# How to solve it?

Instructor: Anna Felikson**Spring and Summer 2023:**The notes (hand-written notes in Russian):

- How to solve it? The table from G. Polya's book "How to solve it" (in English and in Russian)
- 1. Pigeonhole principle.
- 2. Proof by contradiction.
- 3. Induction.
- 4. Extremal principle.
- 5. Invariants.
- 6. Semi-invariants.
- 7. And how to solve it?
- 8. Solving problems about problem solving
- 9. Smile!
- 10. Remainders and leftovers

### Resources:

- 1. 500 Questions on Pigeonhole principle on problems.ru (in Russian)
- 4. Hermit Crabs trade shells (5 min BBC video)

# Geometries

**Winter 2023:**The notes (hand-written notes in Russian):

### Resources:

- 1. Inversion:
- Animation demonstrating Inversion in circles, by Malin Christersson.
- Lipkin's Inversor, on Mathematical Etudes.

- 2. Different types of infinities:
- Where is more?, by Sergei Tabachnikov.

- 4. Spherical Geometry:
- Spherical Droste video, 2-minute video by Henry Segerman.

- 5. Hyperbolic Geometry:
- Make hyperbolic tilings of images, by Malin Christersson.

# Geometry in Figures

In some of lessons we used ideas from the book "Geometry in Figures" by Arseniy Akopyan: links to the book in Russian and in English.**Autumn 2022:**The notes (hand-written notes in Russian):

### Resources:

- Pythagorean spiral on Wikipedia
- Unterweisung der Messung by Albrecht Durer

### Textbook:

- Geometry textbook by O. V. Pogorelov: in Ukranian and in Russian.