The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an approachable and thorough introduction to the topic.
Algebraic Number Theory takes the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more...
The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a...
This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student. The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and...
This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student. The book begins with an infor...
This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods. Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier...
This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and...
Mathematica(r): A Problem-Centered Approach introduces the vast array of features and powerful mathematical functions of Mathematica using a multitude of clearly presented examples and worked- out problems. Each section starts with a description of a new topic and some basic examples. The author then demonstrates the use of new commands through three categories of problems
- the first category highlights those essential parts of the text that demonstrate the use of new commands in Mathematica whilst solving each problem presented;
- the second comprises problems that...
Mathematica(r): A Problem-Centered Approach introduces the vast array of features and powerful mathematical functions of Mathematica using...
This book contains a collection of exercises (called tapas ) at undergraduate level, mainly from the fields of real analysis, calculus, matrices, convexity, and optimization. Most of the problems presented here are non-standard and some require broad knowledge of different mathematical subjects in order to be solved. The author provides some hints and (partial) answers and also puts these carefully chosen exercises into context, presents information on their origins, and comments on possible extensions. With stars marking the levels of difficulty, these tapas show or prove something...
This book contains a collection of exercises (called tapas ) at undergraduate level, mainly from the fields of real analysis, calculus, matrices, conv...
