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Renate Motzer introduces the world of fractions and connects them with decimal numbers. She clearly shows that fractions can be understood as parts of a whole, but also as ratios of two quantities. The author clearly shows why roots cannot be exactly indicated by fractions, how to find good approximations and why an unusual addition of fractions can lead to paradoxical results. Furthermore, she explains the use of fractions in percentage and probability calculations in a practical way and finally discusses different ways of forming mean values. This Springer essential is a translation of the original German 1st edition essentials, Brüche, Verhältnisse und Wurzeln by Renate Motzer, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2018. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors. The contents What are (common) fractions? Fractures as ratios Irrational numbers Conditional probabilities The target groups Lecturers and students of mathematics or students who want to repeat basic knowledge of fractions for their statistics lectures People interested in mathematics, who want to refresh and expand their knowledge from fractions to hypothesis testing from school The Author Dr. Renate Motzer is an academic senior councillor at the Chair for Didactics of Mathematics at the University of Augsburg. Her main focus is the didactic and professional training of future mathematics teachers at various types of schools.
Fraccions --- Nombres fraccionaris --- Nombres trencats --- Aritmètica --- Nombres racionals --- Decimal fractions. --- Mathematics --- Study and teaching. --- Decimals --- Fractions, Decimal --- Fractions --- Algebra. --- Computer arithmetic and logic units. --- Mathematics Education. --- Arithmetic and Logic Structures. --- Study and teaching . --- Arithmetic and logic units, Computer --- Computer arithmetic --- Electronic digital computers --- Mathematical analysis --- Circuits
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Medieval Europe was a meeting place for the Christian, Jewish, and Islamic civilizations, and the fertile intellectual exchange of these cultures can be seen in the mathematical developments of the time. This sourcebook presents original Latin, Hebrew, and Arabic sources of medieval mathematics, and shows their cross-cultural influences. Most of the Hebrew and Arabic sources appear here in translation for the first time.Readers will discover key mathematical revelations, foundational texts, and sophisticated writings by Latin, Hebrew, and Arabic-speaking mathematicians, including Abner of Burgos's elegant arguments proving results on the conchoid-a curve previously unknown in medieval Europe; Levi ben Gershon's use of mathematical induction in combinatorial proofs; Al-Mu'taman Ibn Hūd's extensive survey of mathematics, which included proofs of Heron's Theorem and Ceva's Theorem; and Muhyī al-Dīn al-Maghribī's interesting proof of Euclid's parallel postulate. The book includes a general introduction, section introductions, footnotes, and references.The Sourcebook in the Mathematics of Medieval Europe and North Africa will be indispensable to anyone seeking out the important historical sources of premodern mathematics.
Mathematics, Medieval --- History. --- Medieval mathematics --- Arabic civilization. --- Arabic mathematics. --- Christian civilization. --- Hebrew civilization. --- Hebrew mathematics. --- Islamic civilization. --- Islamic mathematics. --- Islamic world. --- Jewish civilization. --- Latin Catholic Europe. --- Latin civilization. --- Latin mathematics. --- Latin schools. --- Medieval Europe. --- North Africa. --- Spain. --- abbacist schools. --- combinatorics. --- conchoids. --- curricula. --- decimals. --- geometric knowledge. --- intellectual exchange. --- mathematical induction. --- mathematical revelations. --- mathematics. --- medieval Europe. --- medieval Islam. --- medieval mathematics. --- medieval period. --- quadrivium. --- religion. --- universities.
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