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Resources for Algebra II - for more information about the course, please see course outlines.

MLC Drop-In Centre

Students from Algebra II can use the drop-in centre, but we will give priority to first year students. If you see every other table has students, then we would appreciate it if you found another place to sit so that there is room for new students.

Please note that not every staff member in the MLC knows all of the content in Algebra II, there will be times when we can only give general study advice for this course.

Assumed knowledge

The second half of Algebra II concerns vector spaces and linear transformations.. This builds on the content of Mathematics IA and Mathematics IB. The following revision seminars will be helpful for revising this content:

This seminar for Maths IA students from 2014 covers all of the concepts to do with independence, span, subspaces and basis, beginning with what vectors and sets are. (David considers this one of his best revision seminars ever.)

This seminar for Maths IB from 2012 covers linear transformations, focusing especially on kernel and range of linear transformations (unfortunately the last several minutes were cut off from this video).

This revision seminar for Maths IB from 2016 covered orthonormal basis and the Gram-Schmidt process in linear algebra.

The beginning of this seminar for Maths IB from 2017 covers orthogonal diagonalisation.

This seminar for Maths IB from 2014  gives advice for creating proofs in linear algebra involving subspaces, linear transformations and matrices.

Algebra II revision seminars in order of time

These are the seminars that have been given for Algebra II in order of time, with the most recent seminars at the top. Note that the curriculum for Algebra II changes regularly, so some topics in older seminars might not exist in the current version of the course.

2024: Miscellaneous topics

In the 2024 seminar, David discussed how to tell if groups aren't isomorphic (at the start), dual spaces and dual bases (at 25m22s), quotient spaces (at 1h17m40s), and a little bit on bilinear forms (at 1h32m47s).

2023: Groups

In the 2023 seminar, talked about various definitions and theorems and other bits and pieces in the Groups section of the course.

2022: Isomorphism theorem, dual spaces, proofs

In the seminar in 2022, David discussed general advice for proofs, then the first isomorphism theorem (at 12m10s), then dual spaces (at 52m50s), and finally a proof about factor groups (at 1h52m26s).

2021: Vector spaces, Jordan form

In the seminar in 2021, David covered many concepts about vector spaces, using the polynomials of degree up to 2 as an example. Then David talked about Jordan form for matrices. (Note there were technical issues during the seminar, so the video is in two parts.)

2019: Projections, dual spaces, transpose

In the seminar in 2019, discussed ideas on request (trying to figure out some of them on the fly) including projections, dual spaces and transpose.

2018: Ordered bases, Jordan form, adjoints

In the seminar in 2018, David took requests from the students present. He ended up discussing ordered bases, jordan canonical form, and adjoints. (Note that David did not already know about most of these things and only had the lecture notes to go on, and so several times he didn't come to a conclusion about the correct way to do things or their meaning. He hopes it's still useful to see his method of trying to figure stuff out.)

2015: Groups

In the seminar in 2015, David covered various concepts about groups. David talked about symmetries of shapes, permutations in cycle notation, isomorphisms, subgroups and a bit on cosets.