0. THE TRIANGLE GAME. Practice Problem Solutions and Hints. Exercises. 1. THE BEGINNINGS OF NUMBER THEORY. Setting the Table: Numbers, Sets, and Functions. Rules of Arithmetic.

A New System. One's Digit Arithmetic. Practice Problem Solutions and Hints. Exercises. 2. AXIOMS IN NUMBER THEORY. Consequences of the Rules of Arithmetic. Inequalities and Order.

Practice Problem Solutions and Hints. Exercises. 3. DIVISIBILITY AND PRIMES. Divisibility. Greatest Common Divisor. Primes. Practice Problem Solutions and Hints.

Exercises. 4. THE DIVISION AND EUCLIDEAN ALGORITHMS. The Division Algorithm. The Euclidean Algorithm and GCDs. The Fundamental Theorem of Arithmetic. Practice Problem Solutions and Hints. Exercises.

5. VARIATIONS ON A THEME. Applications of Divisibility. More Algorithms. Practice Problem Solutions and Hints. Exercises. 6. CONGRUENCES AND GROUPS.

Congruences. Groups and Other Structures. Practice Problem Solutions and Hints. Exercises. 7. APPLICATIONS OF CONGRUENCES. Divisibility Tests. Days of the Week.

Check Digits. Practice Problem Solutions and Hints. Exercises. 8. RATIONAL NUMBERS AND REAL NUMBERS. Fractions to Decimals. Infinity. Rational Numbers.

Irrational Numbers. How Many Real Numbers? Practice Problem Solutions and Hints. Exercises. 9. INTRODUCTION TO GEOMETRY. Practice Problem Solutions and Hints. Exercises. 10.

POLYGONS AND THEIR CONSTRUCTION. Polygons and Their Angles. Constructions. Practice Problem Solutions and Hints. Exercises. 11. SYMMETRY GROUPS. Symmetric Motions of the Triangle.

Symmetric Motions of the Square. Symmetries of Regular n-gons. Practice Problem Solutions and Hints. Exercises. 12. PERMUTATIONS. Symmetric Motions as Permutations. Counting Permutations and Symmetric Groups.

Even More Economy of Notation. Practice Problem Solutions and Hints. Exercises. 13. POLYHEDRA. Regular Polyhedra. Euler's Formula. Symmetries of Regular Polyhedra.

Reflections and Rotations. Variations on a Theme: Other Polyhedra. Practice Problem Solutions and Hints. Exercises. 14. TESSELLATIONS. Tessellating with a Single Shape. Tessellations with Multiple Shapes.

Variations on a Theme: Polyominoes. Frieze Patterns. Infinite Patterns in Two and Three Dimensions. Practice Problem Solutions and Hints. Exercises. 15. CONNECTIONS. Fibonacci Numbers and the Golden Mean.

Constructible Numbers and Polygons. Practice Problem Solutions and Hints. Exercises. Appendix: Euclidean Geometry Review.