CV, Complex numbers and vectors

To have the courage to think outside the square, we need to be intrigued by a problem. 'Complex Numbers and Vectors' draws on the power of intrigue and uses appealing applications from navigation, global positioning systems, earthquakes, circus acts and stories from mathematical history to explain the mathematics of vectors and the discoveries in complex numbers. The first part of 'Complex Numbers and Vectors' provides teachers with background material, ideas and teaching approaches to complex numbers; models for complex numbers and their geometric and algebraic properties; their role in providing completeness with respect to the solution of polynomial equations of a single complex variable (the fundamental theorem of algebra); the specification of curves and regions in the complex plane; and simple transformations of the complex plane. The second part of this resource provides an introduction to vectors and vector spaces, including matrix representation; covers vectors in two- and three-dimensions; their application to specification of curves; vector calculus and their elementary application to geometric proof. Technology has been used throughout the text to construct images of curves, graphs and two and three dimensional shapes Complex Numbers and Vectors is an informative resource for advanced mathematics teachers or students undertaking advanced maths courses that draws on the power of intrigue and uses appealing applications from navigation, global positioning systems, earthquakes and stories from mathematical history to explain the mathematics of vectors and the discoveries in complex numbers. The title is split into two parts: Part 1 provides teachers with background material, ideas and teaching approaches to complex numbers: o Including models for complex numbers and their geometric and algebraic properties, their role in providing completeness with respect to the solution of polynomial equations of a single complex variable (the fundamental theorem of algebra) and the specification of curves and regions in the complex plane; and simple transformations of the complex plane. Part 2 provides an introduction to vectors and vector spaces: o Including matrix representation (covers vectors in two- and three-dimensions), their application to specification of curves and vector calculus and their elementary application to geometric proof Technology has been used throughout the text to construct images of curves, graphs and two and three dimensional shapes. This book provides teachers with background material, ideas and teachingapproaches to complex numbers; models for complex numbers and their geometricand algebraic properties; their role in providing completeness with respect to thesolution of polynomial equations of a single complex variable (the fundamentaltheorem of algebra); the specification of curves and regions in the complex plane;and simple transformations of the complex plane. It also provides an introduction to vectors and vector spaces, including matrixrepresentation; covers vectors in two and three dimensions; their applicationto specification of curves; and vector calculus and their elementary applicationto geometric proof. Technology has been used throughout the text to constructimages of curves, graphs and two- and three-dimensional shapes Preliminaries; Contents; Introduction; About the author; 1 Complex numbers and vectors in the secondary curriculum; 2 A tale of intrigue and imagination; 3 Secrecy, contrivance and inspiration; 4 Form and structure: A careful exposition on operating with complex numbers; 5 The genius of Gauss; 6 Mathematicians can read maps; 7 Plotting a course; 8 Sailing against the wind; 9 It's a circus; 10 It's now possible to know where we are!; 11 Pons asinorum - the asses' bridge; 12 Curriculum connections; 13 Solution notes to student activities; References and further reading.