Explorations In Mathematics

Provides readers with experience of working on difficult unsolved problems. No deep mathematical background is required.

Grade level: 11, s, t.

This book presents teachers with a sound theoretical framework for encouraging children to explore mathematical concepts and become numerate in the 21st century. It shows that mathematical learning can occur in a variety of ways, including when children explore ideas through play, problem solving and problem posing, engage in a rich variety of multimodal learning experiences, pursue self-directed activities and cooperate with others, and make connections between ideas and experiences in their everyday worlds. - Back cover

Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You will see how the accelerated frames of special relativity tell us about gravity. On the journey, you will discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods. Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.

The investigations in this book stretch students' mathematical imaginations to their limits as they investigate the numeration systems of creatures from another planet, create and solve stories and problems with extreme numbers, use place value to design their own new divisibility strategies, and play with a strange kind of number line specially de

"Disability and Academic Exclusion interrogates obstacles the disabled have encountered in education, from a historical perspective that begins with the denial of literacy to minorities in the colonial era to the later centuries' subsequent intolerance of writing, orality, and literacy mastered by former slaves, women, and the disabled. The text then questions where we stand today in regards to the university-wide rhetoric on promoting diversity and accommodating disability in the classroom." Amazon.com viewed 6/2/2020.

How does mathematics enable us to send pictures from space back to Earth? Where does the bell-shaped curve come from? Why do you need only 23 people in a room for a 50/50 chance of two of them sharing the same birthday? In Strange Curves, Counting Rabbits, and Other Mathematical Explorations, Keith Ball highlights how ideas, mostly from pure math, can answer these questions and many more. Drawing on areas of mathematics from probability theory, number theory, and geometry, he explores a wide range of concepts, some more light-hearted, others central to the development of the field and used daily by mathematicians, physicists, and engineers. Each of the book's ten chapters begins by outlining key concepts and goes on to discuss, with the minimum of technical detail, the principles that underlie them. Each includes puzzles and problems of varying difficulty. While the chapters are self-contained, they also reveal the links between seemingly unrelated topics. For example, the problem of how to design codes for satellite communication gives rise to the same idea of uncertainty as the problem of screening blood samples for disease. Accessible to anyone familiar with basic calculus, this book is a treasure trove of ideas that will entertain, amuse, and bemuse students, teachers, and math lovers of all ages.