As part of the exlean project a group of undergraduates will be formalising Term 2 of the University of Exeter's introductory pure mathematics module, MTH1001. The content covered includes:
- The infinitude of primes. Modular arithmetic. Euclid's algorithm. Irrational numbers.
- Groups
- Axioms, dihedral groups, permutation group, orders of groups and elements.
- Subgroups, cyclic subgroups, cosets and Lagrange's theorem.
- Isomorphisms, homomorphisms, Cayley's thoerem.
- Linear algebra
- Linear independence, span for real vector spaces.
- Bases. Complex vector spaces. Examples. Subspaces.
- Linear maps. Matrices and linear maps.
- Vector spaces with a finite baiss. Dimenson.