Univ. of Calif. – Santa Barbara Math Courses for Prospective H S Teachers
4-credit tri-semester courses
MATH 101A. Classical Number Systems
Prerequisite: Transition to Higher Math courseMathematics 3A
Enrollment Comments: Not open for credit to students who have completed
Mathematics 118A.
Especially suitable for prospective teachers. A conceptual rather than an axiomatic
development starting with the natural numbers and progressing through the integral,
rational, real, and complex number systems. The historical implications of these
developments in number systems.
MATH 101B. Mathematical Systems
Prerequisite: Mathematics 101A.
Enrollment Comments: Not open for credit to students who have completed
Mathematics 118A.
Especially suitable for prospective teachers. The theory of operations within rings and
fields and the foundations of the real number system. Ideals, quotient rings, and
factorization theorems. The history and the historical implications of these developments
in mathematical systems.
MATH 102A. Modern Euclidean and Noneuclidean Geometry
Prerequisite: Calculus II.
Especially suitable for prospective teachers. Topics in plane and solid geometry. The
axioms of pure, euclidean, projective, and noneuclidean geometry. Transformational
geometry (isometries, dilitations, involutions, perspectivities, and projectivities). The
history and the historical implications of these developments in geometry.
MATH 102B. Modern Euclidean and Noneuclidean Geometry
Prerequisite: Mathematics 102A.
Especially suitable for prospective teachers. Topics in plane and solid geometry. The
axioms of pure, euclidean, projective, and noneuclidean geometry. Transformational
geometry (isometries, dilitations, involutions, perspectivities, and projectivities). The
history and the historical implications of these developments in geometry.