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Pure Mathematics


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Geometry: A Very Short Introduction


Maciej Dunajski

January 2022

Very Short Introductions

This book provides a fresh modern introduction to geometry, an ancient branch of mathematics with important applications. It takes readers from Euclidean and non-Euclidean geometries, to curved spaces, and the geometry of space-time inside a black hole, and outlines the role geometry plays in the broader context of science and art.

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Linear Algebra for the 21st Century


Anthony Roberts

October 2020

Linear Algebra for 21st Century Applications adapts linear algebra to best suit modern teaching and application, and it places SVD as central to the text early on to empower the students in these disciplines to learn and use the best techniques.

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Number Theory: Step by Step


Kuldeep Singh

October 2020

Number Theory: Step by Step is an undergraduate-level introduction to number theory that assumes no prior knowledge, but works to gradually increase the reader's confidence and ability to tackle more difficult number theory material.

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Number Theory: A Very Short Introduction


Robin Wilson

May 2020

Very Short Introductions

Number theory is the branch of mathematics primarily concerned with the counting numbers, especially primes. It dates back to the ancient Greeks, but today it has great practical importance in cryptography, from credit card security to national defence. This book introduces the main areas of number theory, and some of its most interesting problems.

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Trigonometry: A Very Short Introduction


Glen Van Brummelen

January 2020

Very Short Introductions

Rooted in ancient astronomy, trigonometry is mathematics' powerful toolkit for scientific measurement. It has been at the heart of the study of infinity, complex and imaginary numbers, and the shape of the space itself. Our experience of the universe has been made possible, and deeply challenged, by this surprisingly deep and fruitful subject.

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Undergraduate Analysis: A Working Textbook


Aisling McCluskey, Brian McMaster

June 2018

An innovative self-contained Analysis textbook for undergraduates, that takes advantage of proven successful educational techniques.

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Infinity: A Very Short Introduction


Ian Stewart

March 2017

Very Short Introductions

Ian Stewart considers the concept of infinity and the profound role it plays in mathematics, logic, physics, cosmology, and philosophy. He shows that working with infinity is not just an abstract, intellectual exercise, and analyses its important practical everyday applications.

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Complexity: A Very Short Introduction


John H. Holland

July 2014

Very Short Introductions

In this Very Short Introduction, John Holland presents an introduction to the science of complexity. Using examples from biology and economics, he shows how complexity science models the behaviour of complex systems.

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Undergraduate Topology: A Working Textbook


Aisling McCluskey, Brian McMaster

July 2014

Point-set topology, important in itself as a research discipline, underpins a wide range of mathematical areas and is consequently taught as a component of many university mathematics degree programmes. This textbook offers an accessible, modern introduction, with a particular focus on helping students to build theory for themselves.

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Linear Algebra: Step by Step


Kuldeep Singh

October 2013

Linear algebra is a fundamental area of mathematics, and arguably the most powerful mathematical tool ever developed. This dynamic and engaging book uses numerous examples, question and answer sections, and historical biographies to provide an introduction to linear algebra for undergraduates in mathematics, the physical sciences and engineering.

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Fractals: A Very Short Introduction


Kenneth Falconer

September 2013

Very Short Introductions

From the contours of coastlines to the outlines of clouds, fractal shapes can be found regularly in nature. This Very Short Introduction explains the basic concepts, presents the 'new geometry' of fractals, explores its wide range of applications, and shows the central place fractals have gained in mathematics and science in recent years.

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Symmetry: A Very Short Introduction


Ian Stewart

May 2013

Very Short Introductions

Symmetry is an immensely important concept in mathematics and throughout the sciences. In this Very Short Introduction, Ian Stewart highlights the deep implications of symmetry and its important scientific applications across the entire subject.

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How to Study as a Mathematics Major


Lara Alcock

January 2013

This no-nonsense book translates mathematics education research-based insights into practical advice for a student audience. It covers every aspect of studying for a mathematics major, from the most abstract intellectual challenges to the everyday business of interacting with lecturers and making good use of study time.

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How to Study for a Mathematics Degree


Lara Alcock

November 2012

This no-nonsense book translates mathematics education research-based insights into practical advice for a student audience. It covers every aspect of studying for a mathematics degree, from the most abstract intellectual challenges to the everyday business of interacting with lecturers and making good use of study time.

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Probability: A Very Short Introduction


John Haigh

April 2012

Very Short Introductions

Making good decisions under conditions of uncertainty requires an appreciation of the way random chance works. In this Very Short Introduction, John Haigh provides a brief account of probability theory; explaining the philosophical approaches, discussing probability distributions, and looking its applications in science and economics.

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Riemann Surfaces


Simon Donaldson

March 2011

Oxford Graduate Texts in Mathematics

An authoritative but accessible text on one dimensional complex manifolds or Riemann surfaces. Dealing with the main results on Riemann surfaces from a variety of points of view; it pulls together material from global analysis, topology, and algebraic geometry, and covers the essential mathematical methods and tools.

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Numbers: A Very Short Introduction


Peter M. Higgins

February 2011

Very Short Introductions

In this Very Short Introduction Peter M. Higgins presents an overview of the number types featured in modern science and mathematics. Providing a non-technical account, he explores the evolution of the modern number system, examines the fascinating role of primes, and explains their role in contemporary cryptography.

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Category Theory

Second Edition


Steve Awodey

June 2010

Oxford Logic Guides

A comprehensive reference to category theory for students and researchers in mathematics, computer science, logic, cognitive science, linguistics, and philosophy. Useful for self-study and as a course text, the book includes all basic definitions and theorems (with full proofs), as well as numerous examples and exercises.

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Statistics: A Very Short Introduction


David J. Hand

October 2008

Very Short Introductions

Statistics has evolved into an exciting discipline which uses deep theory and powerful software to shed light on the world around us: from clinical trials in medicine, to economics, sociology, and countless other subjects vital to understanding modern life. This Very Short Introduction explores and explains how statistics works today.

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An Introduction to the Theory of Numbers

Sixth Edition


G. H. Hardy, E. M. Wright, Roger Heath-Brown, Joseph Silverman, Andrew Wiles

July 2008

The sixth edition of the classic undergraduate text in elementary number theory includes a new chapter on elliptic curves and their role in the proof of Fermat's Last Theorem, a foreword by Andrew Wiles and extensively revised and updated end-of-chapter notes.

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