-selected-proofs-necessary-to-finally-acquire-an-education-in-mathematics","provider":"nature+nurture","version":"1.0","type":"link"}