Mathematics, Science Area of Concentration, Associate of Science
This Associate of Science area of concentration is designed to help students transfer to colleges and universities that offer a baccalaureate degree with a major in Mathematics. Beyond the General Education requirements and options, this concentration should be considered in light of the requirements of the selected transfer institution. Students should consult with a transfer coordinator or an advisor for information about specific requirements.
The required courses listed here assume that the student has a background that includes algebra, geometry, and trigonometry. Students who do not meet these requirements can take the required prerequisite courses at CCBC after placement testing.
Upon successful completion of this degree, students will be able to:
- evaluate limits of one-variable functions and of multi-variable functions; definite, indefinite, and improper integrals; double integrals in rectangular and in polar coordinates; triple integrals in rectangular, cylindrical, and spherical coordinates; line and surface integrals; and solve first order differential equations;
- determine continuity and differentiability of one-variable functions and of multi-variable functions; the derivative of a one-variable function by the definition and by rules; partial derivatives of multi-variable functions by the definitions and by rules; optimal values (extrema) of one-variable functions and of multivariable functions; the convergence/divergence of a sequence and of a series;
- apply theorems (including: Mean Value Theorem, Intermediate Value Theorem, Rolle's Theorem, Fundamental Theorem of Calculus, L'Hôpital's Rule, Green's Theorem, and Stokes' Theorem) and mathematical processes to solve real-world application problems;
- compute eigenvalues, eigenvectors, and eigenspaces; verify that a structure is a vector space by checking the axioms; that a subset is a subspace; and that a set of vectors is a basis;
- graph and analyze polar coordinates, parametric equations, and vectors and vector fields; and
- analyze algebraic and geometric properties of the dot product and of the cross product.