Solutions to Exercises
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Solutions A Solutions to Exercises
Section 1.1 Complex Numbers
Exercises 1.1.7 Exercises
1.1.7.1.
1.1.7.2.
1.1.7.3.
1.1.7.4.
1.1.7.5.
1.1.7.6.
1.1.7.7.
1.1.7.8.
1.1.7.9.
1.1.7.10.
Section 2.1 Examples of groups
Subsection 2.1.1 Permutations
Checkpoint 2.1.2.
Subsection 2.1.2 Symmetries of regular polygons
Checkpoint 2.1.6.
Section 2.2 Definition of a group
Exercises Exercises
2.2.11. Cayley tables.
Section 2.3 Subgroups and cosets
Checkpoint 2.3.2.
Exercises Exercises
2.3.2.
2.3.8. Cosets of a subgroup partition the group, Lagrange's Theorem.
Section 2.4 Group homomorphisms
Section 2.6 Additional exercises
Exercises Exercises
2.6.3. Fermat's Little Theorem.
Section 3.2 Möbius geometry
Exercises 3.2.6 Exercises
Section 3.3 Hyperbolic geometry
Exercises 3.3.6 Exercises
3.3.6.2. Two points determine a line.
3.3.6.3. Dropping a perpendicular from a point to a line.
3.3.6.9. Area of an asymptotic \(n\)-gon.
3.3.6.10. Area of a hyperbolic triangle.
