620-111 Mathematics 1A (Advanced)

Note

Students may only gain credit for one of 620-111, 620-121, 620-142 or the 1997 Handbook subjects 618-111, 618-121, 618-142. Passing 620-111 excludes subsequent credit for any of 620-141, 620-161, 620-162.

Credit Points

Coordinator

Prerequisites

Invitation by the Head of Department, normally requiring a very high level of achievement in VCE Specialist Mathematics 3/4 or in an equivalent secondary school program.

Semester

Contact

Subject Description

This subject gives a more sophisticated treatment of core material in calculus and linear algebra than in 620-121, and an introduction to proof and the mathematical perspective, especially suited to students planning higher-level studies in mathematics and statistics.

Foundations: integers, mathematical induction; topics in elementary number theory; real numbers. Complex numbers including the complex exponential. Topics in elementary geometry. Calculus: functions of one real variable, limits, continuity, derivatives; introduction to Riemann integration, logarithm, exponential function, hyperbolic functions and their inverses; systematic integration; approximate integration; applications of integration, areas, arc lengths, volumes and surface areas of solids of revolution. Vectors and linear equations: vectors in three-dimensional space, dot and cross products; geometrical applications; linear dependence, bases and coordinates, dimension. Solution of simultaneous linear equations, row-reduction, rank, computation of inverses, determinants.

Assessment

Up to 24 pages of written assignments, a three-hour end-of-semester written examination and class tests totalling not more than 1.5 hours.