Compact Textbooks in Mathematics

This book covers the basics of numerical methods. Avoiding the definition-theorem-proof style, it instead focuses on numerical examples and simple pseudo-codes.

The text begins with a chapter on floating point arithmetic before moving on to discuss norms, conditions numbers, solutions of systems of equations, the least squares problem, eigenvalue problems, interpolation, numerical integration, ordinary differential equations, optimization (including a detailed case study), and practical error estimations. Exercises (partly in MATLAB) are provided at the end of each chapter. Suitable for readers with minimal mathematical knowledge, the book not only offers an elementary introduction to numerical mathematics for programmers and engineers but also provides supporting material for students and teachers of mathematics.

This book gives a basic introduction to the algebraic K-theory space K(R) without assuming much knowledge in category theory or homotopy theory.

The work is divided into two parts. Part I introduces all the necessary tools from category theory and simplicial homotopy theory which one needs to define the K-theory space. Part II defines K(R) and studies the basic properties of these spaces.

While many textbooks cover the classical material in algebraic K-theory, this book offers an accessible introduction to this active area of research for graduate students. One can also view these lecture notes as an introduction to the use of categories in homotopy theory, or rather the interaction between the two areas of mathematics.