Monash University Handbook 2010 Undergraduate - Unit

Synopsis

Number systems (natural, rational, real and complex numbers); algebraic structures (groups, rings and fields); countability; functions, graphs, limits; differentiation and integration theory; fundamental theorem of calculus; infinite sequences and series; uniform convergence and power series; fundamental theorem of algebra.

Objectives

On completion of this unit, students will have an understanding of: the mathematical structures arising in various areas of mathematics and the connections between these; the applicability of mathematical ideas to other areas of science; some basic algebraic structures such as the natural numbers, the real numbers, finite rings, fields and the complex numbers; some basic concepts of analysis including limits, derivatives, integrals, sequences and series. Students will have developed skills in: identifying different types of basic algebraic structures; reproducing and developing some simple mathematical proofs; using rigorous mathematical arguments; applying results arising from proofs to the convergence of both iterative techniques and series.

Assessment

Examination (3 hours): 80%
Assignments: 20%

Contact hours

Three 1-hour lectures and one 1-hour tutorial per week

Prerequisites

MTH1030 or MAT1085 or equivalent

Prohibitions

MTH2140, MTH3111 and MTH3140