Theorems in the foundations of mathematics
Codd's theorem states that relational algebra and the domain-independent relational calculus queries, two well-known foundational query languages for the relational model, are precisely equivalent in expressive power. That is, a database query can be formulated in one language if and only if it can be expressed in the other. The theorem is named after Edgar F. Codd, the father of the relational model for database management. The domain independent relational calculus queries are precisely those relational calculus queries that are invariant under choosing domains of values beyond those appearing in the database itself. That is, queries that may return different results for different domains are excluded. An example of such a forbidden query is the query "select all tuples other than those occurring in relation R", where R is a relation in the database. Assuming different domains, i.e., sets of atomic data items from which tuples can be constructed, this query returns different results and thus is clearly not domain independent. Codd's Theorem is notable since it establishes the equivalence of two syntactically quite dissimilar languages: relational algebra is a variable-free language, while relational calculus is a logical language with variables and quantification. Relational calculus is essentially equivalent to first-order logic, and indeed, Codd's Theorem had been known to logicians since the late 1940s. Query languages that are equivalent in expressive power to relational algebra were called relationally complete by Codd. By Codd's Theorem, this includes relational calculus. Relational completeness clearly does not imply that any interesting database query can be expressed in relationally complete languages. Well-known examples of inexpressible queries include simple aggregations (counting tuples, or summing up values occurring in tuples, which are operations expressible in SQL but not in relational algebra) and computing the transitive closure of a graph given by its binary edge relation (see also expressive power). Codd's theorem also doesn't consider SQL nulls and the three-valued logic they entail; the logical treatment of nulls remains mired in controversy. Additionally, SQL has multiset semantics and allows duplicate rows. Nevertheless, relational completeness constitutes an important yardstick by which the expressive power of query languages can be compared. (Wikipedia).
Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem
In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
UHCL 33a Graduate Database Course - BCNF Paired Attribute Algorithm - Part 1
This video corresponds to the unit 6 notes for a graduate database (DBMS) course taught by Dr. Gary D. Boetticher at the University of Houston - Clear Lake (UHCL). The theme is relational database theory. This video looks at how to decompose a relation schema into Boyce-Codd Normal Form (B
From playlist UHCL Graduate Database Course
RailsConf 2019 - Database Design for Beginners by David Copeland
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From playlist RailsConf 2019
What is Normalization in SQL? | Database Normalization Forms - 1NF, 2NF, 3NF, BCNF | Edureka
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From playlist MySQL Tutorial For Beginners | Edureka
UHCL 32a Graduate Database Course - Third Normal Form versus Boyce Codd Normal Form (BCNF)
This video corresponds to the unit 6 notes for a graduate database (DBMS) course taught by Dr. Gary D. Boetticher at the University of Houston - Clear Lake (UHCL). The theme is relational database theory. This video defines Boyce-Codd Normal Form (BCNF) and compares it to third normal form
From playlist UHCL Graduate Database Course
How to Compute a Maclaurin Polynomial
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From playlist A second course in university calculus.
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From playlist Theory of numbers
Introduction to Function Notation
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From playlist Functions, Sets, and Relations
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Holographic Tomography Instructor: Aditya Bhakta, Danny Codd View the complete course: http://ocw.mit.edu/2-71S09 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 2.71 Optics, Spring 2009
SQL - A Quick Overview |¦| SQL Tutorial |¦| SQL for Beginners
SQL is a powerful language for working with databases. Today, we take you on a quick tour of SQL space and highlight the main features of the language. This will give you a bird’s eye view of what you will learn from this series. Our SQL playlist starts here: ↪http://bit.ly/Socratica_S
From playlist Introduction to SQL (Computer Science)
Calculus - The Fundamental Theorem, Part 1
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From playlist Calculus - The Fundamental Theorem of Calculus
Abstract Algebra | Injective Functions
We give the definition of an injective function, an outline of proving that a given function is injective, and a few examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
In this video, I give a very neat and elegant proof of Taylor’s theorem, just to show you how neat math can be! It is simply based on repeated applications of the fundamental theorem of calculus. Enjoy! Note: The thumbnail is taken from https://i.redd.it/kv7lk5kn31e01.jpg
From playlist Calculus
Maria Chudnovsky: Induced cycles and coloring
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Combinatorics
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Free ebook http://bookboon.com/en/learn-calculus-2-on-your-mobile-device-ebook Basic example on Maclaurin series and some applications. In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's deriv
From playlist A second course in university calculus.
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JOIN me for a full beginner’s tutorial on MySQL. Learn the basics of relational databases by recreating AirBnb’s database with raw SQL https://fireship.io/tags/sql/ Buy the MySQL Pillow https://fireshipio-swag.creator-spring.com/listing/mysql-pillow References Diagram https://drawsql.ap
From playlist Backend Development
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From playlist Calculus - The Fundamental Theorem of Calculus
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From playlist Relational Databases
UHCL 34a Graduate Database Course - BCNF Paired Attribute Algorithm - Part 2
This video corresponds to the unit 6 notes for a graduate database (DBMS) course taught by Dr. Gary D. Boetticher at the University of Houston - Clear Lake (UHCL). The theme is relational database theory. This video looks at how to decompose a relation schema into Boyce-Codd Normal Form (B
From playlist UHCL Graduate Database Course
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From playlist Functions, Sets, and Relations