Introduction to Algorithms in Computer Science

Introduction

• This document introduces the concept of algorithms.
• Algorithms are a fundamental concept in computer science.
• Algorithms are a set of steps defining how a task is accomplished.

Algorithms

• Algorithms are used in various tasks, including cooking (recipes), navigating cities (directions), and operating washing machines.
• To use algorithms to achieve a goal, one needs to represent the algorithm in a format understandable to the machine.
• This representation is called a program.
• The process of creating a program or algorithm is programming.
• Algorithms and programs are distinct from computer hardware.

History of Algorithms

• Algorithms were studied in mathematics long before computers were developed.
• Mathematics aimed for finding algorithms for solving specific kinds of problems.
• Euclidean Algorithm and Division Algorithm are examples of early algorithms.

Computing the Greatest Common Divisor

• Euclidean algorithm is a procedure to calculate the greatest common divisor.

Procedure

• The algorithm takes two positive integers (M and N) as input.
• The algorithm assigns M and N the values of the larger and smaller numbers.
• Divide M by N and the reminder is assigned to R
• If R is not 0 , then M is assigned to the value N and N is assigned to R, and the algorithm repeats step 2.
• Otherwise, the greatest common divisor is the value currently assigned to N.

Functionality of Algorithms

• Once an algorithm is found for a task, the execution of that task only requires following instructions (steps) of the algorithm.
• The details of how the algorithm works doesn't need to be understood.
• The logic or intelligence required to solve the task is encoded within the algorithm itself.
• The algorithms form the foundation of functions that machines perform.

Scope of Algorithms and Limitations

• Algorithms have limitations as highlighted by the work of Kurt Gödel in the 1930s.
• Gödel's incompleteness theorems indicate that some statements in mathematical systems can't be proved or disproved using algorithms.
• This work led to the development of computer science as a formal discipline.

Broad Concepts of Computer Science

• Core concepts in computer science are algorithms, abstraction, creativity, data, programming, the Internet, and impact.

Algorithms and Data Storage Limits

• Early computing devices were limited in data storage capacity and program complexity, leading to restrictions on the size of problems tackled by algorithms.
• With advances in technology, machines can handle more complex tasks and bigger data sets.
• Development of algorithms and programming is continuously studied to improve efficiency.

Algorithmic Problem Solving

• Questions explored in algorithmic research include how to improve problem-solving using algorithms, how to represent and communicate algorithms better, and how to analyze and compare different algorithms.
• The study has deep implications for how we manage information, produce simulations, and use technologies for new discoveries.

Abstraction

• Abstraction in computer science focuses on distinguishing between the external characteristics of something and the internal details.
• Abstraction allows disregarding the internal workings of a complex system (e.g., a computer) and treating it as a single entity.
• This is essential for designing and building complex systems, allowing designers to handle components of large systems at different levels of abstraction.

Creativity in Algorithms

• Even though computers execute instructions mechanically, computer science encourages creativity in developing new algorithms.
• This involves inventing new methods for tackling problems faced in the world.
• Computer science extends beyond algorithmic programming and has impacted various artistic fields..

Data in Computer Science

• Computers can represent any data that can be categorized and digitized.
• Handling and converting this digital representation enables discovering patterns, creating simulations, and driving discoveries in many scientific fields, enabling advances in various disciplines, including medicine, engineering and more.

Programming

• Programming involves translating human intentions into executable computer instructions; this is crucial for carrying out more complex problems.
• It's increasingly important to develop programs, and the tools available for programming have evolved significantly.

Internet

• The Internet connects computers and electronic devices globally, profoundly impacting data storage, retrieval, and sharing of information. It has significantly affected how societies function in multiple ways.

Impact

• The influence of computer science extends beyond its technological applications.
• Societal issues like intellectual property, ethical considerations, and government regulations arise due to computer technology advancements. This generates various related ethical and logistical quandaries.

Explore the fundamental concept of algorithms and their significance in computer science. This quiz covers the various applications of algorithms, their historical context, and the relationship between algorithms and programming. Test your knowledge on the basics of algorithm design and implementation.