Contents: (200 pages)
1 Basic Algebra of Polynomials
2 Induction and the Well-ordering Principle
3 Sets
4 Some counting principles
5 The Integers
6 Unique factorization into primes
7 Prime Numbers
8 Sun Ze's Theorem
9 Good algorithm for exponentiation
10 Fermat's Little Theorem
11 Euler's Theorem, Primitive Roots, Exponents, Ro
12 Public-Key Ciphers
13 Pseudoprimes and Primality Tests
14 Vectors and matrices
15 Motions in two and three dimensions
16 Permutations and Symmetric Groups
17 Groups: Lagrange's Theorem, Euler's Theorem
18 Rings and Fields: de nitions and rst examples
19 Cyclotomic polynomials
20 Primitive roots
21 Group Homomorphisms
22 Cyclic Groups
23 Carmichael numbers and witnesses
24 More on groups
25 Finite fields
26 Linear Congruences
27 Systems of Linear Congruences
28 Abstract Sun Ze Theorem
29 The Hamiltonian Quaternions
30 More about rings
31 Tables

Contents: (26 pages)
I. Introduction
II. Separable Equations
III. Linear Equations, Exact Equations and Integrating Factors
IV. Special Differential Equations and Applications
V. Existence and Uniqueness
VI. Second Order Linear Equations
VII. Constant Coefficients Linear Equations
IX. Application to Oscillations
X. Variation of Parameters
XI. Numerical Methods

Contents: (16 pages)
1. Complex Numbers
2. The Complex Plane
3. Addition and Multiplication of Complex Numbers
4. Why Complex Numbers Were Invented
5. The Fundamental Theorem of Algebra
6. The Geometry of Addition in C
7. Distance in the Complex Plane
8. Derivatives in C
9. Complex power series
10. Exp, cos, sin
11. Polar Decomposition
12. The Geometry of Multiplication in C
13. Trig identities
14. Exercises
Appendix A. Explanation of the Factorization Theorem
Appendix B. The addition formula for the exponential function
Appendix C. Complex notation for parametrized curves