{"id":21048,"date":"2023-02-13T02:26:25","date_gmt":"2023-02-13T02:26:25","guid":{"rendered":"https:\/\/www.booksofall.com\/pl\/?post_type=product&p=21048"},"modified":"2023-02-13T02:26:26","modified_gmt":"2023-02-13T02:26:26","slug":"arithmetic","status":"publish","type":"product","link":"https:\/\/www.booksofall.com\/pl\/arithmetic\/","title":{"rendered":"Arithmetic"},"content":{"rendered":"

Arithmetic<\/a> is the basic topic of mathematics. According to the American Heritage Dictionary<\/a>, it concerns \u201cThe mathematics of integers under addition, subtraction, multiplication, division, involution, and evolution.\u201d<\/p>\n

The present text differs from other treatments of arithmetic in several respects:<\/p>\n

The provision of simple but precise definitions of the counting numbers and other notions introduced.<\/p>\n

The use of simple but precise notation that is executable on a computer, allowing experimentation and providing a simple and meaningful introduction to computer programming.<\/p>\n

The introduction and significant use of fundamental mathematical notions (such as vectors, matrices, Heaviside operators, and duality) in simple contexts that make them easy to understand. This lays a firm foundation for a wealth of later use in mathematics.<\/p>\n

Emphasis<\/a> is placed on the use of guesses by speculation and criticism in the spirit of Lakatos, as discussed in the treatment of proofs in Chapter 5.<\/p>\n

The thrust of the book might best be appreciated by comparing it with Felix Klein<\/a>\u2019s Elementary Mathematics<\/a> from an Advanced Standpoint. However, I shun the corresponding title Arithmetic from an Advanced Standpoint because it would incorrectly suggest that the treatment is intended only for mature mathematicians; on the contrary, the use of simple, executable notation makes it accessible to any serious student possessing little more than a knowledge of the counting numbers.<\/p>\n

Like Klein, I do not digress to discuss the importance of the topics treated, but leave that matter to the knowledge of the mature reader and to the faith of the neophyte.<\/p>\n","protected":false},"excerpt":{"rendered":"