This open book is intended to assist teachers, teacher trainers, curriculum designers, editors and authors of textbooks in developing strategies to teach the multiplication of natural numbers based on the experience of the Lesson Study in Japan. This approach to mathematics education dates back to the 1870s and reconciles the emphasis on problem so...

This twenty-third ICMI Study addresses for the first time mathematics teaching and learning in the primary school (and pre-school) setting, while also taking international perspectives, socio-cultural diversity and institutional constraints into account. One of the main challenges of designing the first ICMI primary school study of this kind is the...

This book offers a theory for the analysis of how children learn and are taught about whole numbers. Two meanings of numbers are distinguished – the analytical meaning, defined by the number system, and the representational meaning, identified by the use of numbers as conventional signs that stand for quantities. This framework makes it possible ...

A First Course in Linear Algebra, originally by K. Kuttler, as a first course for the general students who have an understanding of basic high school algebra and intend to be users of linear algebra methods in their profession, from business & economics to science students.
All major topics of linear algebra are available in detail, as well ...

Linear Algebra with Applications by W. Keith Nicholson, traditionally published for many years is now being released as an open educational resource.
Overall, the aim of the book is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of ...

This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. The first two chapters present preliminary topics such as properties of the integers and equivalence relations. The author then explores the first major algebraic structure, the group, progressing as far as the ...

This book helps students to master the material of a standard US undergraduate first course in Linear Algebra.
The material is standard in that the subjects covered are Gaussian reduction, vector spaces, linear maps, determinants, and eigenvalues and eigenvectors. Another standard is book's audience: sophomores or juniors, usually with a ba...

Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research.
The book explains how conceptual hurdles in the development of numbers and number systems were overcome i...

Applied Discrete Structures, is a two semester undergraduate text in discrete mathematics, focusing on the structural properties of mathematical objects. These include matrices, functions, graphs, trees, lattices and algebraic structures. The algebraic structures that are discussed are monoids, groups, rings, fields and vector spaces.
Applied D...

This open book is an introduction to algebra for undergraduates who are interested in careers which require a strong background in mathematics. It will benefit students studying computer science and physical sciences, who plan to teach mathematics in schools, or to work in industry or finance. The book assumes that the reader has a solid background...

In order to represent real life situations mathematically, we often use symbols to represent unknown quantities. We call these symbols variables. Each mathematical subject requires knowledge of manipulating expressions and equations to solve for a variable. Careers such as automobile accident investigators, quality control engineers, and insurance ...