## Topological Solitons

This is the page for the short graduate course in topological solitons for the academic year 2016-17. If you need any more help with the course or you find any typos/mistakes either email me or come and see me in my office.

### Book Recomendations:

Topological Solitons
N.S. Manton and P.M. Sutcliffe
Cambridge Monographs on Mathematical Physics,
Cambridge University Press (2015).
The source of information on the general subject of topoloigcal solitons.

Superfluid States of Matter
B.V. Svistunov, E.S. Babaev and N.V. Prokof'ev
Cambridge Monographs on Mathematical Physics,
CRC Press (2015).
The source of information on the general subject of topoloigcal solitons.

• Topological solitons Week 2-Axioms of a vector space and formal proofs, the dot product (associativity, linearity, calculations) and introduction to $\mathbb{R}^{n}$.
Tutorial solutions here.
Homework model solutions here.
• Proof of Cauchy-Schwarz inequality here.
• Week 3-Cross Product, triple product, geometry of planes and lines and proofs using general products.
Tutorial solutions here.
• Homework model solutions here.
• Week 4- Lines and planes revisted, simulataneous equations and row reduced echelon form.
Tutorial solutions here.
• Week 5- Matricies and their properties (Inverses and Determinants).
• Week 6- More on matricies.
• Week 7- Using determinants and inverses (parallelograms and their properties).
Homework model solutions here.
• Week 8- Linear Independence, spanning sets, bases, the trace and Cramer's rule.
• Week 9- More on linear independence, spanning sets and bases including bases of alternative vector spaces.
• Week 10- Vector subspaces, rank, nullity , rank-nullity theorem, changes of basis and the dreaded magic sqaure question.