MATH1116: Advanced Mathematics and Applications 2
NOTE: This is currently a draft version. Final revisions/comments to be made.
| Runs | Semester 2 |
|---|---|
| Lecturer | Griffith Ware, Loan Licata |
MATH1116 runs in Semester 2 and continues on from the content delivered in MATH1115. Like its predecessor, it is often regarded as a difficult course with a similar assessment structure and style. If you plan on studying further pure math courses then this course is essential. Within computing courses, the linear algebra and multivariable calculus components are often seen as beneficial to most of the Machine-Learning courses offered in later years. More generally, the course will continue to develop you ability to construct rigorous proofs which can be useful in some unexpectedly proof heavy courses such as COMP3600. If you are seeking a more applied course after taking 1115, then it is possible to take MATH1014 instead however, some of the content is repeated from 1115.
Griff will continue the analysis portion of the course by first generalising the theory regarding Reimann-Darboux integration to multiple dimensions. This theory leads on to more calculational content including the evaluation of iterated integrals, derivatives in higher dimensions, limits and continuity in higher dimensions and some deeper theory on how linear algebra overlaps with these areas. Both Taylor Series and Power Series are also introduced towards the end of the course. It is extremely important that the content in these areas from 1115 are well understood as many of the concepts and proof techniques are assumed in building more complex theory.
The linear algebra component importantly introduces more generalised linear algebra tools from 1115. The section begins with a strong emphasis on the theory surrounding linear maps, sums of subspaces, operators and dual spaces/maps. Much of this underpins the rest of the algebra course content so it is essential that the content presented in the first few weeks is understood. The course then develops an understanding of properties of linear maps including eigenvectors/spaces and how they can be used to understand matrices and generally, linear transformations better. Heavier theory regarding generalised inner products, adjoints and singular values take up the late stage of the course. Compared to 1115, the linear algebra in 1116 is more proof-heavy as the content is expanded beyond the use of mere matrices.
The assessment comprises of weekly assignments (30%) a midsemester exam (25-30%), online/lab participation (0-5%) and a final exam (~40%). Because of how sizeable the assignment component is, it is crucial that you are able to give them some focus throughout the week. Labs are extremely helpful in consolidating the weekly lecture content and usually provide some aid to the assignment. Student's also find collaborative work in this subject especially helpful as many of the concepts can be tricky to grasp at first by your own. For both the midsemester and final exam, practice exam content is provided and is similar to the real thing so be sure to make use of this resource. The linear algebra component also closely follows the textbook "Linear Algebra Done Right" by Sheldon Axler and aside from being used in the course, it is a great resource for learning the content so it is highly recommended you have a copy of the textbook.
If you enjoyed this course, then MATH2322 (Algebra 1) and MATH2320 (Analysis 1) could be courses that interest you.