Only Divisible By Itself And One
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The Fundamental Theorem of Algebra
Author: Benjamin Fine
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
The fundamental theorem of algebra states that any complex polynomial must have a complex root. This book examines three pairs of proofs of the theorem from three different areas of mathematics: abstract algebra, complex analysis and topology. The first proof in each pair is fairly straightforward and depends only on what could be considered elementary mathematics. However, each of these first proofs leads to more general results from which the fundamental theorem can be deduced as a direct consequence. These general results constitute the second proof in each pair. To arrive at each of the proofs, enough of the general theory of each relevant area is developed to understand the proof. In addition to the proofs and techniques themselves, many applications such as the insolvability of the quintic and the transcendence of e and pi are presented. Finally, a series of appendices give six additional proofs including a version of Gauss'original first proof. The book is intended for junior/senior level undergraduate mathematics students or first year graduate students, and would make an ideal "capstone" course in mathematics.
Teaching Calculation
Can you demonstrate a clear understanding of primary mathematics? If you are training to be a primary school teacher you need to have, and demonstrate, a clear understanding of primary mathematics. This companion text to the popular Teaching Arithmetic in Primary Schools enables you to audit your knowledge, skills and understanding, making you more aware of the subject and the areas you need to develop further. It includes: self audits on all areas of calculations, supporting trainees to meet the Teachers′ Standards clear links to classroom practice, linking theory with practice advice on next steps for further learning under each chapter If you′re a trainee primary school teacher, this resource, along with its companion title will provide you with all the guidance and support needed to develop your Primary Maths subject knowledge and teaching skills. This book is part of the Transforming Primary QTS Series This series reflects the new creative way schools are beginning to teach, taking a fresh approach to supporting trainees as they work towards primary QTS. Titles provide fully up to date resources focused on teaching a more integrated and inclusive curriculum, and texts draw out meaningful and explicit cross curricular links.
Prime Numbers
Author: Richard Crandall
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-04-07
Bridges the gap between theoretical and computational aspects of prime numbers Exercise sections are a goldmine of interesting examples, pointers to the literature and potential research projects Authors are well-known and highly-regarded in the field