Intruoduction to Mathematics

A lively, accessible history of mathematics throughout the ages and across the globe Mathematics is fundamental to our daily lives. Science, computing, economics—all aspects of modern life rely on some kind of maths. But how did our ancestors think about numbers? How did they use mathematics to explain and understand the world around them? Where do numbers even come from? In this Little History, Snezana Lawrence traces the fascinating history of mathematics, from the Egyptians and Babylonians to Renaissance masters and enigma codebreakers.Like literature, music, or philosophy, mathematics has a rich history of breakthroughs, creativity and experimentation. And its story is a global one. We see Chinese Mathematical Art from 200 BCE, the invention of algebra in Baghdad’s House of Wisdom, and sangaku geometrical theorems at Japanese shrines.Lawrence goes beyond the familiar names of Newton and Pascal, exploring the prominent role women have played in the history of maths, including Emmy N

《數學小史》用親切易懂的語言，帶領讀者走進數學的歷史長河，從古埃及與巴比倫時期，一路走到現代密碼學與數學理論的發展。書中不只介紹牛頓、帕斯卡等熟悉的名字，也細細描寫中國、阿拉伯、日本等地的數學成就，更特別介紹女性數學家的貢獻。這是一本融合人文與科學的溫暖數學故事書，適合對數字與知識充滿好奇的你。A lively, accessible history of mathematics throughout the ages and across the globeMathematics is fundamental to our daily lives. Science, computing, economics—all aspects of modern life rely on some kind of maths. But how did our ancestors think about numbers? How did they use mathematics to explain and understand the world around them? Where do numbers even come from?In this Little History, Snezana Lawrence traces the fascinating history of mathematics, from the Egyptians and Babylonians to Renaissance masters and enigma codebreakers. Like literature, music, or philosophy, mathematics has a rich history of breakthroughs, creativity and experimentation. And its story is a global one. We see Chinese Mathematical Art from 200 BCE, the invention of algebra in Baghdad’s House of Wisdom, and sangaku geometrical theorems at Japanese shrines. La

This Element discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the challenge to explain the (defeasible) justification of our mathematical beliefs ('the justificatory challenge'), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions. And it argues that the challenge to explain their reliability ('the reliability challenge'), arises to the extent that we could have easily had different beliefs. The Element shows that mathematical facts are not, in general, empirically accessible, contra Quine, and that they cannot be dispensed with, contra Field. However, it argues that they might be so plentiful that our knowledge of them is unmysterious. The Element concludes with a complementary 'pluralism' about modality, logic and normative theory, highlighting its surprising implications. Metaphysically, pluralism engenders a kind of perspectivalism and indeterminacy. Methodologically, it vindicates Carnap

Discover modern solutions to ancient mathematical problems with this engaging guide, written by a mathematics enthusiast originally from South Vietnam. Author Dat Phung To provides a theory that defin

Discover modern solutions to ancient mathematical problems with this engaging guide, written by a mathematics enthusiast originally from South Vietnam. Author Dat Phung To provides a theory that defin

Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Löwenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continu

A noted educator's account of some of the more stimulating and surprising branches of mathematics, this volume profiles the mathematical mind and the aims of mathematics. Five introductory chapters of

Understanding Policy Changes: The Mixture Model of Politics offers a new theoretical and methodological approach to the study of policy changes.

學習數學，就是學習如何好好生活數學不止是解題，更能讓我們了解自己和世界「很少有東西像數學一樣，美麗又迷人，道破人生，對人生目標的追求來說如此重要。」――里昂・波特斯坦，開放社會大學網絡校長李信昌　數學網站「昌爸工作坊」站長李政憲　教育部師鐸獎得主、新北市立林口國民中學教師、「藝數摺學」臉書社團創辦人洪萬生　臺灣數學史教育學會榮譽理事長、臺灣師範大學數學系退休教授張瑞棋　「科學棋談」版主、科學史作家――推薦思考數學的過程，是你我生活的縮影，數學本身也是！為什麼要學數學？這是許多人的疑惑，尤其如果你在學時的數學成績不是很理想，大概早已問這個問題好幾百遍了，但數學能給你的其實比想像中更多，把數學腦運用在生活的各個層面，能讓你有更深入的生命體驗。你手上的這本書，就將透過46個數學概念，帶你看見數學與生活的連結。閱讀時，你無須使用複雜的公式，只需要思考，並且經歷思考數學時帶給你的一切──你會發現自己在數學裡是自由、勇敢、能欣賞美且充滿彈性的。這可能是你的本質，也可能是數學給你的，就像我們也分不清楚究竟是生活裡有數學，還是我們就活在數學裡。但是這些不重要，重要的是，透過書中的引導，你會漸漸將數學放進心裡，處處留意它，令你更能擁抱改變，相信自己，也對世界抱有更大的好奇心，重新意識到那些你過去不曾察覺的意義與美麗。當你開始留意生活裡的數學時，你會⋯⋯●從賽局理論領悟到與人合作的重要●看到具有二十面體對稱性的噬菌體，如何有效率地做事●從微積分裡學到，分而攻之或許是解決難題的好方法●透過非歐幾何學習應該欣然接受改變你還能⋯⋯●從費波那契數中，發現自然排列之美●從愛因斯坦的經歷中學習面對失敗●從混沌理論中，知道不需要和他人比較●從模糊邏輯中，領悟到待人接物需要保持彈性▍好評讚譽作者精鍊的文筆引領你掌握思考重點，手繪草圖增添了閱讀與學習上的樂趣，同時喚醒你探索數學的好奇初衷。透過本書，你可以重新認識數學的本質，釋放原本深藏的數學潛能。――李信昌，數學網站「昌爸工作坊」站長看一個本來對數學絕望的作者，如何用她的理解，闡述數學與生活的連結。從頭開始細讀，你會發現其實數學應用於生活上，真的是無所不在。期待每位讀者都能開發你們尚未開發的數學潛能！――李政憲，教育部師鐸獎得主、新北市立林口國民中學教師、「藝數摺學」臉書社團創辦人這本書很有趣，有珍貴的數學知識，但和現實生活產生連結，還以巧妙的步調吸引