| Basics | Sets, lists, linear algebra, computation in the integers. |
| Algebraic integers | Extension of the integers by the root of a polynomial. | Modular Arithmetic | Polynomials and matrices mod n. | Finite Fields | Constructing and doing arithmetic in finite fields. |
| Integers | Basic computations in the integers. | Polynomial Rings | Polynomial rings, their quotients, evaluation of polynomials. | Finite Fields | Finite field and their extensions. | Reed-Solomon Codes | Constructing the generator and check matrices, systematic encoding. | Decoding of Reed-Solomon Codes | The Berlekamp-Massey algorithm, and computation of the error values using Sec 8. |