Intro Math Best book for understanding arithmetic?

Thread starter Antisthenes
Start date Jan 9, 2018
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Arithmetic Book

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The discussion centers around finding a comprehensive and pedagogical arithmetic book suitable for self-study, ideally authored by respected mathematicians. The original poster seeks a resource that thoroughly explains fundamental arithmetic concepts without skipping steps, emphasizing the importance of understanding the logic behind mathematical operations. They express a desire to build a solid foundation in arithmetic to facilitate problem-solving in various contexts, acknowledging their struggles with applying mathematical tools.Participants suggest several books, including titles by Serge Lang and Gelfand, as well as resources like Openstax's PreAlgebra, which is noted for its structured approach to topics. The conversation also touches on the historical development of arithmetic and the need for a deep understanding of mathematical principles. Some contributors recommend exploring the philosophical aspects of mathematics, while others emphasize the necessity of practice and application to develop problem-solving skills.The discussion highlights the challenge of finding materials that balance depth and accessibility, with a consensus that a strong grasp of basic arithmetic is essential before progressing to more advanced mathematical concepts like algebra and calculus.

Jan 11, 2018

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for another perspective on what arithmetic is, see this book by J.P. Serre, Fields medalist: it includes quadratic forms, modular forms, Gaussian reciprocity, group characters and representations, and Dirchlet's theorem on primes in arithmetic progressions via complex analysis and analytic continuation. the goal of the last result being to answer for instance the question: since primes greater than 5 must end in either 1,3,7, or 9, is any of these endings preferred, or do they all occur essentially the same number of times?

https://www.amazon.com/Course-Arithmetic-Graduate-Texts-Mathematics/dp/0387900403/ref=sr_1_1?s=books&ie=UTF8&qid=1515714781&sr=1-1&keywords=serre,+course+in+arithmetic

Last edited: Jan 11, 2018