7 Thematic Index

7.1 Euclidean Algorithm

2-4, 2-5, 2-6; p. 15, 18-21.
2-19; p. 16, 31 (for polynomials).
2-23; p. 36, 159.
2-28; 2-29; p. 37, 159.
2-55; p. 39, 161.

7.2 Modular Arithmetic

1-5; p. 5, 9.
2-10, 2-11, 2-12, 2-13, 2-14; p. 16, 23-27.
2-27; p. 37, 159.
2-31, 2-32; p. 37, 159.
2-35, 2-36, 2-37, 2-38, 2-39, 2-40, 2-41, 2-42, 2-43; p. 37-38, 159.
2-53; p. 39, 160.
6-1; p. 131, 134.
6-19, 6-20; p. 154, 167.

7.3 Geometric Transformations

3-2; p. 41, 44 (inversion).
3-5; p. 41, 47 (inversion).
3-6; p. 41, 48 (homothety, similarity).
3-9; 3-10; p. 41, 50-53 (homothety, similarity, central projection).
3-12; p. 41, 54 (axial symmetry).
3-15; p. 42, 57 (motions).
3-16; p. 42, 58 (axial symmetry, reflection).
3-25; p. 43, 67 (polar transformation).
3-30, 3-31; p. 69, 162 (similarity).
3-35, 3-36; p. 69, 162 (axial symmetry, reflection).
3-41; p. 70, 162 (axial symmetry).
3-42; p. 70, 162 (similarity).
3-43, 3-44; p. 70, 162 (homothety, similarity, central projection).
3-54; p. 71, 163 (polar transformation).
4-3; p. 72, 75 (axial, central symmetry).
4-19; p. 73, 91 (central symmetry).
4-46; p. 97, 165 (symmetry).
4-49; p. 108, 165 (axial symmetry).
5-7; p. 99, 106.
6-9; p. 132, 139.
6-15; p. 133, 148 (homothety and rotation; continuous transformations).
6-30; p. 156, 167 (similarity).

7.4 Graphs

1-16; p. 7, 11.
1-20, 1-21, 1-22; p. 7, 12.
1-25; p. 8, 13.
3-23; p. 43, 66 (Steinitz’s theorem on planar graphs of polyhedra).
5-12; p. 100, 111.
5-15; p. 100, 115 (Euler’s theorems, Pontryagin-Kuratowski theorem).
5-18, 5-19; p. 100, 118-120 (tournaments, companies).
5-21; p. 101, 122 (finite projective plane).
5-36, 5-37; p. 128, 166.
5-41, 5-42; p. 129, 166.
6-7; p. 131, 137.
6-10; p. 132, 140-142 (composition of homothety and rotation).
6-40; p. 158, 168 (bipartite graph).

7.5 Diophantine Equations

2-1, 2-2; p. 15, 17 (linear equations in integers).
2-7; p. 15, 21.
2-23; p. 36, 159.
2-25; p. 36, 159.
2-32, 2-33, 2-34; p. 37, 159.
2-36, 2-37; p. 37-38, 159.
2-55; p. 39, 161.
5-3; p. 99, 103.
5-19; p. 100, 120.
5-24; p. 127, 165.
5-26; p. 127, 165.
5-32; p. 128, 166.
5-40; p. 129, 166.

7.6 Dirichlet Principle

2-9; p. 16, 23.
2-31; p. 37, 159.
4-22; p. 74, 93.
4-23; p. 74, 93 (continuous analog).
4-29; p. 96.
4-32; p. 96, 163.
4-48; p. 97, 165.
6-1; p. 131, 134.
6-8; p. 132, 138-139.
6-12; p. 132, 143-144.
6-14; p. 133, 147-148.

7.7 Invariant

6-7; p. 131, 137-138.
6-10; p. 132, 140-142.
6-12; p. 132, 143-144.
6-35, 6-36; p. 156, 168.
6-40; p. 158, 168.

7.8 Combinatorics

2-16; p. 16, 28.
2-30; p. 37, 159.
3-18, 3-19; p. 42, 61-63.
4-24; p. 74, 94-95.
5-4, 5-5; p. 99, 104-105.
5-14, 5-15, 5-16; p. 100, 115-117.
5-18, 5-19, 5-20, 5-21, 5-22; p. 100-101, 118-127, 165.
**5-25