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Towards Higher Mathematics: A Companion 1st Edition

by Richard Earl (Author)
4.8 4.8 out of 5 stars 40 ratings
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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.
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  1. ISBN-10
    1316614832
  2. ISBN-13
    978-1316614839
  3. Edition
    1st
  4. Publisher
    Cambridge University Press
  5. Publication date
    October 17, 2017
  6. Language
    English
  7. Dimensions
    6.69 x 1.23 x 9.61 inches
  8. Print length
    544 pages
  9. See all details
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Editorial Reviews

Review

'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

Book Description

This book allows students to stretch their mathematical abilities and bridges the gap between school and university.

Product details

  • Publisher ‏ : ‎ Cambridge University Press; 1st edition (October 17, 2017)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 544 pages
  • ISBN-10 ‏ : ‎ 1316614832
  • ISBN-13 ‏ : ‎ 978-1316614839
  • Item Weight ‏ : ‎ 2.12 pounds
  • Dimensions ‏ : ‎ 6.69 x 1.23 x 9.61 inches
  • Customer Reviews:
    4.8 4.8 out of 5 stars 40 ratings

About the author

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Richard Earl

Richard Earl

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Richard Earl is a departmental lecturer in the Mathematical Institute, University of Oxford, and a Tutor in Mathematics at Worcester College. From 2013-2022 he was Director of Undergraduate Studies in the Institute. 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. He is currently the academic lead on the Mathematics and Computer Science Opportunity Oxford programme which includes a fortnight-long residential prior to the academic year and which supports students in their transition to university.

Customer reviews

4.8 out of 5 stars
4.8 out of 5
40 global ratings

Top review from the United States

ERW
2.0 out of 5 stars A true companion indeed and nothing more
Reviewed in the United States on April 13, 2019
I browsed through this book in a bookstore and what caught my attention was a paragraph on the Fibonacci numbers followed by another one on the binomial formula, both tricky subjects. Here was Binet's formula but why was the paragraph so very short? Binet's formula was a fascinating discovery since even though it contains radicals, the results are integer Fibonacci numbers. It soon became clear, the demonstration was using the induction method. In other words, the formula is offered without demonstration and it is only shown that if it works for number "n" it also works for "n+1". The binomial formula is a nice example of how math teachers try to simplify their tasks. To do it right they'd have to explain permutations, arrangements and combinations. However, with the induction you'll get a proof without understanding anything. Basically what all this means in what concerns learning mathematics is that if you are a blind man and you need to get somewhere, a companion will take you there, but you'll still be blind when you reach your destination.
5 people found this helpful
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Top reviews from other countries

P.K. Thiruvikraman
5.0 out of 5 stars A useful book for anyone who uses mathematics at the University level
Reviewed in India on September 20, 2020
Verified Purchase
"Towards higher mathematics" will be a very useful companion not only for students who are planning to take up higher level mathematics at an Univeristy, but also for students of Physics and Engineering. It has an excellent collection of problems which are categorized as per their level of difficulty. Hints are provided for solving some of the problems. It also gives interesting historical anecdotes about mathematicians. Essential for any student (or teacher) of Physics, mathematics, or engineering.
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Richard Earl
5.0 out of 5 stars Review passed on to the author from a Year 13 student
Reviewed in the United Kingdom on November 8, 2017
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Review passed on to the author from a Year 13 student, and reproduced with permission.

Although it tackles complex ideas, Richard Earl's book is an easy and enjoyable read, making the subject matter accessible and inviting. I found the historical sections particularly interesting as they provided context and gave me an appreciation of how our understanding of maths has evolved over time- something which isn't usually taught in school.
There are plenty of challenging exercises containing a good variety of questions, each with a clear indication of its difficulty level (although the notation takes a bit of getting used to). The questions within each topic are not overly technical so don't require unnecessary knowledge outside the A level syllabus. Instead, they are carefully constructed to ensure you think creatively, applying an assortment of mathematical skills in order to progress. For example, whilst learning about complex numbers, my geometry skills improved.
Topics are linked in logical, yet unexpected ways, so familiar ideas seem new and exciting. We meet probability and the binomial distribution alongside proof by induction, graph theory links to matrices and hyperbolic trigonometric functions are explored in the context of integration.
I had a clear sense of deepening my current understanding of maths and, therefore, moving towards university learning. The book teaches you how to think for yourself.
5 people found this helpful
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Eckhard Ratgeber
5.0 out of 5 stars good book
Reviewed in the United Kingdom on June 18, 2022
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good book quality delivery .
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Jack Ndong
5.0 out of 5 stars Five Stars
Reviewed in the United Kingdom on November 19, 2017
Verified Purchase
Great book! Extremely helpful for undergraduate math students.
3 people found this helpful
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