Mathematics (9)

• Mathematics
• Textbooks and Learning Guides

Representation Theory: A Categorical Approach

• Jan E. Grabowski

This volume offers a fresh and modern introduction to one of abstract algebra’s key topics. Guiding readers through the transition between structure theory and representation theory, this textbook explores how algebraic objects like groups and rings act as symmetries of other structures. Using the accessible yet powerful language of category theory, the book reimagines standard approaches to topics such as modules and algebras in a way that unlocks modern treatments of more advanced topics such as quiver representations and even representations of Hopf algebras and categories.

• Education
• Mathematics

Breaking Images: Iconoclastic Analyses of Mathematics and its Education

• Brian Greer
• David Kollosche
• Ole Skovsmose

These twenty 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 teaching methods. In particular, the book contrasts the effectiveness of mathematics and science in modelling physical phenomena and solving technical problems with its ineffectiveness in modelling social phenomena and solving human problems, and urges us to consider how mathematics might better meet the urgent crises of our age.

• Biography
• European Studies: English and Irish Studies
• Mathematics
• Science: History of Science

Augustus De Morgan, Polymath: New Perspectives on his Life and Legacy

• Karen Attar
• Adrian Rice
• Christopher Stray

When Augustus De Morgan died in 1871, he was described as ‘one of the profoundest mathematicians in the United Kingdom’ and even as ‘the greatest of our mathematicians’. But he was far more than just a mathematician. Because much of his voluminous written output on various subjects was scattered throughout journals and encyclopaedias, the breadth of his interests and contributions has been underappreciated by historians. Now, renewed interest in De Morgan’s life and work has coincided with the digitization of his extensive library, revealing the extent to which he pioneered and influenced the development of not merely mathematics but also logic, astronomy, the history of mathematics, education, and bibliography.

• Education
• Mathematics

Landscapes of Investigation: Contributions to Critical Mathematics Education

• Miriam Godoy Penteado
• Ole Skovsmose

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 mathematics teacher education programmes.

• Business and Management
• Mathematics
• Science: Applied Science
• Textbooks and Learning Guides

Inventory Analytics

• Roberto Rossi

Inventory Analytics is the first book of its kind to adopt a practicable, Python-driven approach to illustrating theories and concepts via computational examples, with each model covered in the book accompanied by its Python code.

• Mathematics
• Textbooks and Learning Guides

Making up Numbers: A History of Invention in Mathematics

• Ekkehard Kopp

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.

• Mathematics
• Textbooks and Learning Guides

Advanced Problems in Mathematics: Preparing for University

• Stephen Siklos

This book is intended to help students prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Papers), and is recommended as preparation for any undergraduate mathematics course. The questions analysed in this book are all based on recent STEP questions, and each 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.

• Mathematics
• Textbooks and Learning Guides

The Essence of Mathematics Through Elementary Problems

• Alexandre Borovik
• Tony Gardiner

The Essence of Mathematics consists of a sequence of 270 problems – with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, s/he should want to understand something of mathematics beyond the classroom, and be willing to engage with (and to reflect upon) challenging problems that highlight the essence of the discipline.

• Mathematics
• Textbooks and Learning Guides

Teaching Mathematics at Secondary Level

• Tony Gardiner

Teaching Mathematics is nothing less than a mathematical manifesto. This handbook for teachers will help them broaden and enrich their students’ mathematical education. It avoids specifying how to teach, and focuses instead on the central principles and concepts that need to be borne in mind by all teachers and textbook authors—but which are little appreciated in the UK at present.