10 Euclidean Algorithm: Number theory is the mathematics of integer arithmetic. In this chapter we will restrict ourselves to integers,

Date Added: 8/6/2008 | Visits: 32958

8 Horner's Algorithm: Horner's algorithm is an excellent example of an algorithm. It is a simple and useful algorithm, but it does not have much to do with discrete mathematics.

Date Added: 8/6/2008 | Visits: 31717

7 Graph Searching: Algorithms for searching graphs go back at least to the nineteenth century when they were used for mazes. Until the advent of computers they were an extremely obscure topic (as was graph theory). We are going to look at two algorithms which represent the two main approaches to searching graphs.

Date Added: 8/6/2008 | Visits: 32120

6 Induction: The principle of induction is a one of the most fundamental laws of mathematics. Students come across it, as here, as a method of proof. However, it is a basic property of the natural numbers (i.e. the positive integers) and can be considered as part of the definition of the natural numbers. Since we do not define the natural numbers here, the principle will be simply given as an axiom.1

Date Added: 8/6/2008 | Visits: 31793

5 Recursive Algorithms: Recursion is a form of definition and of algorithms that is very important in computer science theory as well as in practice. Recursive algorithms can be inefficient or efficient.1 A recursive definition or a recursive algorithm is characterized by self-reference.

Date Added: 8/6/2008 | Visits: 33805

16 Multinomials: Let us slightly generalize the problem of selecting r out of n objects without respect to order. Suppose, for example, that I have 20 students.

Date Added: 8/6/2008 | Visits: 33828

3 Integer Functions: The integer function that is the heart of this section is the modulo function. However, before getting to it, let us look at some very simple functions. The first (and most important) of these is the floor function. We denote this function by lxm although it can be denoted by floor(x) It is also widely known as the greatest integer function and is found in some computer languages as the integer function (sometimes denoted INT(x)).

Date Added: 8/6/2008 | Visits: 31582

25 Sigma Notation: The sign 3, called sigma, is a glorified symbol for addition that can be quite useful. It is utilized throughout mathematics, statistics, computer science and all other mathematical disciplines. With the 3 there is usually an index that typically is an i or j.

Date Added: 8/6/2008 | Visits: 33715

1 Relations: This book starts with one of its most abstract topics, so don't let the abstract nature deter you. Relations are quite simple but like virtually all simple mathematical concepts they have their subtle aspects. Relations are defined on collections (or sets) of objects.

Date Added: 8/6/2008 | Visits: 33338

Preface: This book was begun around January 1991, as a response to a need I perceived in the classroom. Students who have not had calculus but intend to pursue the mathematical sciences are not ready for a formalistic proof-laden treatment of the subject.

Date Added: 8/6/2008 | Visits: 33600