素数无穷性质证明的分层教学设计

Hierarchical Teaching Design of Proving the Infinitude of Primes

素数无穷性质的证明有多种,其证明过程和难度各异。素数作为数论和密码学中必不可少的教学内容在信息安全等领域有相当重要而广泛的运用。让更多人理解和掌握素数无穷性质的证明,是提高他们对素数认识的重要教学环节。本文旨在提出多种针对不同层次学生的分层次素数无穷性质证明的教学设计,由浅入深,用不同的教育方式使更多人理解掌握素数的无穷性质证明及其应用。

Numerous proofs that there are infinitely many primes have been devised,and the proofs vary the proving process as well as the difficulty.As an essential teaching content in the courses of number theory and cryptography,the prime has important and wide applications in fields such as information security.Helping more student understand and master the proof of the infinitude of primes is an important teaching link to improve their comprehension to the prime numbers.This paper presents several hierarchical teaching designs of proving the infinitude of primes for different levels of students from the easy to the complicated,and various education methods are utilized to promote understanding and mastering of die proofs of infinitude of primes and relevant applications.