A NOTE ON AN ADDITIVE PROPERTY OF PRIMES 1. Introduction
... factors. But what is the behavior of primes in the “ additive context”? It is easy to check that a theorem like FTA can not be true. In fact all the integers of the form p + 5, being p a prime, can be written as p + 2 + 3 as well. In this way one provides an infinite family of integers admitting at ...
... factors. But what is the behavior of primes in the “ additive context”? It is easy to check that a theorem like FTA can not be true. In fact all the integers of the form p + 5, being p a prime, can be written as p + 2 + 3 as well. In this way one provides an infinite family of integers admitting at ...
PDF sample
... identities such as the ‘difference of two squares’ x 2 − y 2 = (x + y)(x − y). Beyond this it is vital that you are willing to allow your mind to engage with extensive bouts of systematic logical thought. As I pointed out above, you don’t need to know anything about calculus to read most of this boo ...
... identities such as the ‘difference of two squares’ x 2 − y 2 = (x + y)(x − y). Beyond this it is vital that you are willing to allow your mind to engage with extensive bouts of systematic logical thought. As I pointed out above, you don’t need to know anything about calculus to read most of this boo ...
View - Ministry of Education, Guyana
... 1. Use this termly schedule of topics, together with the Ministry of Education’s Curriculum Guides. 2. The recommended texts: Mathematics for Secondary Schools in Guyana Book 2 and Mathematics for Secondary School Book 2 are not the only text you can use to give students practice exercises. 3. Use a ...
... 1. Use this termly schedule of topics, together with the Ministry of Education’s Curriculum Guides. 2. The recommended texts: Mathematics for Secondary Schools in Guyana Book 2 and Mathematics for Secondary School Book 2 are not the only text you can use to give students practice exercises. 3. Use a ...
Notes on the History of Mathematics
... didn’t come up with modern algebraic notation until the 1600s or so).3 • In these cultures, mathematics was concerned with solving applied, practical problems. Rather than talking about the area of a circle, the problem talks about a “round field”. There is little, if any, geometric abstraction in e ...
... didn’t come up with modern algebraic notation until the 1600s or so).3 • In these cultures, mathematics was concerned with solving applied, practical problems. Rather than talking about the area of a circle, the problem talks about a “round field”. There is little, if any, geometric abstraction in e ...
History of mathematics
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. The most ancient mathematical texts available are Plimpton 322 (Babylonian mathematics c. 1900 BC), the Rhind Mathematical Papyrus (Egyptian mathematics c. 2000-1800 BC) and the Moscow Mathematical Papyrus (Egyptian mathematics c. 1890 BC). All of these texts concern the so-called Pythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans, who coined the term ""mathematics"" from the ancient Greek μάθημα (mathema), meaning ""subject of instruction"". Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning and mathematical rigor in proofs) and expanded the subject matter of mathematics. Chinese mathematics made early contributions, including a place value system. The Hindu-Arabic numeral system and the rules for the use of its operations, in use throughout the world today, likely evolved over the course of the first millennium AD in India and were transmitted to the west via Islamic mathematics through the work of Muḥammad ibn Mūsā al-Khwārizmī. Islamic mathematics, in turn, developed and expanded the mathematics known to these civilizations. Many Greek and Arabic texts on mathematics were then translated into Latin, which led to further development of mathematics in medieval Europe.From ancient times through the Middle Ages, bursts of mathematical creativity were often followed by centuries of stagnation. Beginning in Renaissance Italy in the 16th century, new mathematical developments, interacting with new scientific discoveries, were made at an increasing pace that continues through the present day.