Speaker A
Foreign. Welcome back. Algebra is one of the broad areas of mathematics. We would have come across various algebra branches. Let's take abstract algebra, where abstract algebra is to study the algebraic structures such as groups, rings, fields, and abstract algebra has its wide application area in the field of cryptography. Coming to linear algebra, linear algebra deals with linear equations, linear mappings, and is used in application areas like weather forecasting. Coming to Boolean algebra, Boolean algebra deals with variables that are with the truth values true or false, and Boolean algebra has its widespread applications in the areas of digital circuitry design in personal computers, pocket calculators, CD players, cell phones, and other electronic products. One such algebra that we are going to focus on in today's presentation is relational algebra, and in today's presentation, we are going to focus on the basics of relational algebra. While waiting, let's step into the topic of the day, the relational algebra. Relational algebra is basically a procedural query language. What do we mean by this? It means we need to instruct what to do, how to do. We are expecting the result from the database, and the result is going to be a table or a relation. In order to get that result, the table or the relation, we need to instruct what is required and how to retrieve that data or how to retrieve the result, and that is why we refer to relational algebra as a procedural query language. If you are directly watching this lecture, I request you to navigate to chapter 1 of this playlist and find the lecture database languages, where I have explained about the database languages, the procedural query language, and the non-procedural query language with examples. For now, just understand relational algebra is a procedural query language, and what it actually does. Basically, relational algebra is a set of operations on relations. This is like the normal algebraic operation where it's going to take input and it's going to produce the output. Likewise here also, relational algebra is basically a set of operations on relations, so it's going to work on the relation and does the operation and gives the result as a relation only, and that's why we say relational algebra is basically a set of operations, and to be precise, it is like a set of algebraic operations. These algebraic operations like addition, subtraction, all these take some values as the input and do the operation and produce the output. Likewise here also, relational algebra is going to take relations as input, do the operation, and generate the output, which is also a relation. In simple terms, relational algebra is a set of operations which takes one or more relations as input and produces a relation as an output. So, that's what the next point says: the input is going to be one or more relations, and the output is going to be a relation. And why one or more relations? There are certain relational algebra operators which are unary operators, where it takes only one relation as an input. There are certain relational algebra operators which take two or more inputs, so they are binary or ternary. So what I mean to say is, in a nutshell, it takes one or more relations as an input and produces another relation as an output. And why do we need to study this relational algebra? Because it provides a theoretical foundation for relational databases. We know the power of relational databases in this contemporary world. When we want to work on the relational database or when we want to know the foundations of the relational database, it's always recommended to have a sound knowledge of relational algebra because it provides a theoretical foundation for relational databases. The well-known DBMS language that is widely used in today's world is the structured query language, SQL, and when you want to become proficient with SQL, knowing relational algebra will give an additional advantage. And not only that, when we have sound knowledge in relational algebra, obviously it allows us to understand database operations in more detail, and also it motivates us to write optimized queries. We know databases are going to respond to queries. When we supply a query to the database, the database accepts the query, does the operation, and gives the result. If we want to get that output, there may be multiple ways. If we want an output from the database, I mean a relation or a table, there can be multiple queries where these queries give the same output, but giving an optimized query is always good because your databases will not take more time or more memory to execute that query. So what I mean to say is, instead of giving a query to the database, if we give an optimized query, the database will respond easily because these optimized queries will be having lower cost. Cost is one of the factors that are used to measure query optimization. In simple terms, relational algebra helps us to write optimized queries, and also it helps us to understand the database operations in more detail—what's happening at the back end, how queries are processed, how query execution plans are generated, how the plans are executed. All these things, no worries. In the coming lectures, we are going to focus on query optimization techniques. At that time, I will explain to you how query optimization is actually taken care of by the database. We are done with the basics of relational algebra. Before we move on to the next slide, just revisit: what is relational algebra? It is a set of operations. What are the operations that relational algebra contains? That's what we are going to see now. Basically, the relational algebra operations are classified into two categories: number one, the fundamental operations, and number two, the additional operations. Let's just focus on the names of the operations in this lecture. In the coming lectures, we are going to focus on all the operations one by one in detail with required examples. For now, let's just know the operation names. Talking about the fundamental operations, there are six fundamental operations as far as relational algebra is concerned. The first operation is select. The second operation is project. The third one is union. The fourth one is the set difference. The fifth one is the Cartesian product. And the last fundamental operation in relational algebra, the sixth one, is the rename operation. These six operations are the fundamental operations in relational algebra. Coming to the additional operations, we have various additional operations in relational algebra. They are the set intersection operation, the assignment operation, the inner join, where in inner join we are going to focus on the natural join, equi join, and theta join, but our emphasis in this subject will be more on natural join. The next additional operation is the division operation, and the last additional operation that we are going to focus on in this subject is the outer join, where we are going to see three forms of outer join: the left outer join, the right outer join, and the full outer join. So we have seen about the various fundamental and additional operations. In the coming lectures, we are going to focus on all the operations one by one with examples. And that's it, guys. I hope you guys enjoyed this presentation, and thank you for watching.
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