MATH1115: Advanced Mathematics and Applications 1
| Runs | Semester 1 |
|---|---|
| Lecturer | Griffith Ware, Stephen Roberts |
MATH1115 (triple-one five) is a first year first semester maths course. It is generally regarded as very difficult and theoretical. In most cases you can choose to take the easier, more applied MATH1013 instead.
It is essentially two courses in one: real analysis (taught by Griff) and linear algebra (taught by Stephen). There are 4 lectures a week, 2 per course. There is a weekly lab, a weekly assignment which is fairly time consuming, a mid-semester exam and a final exam. The lecturers, tutors, lab worksheets and assignments are all excellent.
Griff will teach you about the theoretical underpinnings of calculus and how to do formal proofs. In your prerequisite high school maths courses you should have learned about limits, integration and differentiation in a single variable. In 1115 you will learn how these concepts can be rigorously formalised and proven to behave correctly. For instance, you will learn the formal epsilon-delta definition of limits and prove that all the laws you may know for manipulating them are valid. You will build up to the Riemann-Darboux definition of integration and then to proving the fundamental theorem of calculus at the end (differentiation and integration are inverses) from first principles. The content is deceptively difficult - you cover concepts you already know in far greater depth, and build up a better intuition for them and how to construct proofs along the way.
Stephen will teach you about linear algebra, a type of maths that uses vectors and matrices instead of numbers. Many high school curricula (eg HSC maths in NSW) do not cover matrices, so you may be in catch-up mode for the first few weeks. Long story short, matrices are like tables of numbers that transform vectors via an unintuitive "multiplication" operation. You will learn how to compute matrix operations, how to do algebra with them (they have slightly different rules to normal numbers, like multiplication order matters), and about theory like vector spaces. Linear algebra is essential in machine learning and many other disciplines, so it's worth taking good notes!
MATH1115 leads into MATH1116 (also taught by Griff) which continues teaching real analysis and linear algebra in greater depth. In most degrees you can take MATH1013 and MATH1014 instead of MATH1115 and MATH1116 (or you can do MATH1115 and MATH1014). The 1013/1014 courses are much more applied, like continuations of your high school maths classes. They cover limits, calculus and linear algebra but not in as much depth or with anywhere near as many proofs. They are less difficult and better suited to many people - if you don't enjoy pure maths you probably won't enjoy 1115!