The course contains the materials delivered at the "Teoria de Codis" class of the Fall semestrer of 2008-2009 at the "Facultat de Matemàtiques i Estadística" of the "Universitat Politècnica de Catalunya".

Outline:

1. Informal presentation: the digital era
2. Introduction to block error-correcting codes
3. Linear codes
4. Finite fields
5. Cyclic codes and the The Meggitt decoder
6. Alternant codes (includes two decoding algorithms)
7. Hadamard codes

This resource consists of a set of pdf files in English with the following index:

1. Notations and conventions
2. Integral calculus
3. Maxwell's equations
4. Mathematical underpinnings

The document is a short Introduction of MathML and its use within DAISY books. It is meant to be a starter with further references and aims to address primarily teachers, students, publishers and software and service developers. Given the subject, it is of somewhat technical nature, but should be understandable by the general audience.

The document is available as DAISY book (as a XML file without audio content).

Polynomial Division can be used to find Taylor polynomials of rational functions easily and quickly. The polynomial division that does this trick is inverted in the sense that, instead of canceling out the leading terms at each step, one cancels out the trailing terms. Otherwise everything goes just like in the ordinary long division of polynomials.

Testing the repository

This is a test

This video explains why the geometric series 1/2 + 1/4 + 1/8 + ... converges using an elementary argument. The video is meant to be preparatory materials for students to view before the discussion of geometric series takes place in a class room. The video finishes with an intriguing example.

English version in YouTube

This is a short video that discusses the paradox of Zeno. It turns out that this paradox is not a paradox but rather an easy way to show that a geometric series converges (if |q| < 1) and to find a formula for the sum. Suitable for high schools.

English version in YouTube

Translation to Spanish in YouTube

The resource is the complete diagnostic testbank used for testing students entering the first calculus course at the University of Helsinki. This diagnostic test covers a large part of the normal high school curriculum in Finland. The test was originally written by Andre Heck and later slightly edited by Mika Seppälä. Actual diagnostic tests used contain a part of these questions, not all of them.

This set of exercises will teach the student to compute limits of functions. A WebALT service.

The Online Single Variable Calculus is a full course at university level covering topics from Real Numbers, Functions, Differentiation, Integration, Series and Differential Equations. Each topic is organized in a module consisting of a Ten Minute Talk accompanied by Open Problems and Solved Problems. The material has been designed especially for online delivery.