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1. LECTURE 3.11.2022: Some algebraic background.
2. LECTURE 10.11.2022: Volume, convex body, module, lattice, determinant, linear map.
3. LECTURE 17.11.2022: Jacobian, lattice, determinant, linear map up to (30).
4. LECTURE 24.11.2022: Linear map, Blichfeldt's theorem, The first Minkowski's convex body theorem/Non-compact version, A Diophantine equation.
5. LECTURE 1.12.2022: The first Minkowski's convex body theorem/Compact and linear map versions. Applications to linear forms.
6. LECTURE 12.1.2023: The first Minkowski's convex body theorem/Applications to linear forms, diophantine inequalities over reals, Dirichlet's theorem.
7. LECTURE 19.1.2023: The first Minkowski's convex body theorem/Applications to simultaneous linear forms.
8. LECTURE 26.1.2023: Successive minima, The first Minkowski's convex body theorem revised by the first minimum.
9. LECTURE 9.2.2023: Successive minima, The first Minkowski's convex body theorem revised by the first minimum, shortest vector in a lattice.
10. LECTURE 16.2.2023: Successive minima, an estimate for shortest vectors in a lattice, examples.
11. LECTURE 23.2.2023: Lattice packing, lattice packing density, The second revision of the first Minkowski's theorem.
12. LECTURE 2.3.2023, LAST LECTURE: Lattice sphere packing, lattice sphere packing density, a refined estimate for shortest vectors in a lattice, the SVP-problem, Kepler problem, The third revision of the first Minkowski's theorem.
Exercises, 1. set: problems 1--7. Deadline 8.12.2022 at 14--16. Solutions of the homework exercises: on Thursday 8.12.2022 at 14--16, room M205.
Exercises, 2. set: problems 8--13. 15.12.2022 at 14--16. Solutions of the homework exercises: on Thursday 15.12.2022 at 14--16, room M205. New deadline 27.1.2023 at 12:00 (noon).
Exercises, 3. set: problems 14--19. Deadline 30.1.2023 at 12:00 (noon). Solutions of the homework exercises: on Thursday 2.2.2023 at 12--14, room M3.
Exercises, 4. set: problems 20--25. Deadline 17.2.2023 at 12:00 (noon).
Exercises, 5. set: problems 26--30. Deadline 6.3.2023 at 12:00 (noon).
GEOMETRY OF NUMBERS 2022-2023; SLIDES PART A/TOOL BOX. Updated 16.1.2023 at 12:28.
GEOMETRY OF NUMBERS 2022-2023; SLIDES PART B. Updated 19.11.2022 at 17:24.
GEOMETRY OF NUMBERS 2022-2023; SLIDES PART C. Updated 7.2.2023 at 19:20.
GEOMETRY OF NUMBERS 2022-2023; SLIDES PART D. Updated 7.2.2023 at 19:20.
GEOMETRY OF NUMBERS 2022-2023; SLIDES PART E. Updated 30.3.2023 at 16:20.
GEOMETRY OF NUMBERS 2022-2023; EXERCISES. Updated 26.2.2023 at 22:53.