Central Library

Normal view MARC view ISBD view

Sequences and mathematical induction [electronic resource] : in mathematical olympiad and competitions / by Zhigang Feng ; translated by Ma Feng, Wang Youren ; edited by Ni Ming, Kong Lingzhi.

By: Zhang, Feng.
Contributor(s): Ma, Feng | Wang, Youren | Ni, Ming | Kong, Lingzhi.
Material type: materialTypeLabelBookSeries: Mathematical Olympiad series: vol.16.Publisher: Singapore : Shanghai, China : East China Normal University Press, World Scientific Publishing ; [2020]Edition: 2nd edition.Description: 1 online resource (xvi, 202 p.).ISBN: 9789811211041; 9811211043.Subject(s): International Mathematical Olympiad ǂv Study guides | Mathematics ǂx Competitions ǂv Study guides | Sequences (Mathematics) ǂv Problems, exercises, etc | Mathematics ǂv Problems, exercises, etcGenre/Form: Electronic books.DDC classification: 510.76 Online resources: Access to full text is restricted to subscribers.
Contents:
Knowledge and technique. The first form of mathematical induction ; The second form of mathematical induction ; Well-ordering Principle and Infinite Descent ; General terms and summation of sequences ; Arithmetic sequences and geometric sequences ; Higher-order arithmetic sequences and the method of differences ; Recursive Sequences; Periodic Sequences ; Exercise Set 1 -- Selected topical discussions. The fibonacci sequence ; Several proofs of AM-GM inequality ; Choosing a proper span ; Choosing the appropriate object for induction ; Make appropriate changes to the propositions ; Guessing before proving ; Problem regarding existence with sequences ; Exercise set 2 -- Solutions to exercises. Solutions to exercise set 1 ; Solutions to exercise set 2 -- Bibliography.
Summary: "The author attempts to use some common characteristics of sequence and mathematical induction to fundamentally connect Math Olympiad problems to particular branches of mathematics. In doing so, the author hopes to reveal the beauty and joy involved with math exploration and at the same time, attempts to arouse readers' interest of learning math and invigorate their courage to challenge themselves with difficult problems"--Publisher's website.
    average rating: 0.0 (0 votes)
No physical items for this record

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Knowledge and technique. The first form of mathematical induction ; The second form of mathematical induction ; Well-ordering Principle and Infinite Descent ; General terms and summation of sequences ; Arithmetic sequences and geometric sequences ; Higher-order arithmetic sequences and the method of differences ; Recursive Sequences; Periodic Sequences ; Exercise Set 1 -- Selected topical discussions. The fibonacci sequence ; Several proofs of AM-GM inequality ; Choosing a proper span ; Choosing the appropriate object for induction ; Make appropriate changes to the propositions ; Guessing before proving ; Problem regarding existence with sequences ; Exercise set 2 -- Solutions to exercises. Solutions to exercise set 1 ; Solutions to exercise set 2 -- Bibliography.

"The author attempts to use some common characteristics of sequence and mathematical induction to fundamentally connect Math Olympiad problems to particular branches of mathematics. In doing so, the author hopes to reveal the beauty and joy involved with math exploration and at the same time, attempts to arouse readers' interest of learning math and invigorate their courage to challenge themselves with difficult problems"--Publisher's website.

There are no comments for this item.

Log in to your account to post a comment.