MATH135 - Mathematics IA
This is the first mainstream mathematics unit offered at Macquarie University. It is essential study for students in science and technology, and recommended for students in many other areas who wish to enhance their mathematical skills.
Apart from some brief discussion on complex numbers and congruences, the main topic in the algebra half of this unit concerns linearity and the interplay between algebra and geometry. Plane geometry is first used to motivate the study of systems of linear equations. Algebraic techniques involving matrices and determinants are then developed to study these problems further. The algebraic machinery developed is then used to study geometrical problems in 3-dimensional space.
The notion of a limit is developed to a more sophisticated level than in secondary school mathematics, and this is used to study the differential and integral calculus involving functions of one real variable to a far greater depth than before. Some simple numerical techniques on integration are also discussed.
Prerequisites: HSC Mathematics Band 4 or HSC Mathematics Extension 1 Band E2 or HSC Mathematics Extension 2 Band E2 or MATH130(P) or equivalent (including MATH132(F) with permission of Dean of ICS).
Corequisites: None.
Not Counted for Credit With: HSC Mathematics Extension 1 Band E4, HSC Mathematics Extension 2 Band E3, MATH132.