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 Student Outcomes Students solve quadratic equations with complex solutions. Students understand the geometric origins of the imaginary unit i in terms of 90degree rotations. Students use this...

 Student Outcomes Students determine the complex roots of polynomial equations of the form xn = 1 and, more generally, equations of the form xn = k positive integers n and positive real numbers k....

 Student Outcomes Students apply their understanding of polynomial identities that have been extended to the complex numbers to find the square roots of complex numbers.

 Student Outcomes Students determine all solutions of polynomial equations over the set of complex numbers and understand the implications of the fundamental theorem of algebra, especially for...

 Topic A brings students back to the study of complex roots of polynomial functions. Students briefly review quadratic and cubic functions and then extend familiar polynomial identities to both...

 Student Outcomes Students will create a short animation in ALICE 3.1 using onestep procedures. Students will apply their understanding of the mathematics of projecting threedimensional images onto...

 Student Outcomes Students learn to project points in 3dimensional space onto a 2dimensional plane. Students learn how to simulate 3dimensional turning on a 2dimensional screen.

 Student Outcomes Through discovery, students will understand how challenging it is to project threedimensional objects onto a twodimensional space. Students will understand that vanishing points...

 In Topic E students apply the knowledge developed in this module to understand how firstperson video games use matrix operations to project threedimensional objects onto twodimensional screens and...

 Student Outcomes Students apply linear transformations and vectors to understand the conditions required for a sequence of transformations to preserve the solution set to the system of equations.

 Student Outcomes Students write parametric equations for a line through two points in ℝ2 and ℝ3 and for a line segment between two points in ℝ2 and ℝ3. Students write parametric equations for the...

 Student Outcomes Students solve problems involving physical phenomena that can be represented by vectors.

 Student Outcomes Students write the equation for a line in ℝ2 or ℝ3 using vectors. Students write the parametric equations for a line in ℝ2 or ℝ3 . Students convert between parametric equations and...

 Student Outcomes Students understand the forces involved in constructing a stone arch. Students add and subtract vectors given in magnitude and direction form. Students solve problems that can be...

 Student Outcomes Students find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. Students add vectors endtoend using the...

 Student Outcomes Students use vectors to define a translation map and translate geometric figures in ℝ and ℝ . Students represent and perform calculations with threedimensional vectors and...

 Student Outcomes Students add and subtract vectors and understand those operations geometrically and componentwise. Students understand scalar multiplication graphically and perform it component...

 Topic D opens with a formal definition of a vector. The arithmetical work for vector addition, subtraction, scalar multiplication, and vector magnitude is explored along with the geometrical...

 Student Outcomes Students represent complicated systems of equations, including 4×4 and 5×5 systems of equations, using matrix equations in the form Ax = b, where A represents the coefficient matrix...

 Student Outcomes Students will represent systems of three or more simultaneous equations as a linear transformation in the form Ax = b, where A represents the linear transformation, x represents the...

 Student Outcomes Students will represent systems of equations as linear transformations of the form Lx = b, using matrix notation. Students will discover that the systems of equations written in the...

 Topic C provides a third context for the appearance of matrices via the study of systems of linear equations. Students see that a system of linear equations can be represented as a single matrix...

 Student Outcomes Students study and practice the properties of matrix multiplication. Students understand the role of the multiplicative identity matrix.

 Student Outcomes Students discover and verify that matrix multiplication is distributive. Students discover and verify that matrix multiplication is associative.