*"Candidates demonstrate computational proficiency, including a conceptual understanding of numbers, ways of representing number, relationships among number and number systems, and meanings of operations."*

**Reflection on the Standard:**

One of the courses I have taken to fulfill this standard is Linear Algebra. This course covered systems of linear equations, matrix theory, vector spaces, linear transformations, determinants, eigenvalues, and eigenvectors. In this course I gained a conceptual understanding of vectors and matrices as systems that have some of the properties of the real number system (meeting indicator 9.9).

Another course I have taken to fulfill this standard is Abstract Algebra. This course covered algebraic structures, elementary properties of numbers, polynomials, groups, rings, integral domains, and fields. In this course I analyzed and explained the mathematics that underlies the procedures used for operations involving integers, rational, real and complex numbers (meeting indicator 9.1), compared and contrasted the properties of numbers and number systems including Z, Q, R, C, Zm, Z[x], Q[x], Z[root n], and Z[i] (meeting indicator 9.7), represented, used, and applied complex numbers (meeting indicator 9.), and gained an understanding of the historic development of numbers and number systems by reading Unknown Quantity (Derbyshire, 2006) (meeting indicator 9.10).

**Artifact:**

To illustrate this standard, I have selected a homework assignment on complex numbers from Abstract Algebra. Please click the artifact icon below to view this assignment:

**Explanation of Artifact in Relation to the Standard:**

In this assignment, I analyze the mathematics that underlies the procedures used for operations involving complex numbers (meeting indicator 9.1) and use the properties of the complex number system to determine various roots of complex numbers (meeting indicator 9.7).