Notes for the Course of Algorithms

Deal with how to design good algorithms, which is about the mathematical theory behind the design of good programs.

**Tag(s):**
Algorithms and Data Structures

**Publication date**: 31 Dec 1998

**ISBN-10**:
n/a

**ISBN-13**:
n/a

**Paperback**:
n/a

**Views**: 225,002

**Type**: N/A

**Publisher**:
n/a

**License**:
n/a

**Post time**: 18 Feb 2007 07:20:34

Notes for the Course of Algorithms

Deal with how to design good algorithms, which is about the mathematical theory behind the design of good programs.

Terms and Conditions:

Document Summary:

What is algorithm design? An algorithm was defined to be any well-defined computational procedure that takes some values as input and produces some values as output. Like a cooking recipe, an algorithm provides a step-by-step method for solving a computational problem.

A good understanding of algorithms is essential for a good understanding of the most basic element of computer science: programming. Unlike a program, an algorithm is a mathematical entity, which is independent of a specific programming language, machine, or compiler. Thus, in some sense, algorithm design is all about the mathematical theory behind the design of good programs.

One of the elements that this course focuses on is to try to study algorithms as pure mathematical objects, and so ignore issues such as programming language, machine, and operating system. This has the advantage of clearing away the messy details that affect implementation. But these details may be very important.

Document Organization:

The notes will consist of three major sections. The first is on the mathematical tools necessary for the analysis of algorithms. This will focus on asymptotics, summations, recurrences. The second element will deal with one particularly important algorithmic problem: sorting a list of numbers. The notes will show a number of different strategies for sorting, and use this problem as a case study in different techniques for designing and analyzing algorithms. The final third of the course will deal with a collection of various algorithmic problems and solution techniques. Finally the notes will close with a very brief introduction to the theory of NP-completeness. NP-complete problem are those for which no efficient algorithms are known, but no one knows for sure whether efficient solutions might exist.

Dave Mount wrote:Copyright, David M. Mount, 1998, Dept. of Computer Science, University of Maryland, College Park, MD, 20742. These lecture notes were prepared by David Mount for the course CMSC 251, Algorithms, at the University of Maryland, College Park. Permission to use, copy, modify, and distribute these notes for educational purposes and without fee is hereby granted, provided that this copyright notice appear in all copies.

Document Summary:

What is algorithm design? An algorithm was defined to be any well-defined computational procedure that takes some values as input and produces some values as output. Like a cooking recipe, an algorithm provides a step-by-step method for solving a computational problem.

A good understanding of algorithms is essential for a good understanding of the most basic element of computer science: programming. Unlike a program, an algorithm is a mathematical entity, which is independent of a specific programming language, machine, or compiler. Thus, in some sense, algorithm design is all about the mathematical theory behind the design of good programs.

One of the elements that this course focuses on is to try to study algorithms as pure mathematical objects, and so ignore issues such as programming language, machine, and operating system. This has the advantage of clearing away the messy details that affect implementation. But these details may be very important.

Document Organization:

The notes will consist of three major sections. The first is on the mathematical tools necessary for the analysis of algorithms. This will focus on asymptotics, summations, recurrences. The second element will deal with one particularly important algorithmic problem: sorting a list of numbers. The notes will show a number of different strategies for sorting, and use this problem as a case study in different techniques for designing and analyzing algorithms. The final third of the course will deal with a collection of various algorithmic problems and solution techniques. Finally the notes will close with a very brief introduction to the theory of NP-completeness. NP-complete problem are those for which no efficient algorithms are known, but no one knows for sure whether efficient solutions might exist.

Tweet

About The Author(s)

David Mount is a professor in the Department of Computer Science and UMIACS. He is a member of the Algorithms and Theory Group at the University of Maryland. He does research on the design, analysis, and implementation of data structures and algorithms for geometric problems, particularly problems with applications in areas such as image processing, pattern recognition, information retrieval, and computer graphics.

Book Categories

Computer Science
Introduction to Computer Science
Introduction to Computer Programming
Algorithms and Data Structures
Artificial Intelligence
Computer Vision
Machine Learning
Neural Networks
Game Development and Multimedia
Data Communication and Networks
Coding Theory
Computer Security
Information Security
Cryptography
Information Theory
Computer Organization and Architecture
Operating Systems
Image Processing
Parallel Computing
Concurrent Programming
Relational Database
Document-oriented Database
Data Mining
Big Data
Data Science
Digital Libraries
Compiler Design and Construction
Functional Programming
Logic Programming
Object Oriented Programming
Formal Methods
Software Engineering
Agile Software Development
Information Systems
Geographic Information System (GIS)

Mathematics
Mathematics
Algebra
Abstract Algebra
Linear Algebra
Number Theory
Numerical Methods
Precalculus
Calculus
Differential Equations
Category Theory
Proofs
Discrete Mathematics
Theory of Computation
Graph Theory
Real Analysis
Complex Analysis
Probability
Statistics
Game Theory
Queueing Theory
Operations Research
Computer Aided Mathematics

Supporting Fields
Web Design and Development
Mobile App Design and Development
System Administration
Cloud Computing
Electric Circuits
Embedded System
Signal Processing
Integration and Automation
Network Science
Project Management

Operating System
Programming/Scripting
Ada
Assembly
C / C++
Common Lisp
Forth
Java
JavaScript
Lua
Microsoft .NET
Rexx
Perl
PHP
Python
R
Rebol
Ruby
Scheme
Tcl/Tk

Miscellaneous
Sponsors