Towards Higher Mathematics： A Companion

基本信息

Format:Paperback / softback 540 pages, Worked examples or Exercises; 35 Halftones, black and white; 65 Line drawings, black and

Publisher:Cambridge University Press

Imprint:Cambridge University Press

ISBN:9781316614839

Published:7 Sep 2017

Classifications:Mathematics

Weight:958g

Dimensions:175 x 245 x 33 (mm)

Pub. Country:United Kingdom

页面参数仅供参考，具体以实物为准

书籍简介

Containing a large and varied set of problems, this rich resource will allow students to stretch their mathematical abilities beyond the school syllabus, and bridge the gap to university-level mathematics. Many proofs are provided to better equip students for the transition to university. The author covers substantial extension material using the language of sixth form mathematics, thus enabling students to understand the more complex material.

Exercises are carefully chosen to introduce students to some central ideas, without building up large amounts of abstract technology. There are over 1500 carefully graded exercises, with hints included in the text, and solutions available online. Historical and contextual asides highlight each area of mathematics and show how it has developed over time.

这个丰富的资源包含了大量和各种各样的问题，可以让学生在学校的教学大纲之外扩展他们的数学能力，并缩小与大学水平的数学差距。为学生更好地适应大学生活提供了依据。作者运用六年级数学的语言涵盖了大量的延伸材料，使学生能够理解更复杂的材料。

练习是精心挑选的，以向学生介绍一些中心思想，而不是建立大量的抽象技术。有超过1500个经过仔细分级的练习，在文本中有提示，并且可以在网上找到解决方案。历史和上下文旁白突出数学的每个领域，并显示它如何随着时间发展。

目录

Introduction; 介绍

1. Complex numbers; 复杂的数字

2. Induction; 证明

3. Vectors and matrices; 向量和矩阵

4. More on matrices;更多关于矩阵

5. Techniques of integration;积分的技巧

6. Differential equations; 微分方程

7. Hints to selected exercises; 所选练习的提示

Bibliography; 参考书目

Index.索引

评论

'The text is quite reader friendly, with over 1,500 graded exercises (most with hints) presented throughout the text, not just at the ends of sections or chapters. As a result, readers are encouraged and motivated to take the time and make the effort to understand each concept as they proceed. Earl exerts a positive influence on beginning students as they decide whether to pursue a degree in mathematics. Perhaps best of all, students get a glimpse of the breadth of areas they can pursue within the mathematics realm - even at the early stages of their study. Summing Up: Recommended.' J. T. Zerger, Choice

'The biggest stumbling-block for many students about to go to university to study mathematics is not the lack of syllabus covered but the lethal attitude 'you don't need this for the exam'. This book will provide much of what they need ... It is also a good resource for school and college departments looking for questions on FM material that will stretch their best learners.' Owen Toller, Mathematical Gazette

文本非常适合读者阅读，有超过1500个评分练习(大多数带有提示)贯穿整个文本，而不仅仅是在章节或章节的结尾。因此，读者会受到鼓励和激励，在阅读过程中花时间和精力去理解每一个概念。厄尔对初学数学的学生在决定是否攻读数学学位时产生了积极的影响。也许最好的是，学生可以对他们在数学领域中可以追求的领域有一个大致的了解——甚至在他们学习的早期阶段。总结:建议。——泽格(j.t. Zerger)的《选择》(Choice)

对于许多即将进入大学学习数学的学生来说，障碍不是课程大纲的缺乏，而是‘考试不需要这个’这种致命的态度。”这本书将提供他们所需要的许多东西。它也是一个很好的资源，为学校和大学部门寻找问题的FM材料，将舒展他们最好的学习者。——Owen Toller，《数学公报》

作者简介

Richard Earl is currently Director of Undergraduate Studies in the Mathematical Institute, University of Oxford, and a Tutor in Mathematics at Worcester College. From 2003-13, he was Admissions Coordinator and Schools Liaison Officer in the department and has over a decade's experience setting the MAT (Oxford's Mathematics Admissions Test). He has won several teaching awards within the University for his teaching and lecturing. This book grew out of a residential week he ran for several years in Oxford for new students who had not had the chance to study Further Mathematics at A-Level.

Richard Earl目前是牛津大学数学研究所的本科生研究主任，也是伍斯特学院的数学导师。从2003年到2013年，他担任招生协调员和学校联络官，并有超过十年的设置牛津数学入学考试(MAT)的经验。他在学校的教学工作中多次获奖。这本书是他几年来在牛津为那些没有机会在高级水平考试中进一步学习数学的新生所写的。