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The syllabus will be updated as the course progresses. Unless otherwise indicated, section numbers and exercises refer to the text Naive Lie Theory by John Stillwell.
| Date | Text Sections | Material | Recommended Exercises |
| Jan 6 | 1.1 | Introduction, a categorical definition of Lie groups, examples. | 1.1.1–1.1.5 |
| Jan 11 | 1.2, 1.3 | Rotations of the plane, quaternions. | 1.2.1–1.2.5; 1.3.1–1.3.8 |
| Jan 13 | No class. Make-up class to be held on January 21 at 11:30am. | ||
| Jan 18 | 1.4, 1.5 | Quaternions and space rotations. | 1.4.1–1.4.4; 1.5.1–1.5.4 |
| Jan 20 | 2.3, 2.4 | SU(2) and SO(3), The Cartan-Dieudonné Theorem. | 2.1.3–2.1.6; 2.2.1–2.2.5; 2.3.1–2.3.5 |
| Jan 21 | 2.5–2.7 | Make-up class, LMX 242, 11:30am–1:00pm. Quaternions and rotations in R4, SU(2)xSU(2) and SO(4). | 2.6.1–2.6.3; 2.7.1–2.7.5 |
| Jan 25 | 3.1–3.4 | Matrix Lie groups: definitions and examples. | 3.3.1–3.3.6 |
| Jan 27 | 3.4, 8.6 | The symplectic groups, connectedness. | 3.2.1–3.2.3; 3.4.1–3.4.5 |
| Feb 1 | 3.2–3.3 | Connectedness. | |
| Feb 3 | 8.1–8.4 | Compactness. | 8.2.1–8.2.3 |
| Feb 8 | 3.5–3.6 | Maximal tori. | 3.5.2–3.5.6; 3.6.1–3.6.2 |
| Feb 10 | 3.7–3.8 | Centres and discrete subgroups. | 3.7.1–3.7.3; 3.8.1–3.8.5 |
| Feb 22 | 4.1–4.4 | The exponential map, Lie algebras. | 4.1.3–4.1.4; 4.2.1–4.2.3; 4.3.2–4.3.3 |
| Feb 24 | Midterm exam (covers up to and including the material covered before the reading break). | ||
| Mar 1 | 4.5, 5.1 | The matrix exponential, tangent spaces. | 4.5.1–4.5.6 |
| Mar 3 | 5.2–5.5 | Tangent spaces (cont.), the Lie algebra of a Lie group. | 5.2.1–5.2.8; 5.3.6; 5.3.7; 5.4.1–5.4.5 |
| Mar 8 | 5.6, 7.1 | Complexification, the matrix logarithm. | 5.6.1; 5.6.4–5.6.8; 7.1.6 |
| Mar 10 | 7.1–7.3 | The matrix logarithm, the exponential map. | 7.2.1; 7.2.4–7.2.6; 7.3.1; 7.3.2 |
| Mar 15 | 7.4 | The matrix logarithm, the exponential map (cont.). | 7.4.1; 7.4.2 |
| Mar 17 | Hall 2.4, 2.6 | One parameter subgroups, the functor from Lie groups to Lie algebras. | 7.4.1; 7.4.2 |
| Mar 22 | Stillwell 7.5 and Hall 2.6, 2.7 | The adjoint mapping, normal subgroups and Lie algebras. | 7.5.2–7.5.4. |
| Mar 24 | 7.6 | The Campbell-Baker-Hausdorff Theorem. | 7.6.1–7.6.4 (note that 7.6.3 and 7.6.4 only apply in a neighbourhood of the identity); 7.7.1–7.7.2 |
| Mar 29 | 8.7 | Teaching evaluations. Simple connectedness. | 8.7.1–8.7.5 |
| Mar 31 | 9.1, 9.2 | Simple connectedness, simply connected Lie groups. | 9.1.3; 9.1.4 |
| Apr 7 | 9.4–9.6 | Simply connected Lie groups and their characterization by Lie algebras. | |
| Apr 12 | Hall 3.7 | Covering groups. |