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Advanced Problems in Mathematics: Preparing for University
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 ...
Advanced Problems in Core Mathematics
This booklet is intended to help you to prepare for STEP examinations. It should also be useful aspreparation for any undergraduate mathematics course, even if you do not plan to take STEP.The questions are all based on recent STEP questions. I chosethe questions either because they are'nice' - in the sense that you should get a lot of pleasure fromtackling them - or because I felt Ihad something interesting to say about them. In this booklet, I have restricted myself (reluctantly)to the syllabus for Papers I and II, which is the A-level core (i.e. C1 to C4) with a few additions.This material should be familiar to you if you are taking the International Baccalaureate, ScottishAdvanced Highers or other similar courses.
How to Think Like a Mathematician
Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.
Landscapes of Investigation
Creating landscapes of investigation is a primary concern of critical mathematics education. It enables us to organise educational processes so that students and teachers are able to get involved in explorations guided by dialogical interactions. It attempts to address explicit or implicit forms of social injustice by means of mathematics, and also to promote a critical conception of mathematics, challenging the assumption that the subject represents objectivity and neutrality. Landscapes of Investigation provides many illustrations of how this can be done in primary, secondary, and university education. It also illustrates how exploring landscapes of investigation can contribute to mathemat...
Solving Mathematical Problems
Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the tactics involved in solving mathematical problems at the Mathematical Olympiad level. With numerous exercises and assuming only basic mathematics, this text is ideal for students of 14 years and above in pure mathematics.
Breaking Images
Mathematics is an activity—something we do—not just something inert that we study. This rich collection begins from that premise to explore the various social influences, institutional forces and lived realities that shape and mould the study and practice of mathematics, and are moulded by it in turn. These twenty-one essays explore questions of mathematics as a topic of philosophy, but also the nature and purpose of mathematics education and the role of mathematics in moulding citizens. It challenges the biases and prejudices inherent within uninformed histories of mathematics, including problems of white supremacy, the denial of cultural difference and the global homogenization of teac...
Mathematics for Economics and Finance
Accessible, concise, and interactive, this book introduces the mathematical methods that are indispensable in economics and finance. Fully updated to be as student friendly as possible, this edition contains extensive problems, worked examples and exercises (with full solutions at the end of the book). Two brand new chapters cover coupled systems of recurrence/differential equations, and matrix diagonalisation. All topics are motivated by problems from economics and finance, demonstrating to students how they can apply the mathematical techniques covered. For undergraduate students of economics, mathematics, or both, this book will be welcomed for its clarity and breadth and the many opportunities it provides for readers to practise and test their understanding.
The Rise of the People’s Bank of China
With $4.5 trillion in total assets, the People’s Bank of China now surpasses the U.S. Federal Reserve as the world’s biggest central bank. The Rise of the People’s Bank of China investigates how this increasingly authoritative institution grew from a Leninist party-state that once jealously guarded control of banking and macroeconomic policy. Relying on interviews with key players, this book is the first comprehensive and up-to-date account of the evolution of the central banking and monetary policy system in reform China. Stephen Bell and Hui Feng trace the bank’s ascent to Beijing’s policy circle, and explore the political and institutional dynamics behind its rise. In the early ...
Central Banking in the Twentieth Century
Central banks are powerful but poorly understood organisations. In 1900 the Bank of Japan was the only central bank to exist outside Europe but over the past century central banking has proliferated. John Singleton here explains how central banks and the profession of central banking have evolved and spread across the globe during this period. He shows that the central banking world has experienced two revolutions in thinking and practice, the first after the depression of the early 1930s, and the second in response to the high inflation of the 1970s and 1980s. In addition, the central banking profession has changed radically. In 1900 the professional central banker was a specialised type of banker, whereas today he or she must also be a sophisticated economist and a public official. Understanding these changes is essential to explaining the role of central banks during the recent global financial crisis.
Advanced Problems in Mathematics: Preparing for University
This new and expanded edition 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 for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and 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 anyone interested in advanced mathematics.
