Advanced Problems in Mathematics: Preparing for University by Stephen Siklos (PDF)

Description

This book is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge colleges as the basis for conditional offers. They are also used by Warwick University, and many other mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics is recommended as preparation for any undergraduate mathematics course, even for students who do not plan to take the Sixth Term Examination Paper. The questions analysed in this book are all based on recent STEP questions selected to address the syllabus for Papers I and II, which is the A-level core (i.e. C1 to C4) with a few additions. Each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anybody interested in advanced mathematics.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I simply love this book. It contains an amazing number of questions on a wide range of topics in mathematics. It is a must for maths lovers. Besides, this book also contains comments at the end of each question and these help to better understand the different ways of tackling the problems.I guess that the content of the book should be accessible to A level students studying maths as a main subject.

⭐I’m not in the target audience for this book as I’m not intending to sit STEP papers, but for me it was a great source of problems at about my level. The format is that an exam question is stated, followed by a commentary which includes some hints and, over the page, the solution and further comments. This works well if you do as the author intends and have a really good attempt at the problem before looking at the comments and solution. The nine page introduction is a brilliant manifesto on how to study mathematics.Problem 21. The author states that the final answer is 1/240. I got 1/280. As no working is given for this part of the question I can’t tell if the mistake is mine or if this is a typo.Problem 24. Ignore the title. This problem is NOT about sketching the graph of x^m(1-x)^n. Read the full problem statement: the problem is about sketching the graph of x^m(x-1)^n, which is significantly different!In a way this is unlike university mathematics. At university you study one, or several, topics at a time in depth. Here, as in an Olympiad, you jump from topic to topic.The binding is alright, but this is a book that you need to lie open whilst you work on the problems so a spiral binding would be preferable.It’s strange that a book published in 2016 mostly uses exam questions from 1987 to 2002 but as the mathematics was all developed over a hundred years ago I suppose it doesn’t really matter.These are minor quibbles. For anyone intending to sit STEP papers, or anyone wanting to do some challenging maths at the level of top A-level students and first year undergraduates, this is a super collection of problems and, much more important, worked solutions.

⭐This book is an absolute god-send. I was starting to revise for my A-Levels and having difficulty with STEP revision for Cambridge. I was trying past paper questions and I wasn’t getting anywhere. Onto The Student Room I went and searched for help; fortunately I stumbled upon this book. What a life-saver!This book is roughly 200 pages long filled with useful content. There is a lovely introduction with two nicely worked examples and many questions to practice from. Each question has a few comments that help the reader to get started and a solution and post-mortem follow each question.There is a also a PDF version of this book available online if you don’t want to spend any money on it, however the physical presence of the book on my desk does help me to start revising.One drawback is that the book doesn’t contain any STEP III questions but loads of STEP I and II instead. Thank you Dr Siklos

⭐This is a paper version of an online ‘book’ compiled by Dr Siklos, who for many years was the admissions tutor for Cambridge undergraduate mathematics. Its purpose is to help mathematically able students to prepare for the Cambridge Sixth Term Mathematics (STEP) examinations. As such, it does the job admirably. Solutions are very full, with alternatives given and there are interesting comments on the setting of the questions and the sometimes unexpected responses to them. It is also ideally suited for teachers who are expecting to prepare students for these demanding papers, especially for those who do not necessarily have able students every year.As Dr Siklos himself writes, a really important way of preparing for STEP is to DO THE QUESTIONS. So students using the book should have a go first and then consult both the given (very full) answer and also the insightful comments supplied.

⭐Really useful so far, but I hope the work I’ve put in will pay off for the actual exam…

⭐Great preparatory course

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