1 / 47

Exploring Family Trees: A Mathematical Approach to Cousins and Holiday Earnings

In this module, we delve into the complexities of family trees, exploring how to calculate the number of first and second-degree cousins, as well as the total number of relatives in a family clan. We also examine how many total great-grandchildren exist in the family and compute potential Christmas earnings from relatives. By organizing family data through simple mathematical models, we can analyze relationships while understanding the evolution of database design. This study serves as both an exploration of familial connections and a practical application of data modeling concepts.

caine
Télécharger la présentation

Exploring Family Trees: A Mathematical Approach to Cousins and Holiday Earnings

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Module 2:1 Introduction

  2. Describing a Family Tree • Both my great grandparents had 2 children each. My Father had 4 siblings with 3 children each. My Mother had 3 siblings with 2 children each. My Father had 2 other Cousins with 2 children each. My Mother had 2 cousins with 3 children each. We are 5 in my family

  3. Question • How many 1st degree cousins do I have? 2nd degree? How many cousins do we have in the whole clan? Great grand children? • Given that all my titos and titas will give my 500 for christmas, how many will I receive by the 26th? • How many are we all in all?

  4. Math • Solve for all cousins: • Father Side • Father siblings = 4 x 3 children each = 12 • Father cousin = 2 x 2 children each = 4 • Father side = Father sibling + Father cousin • Father side = 16 children • Mother Side • Mother sibling = 3 x 2 children each = 6 • Mother cousin = 2 x 3 children each = 6 • Mother side = Mother sibling + Mother cousin • Mother side = 12 • Cousins = Motherside + Fatherside = 16+12 = 28

  5. Math • Solve for all greatgrandchildren: • Since Father Side = 16 and Mother Side =12 • And FatherMotherchildren = 5 children • FS+MS+FMC= 16+12+5 = 33 • Solve for Titostitas: • Fatherside: • Let FGGParents = (FGParentsA + FGParentsB) x 2 • FGParentsA= 2 ; FGParentsB = 4 • FGGParents = (2+4)2 = 12 • Motherside • MGGParents = (MGParentsA + MGParentsB) x 2 • MGParentsA= 2 ; FGParentsB = 3 • MGGParents = (2+3)2= 10 • Christmas_Aguinaldo=(Motherside+Fatherside)xP500 • Christmas_aguinaldo=(10+12)x500=(22)xP500)=11,000

  6. Math • How many are we all in all • Since all siblings = 33 • Titos and Titas = 22 • Grandparents = 2 x 2 = 4 x 2 = 8 • Great grand parents = 2 x 2 = 4 • Parents = 2 • Allinall=33+22+8+4+2= 69

  7. Interpret data as a Diagram

  8. Introduction • Data models… • Relatively simple representations • Usually graphical • Of a more complex real-world data structure • …supported by powerful database design tools have made it possible to substantially diminish the errors of database design.

  9. Function of a Data Model • help understand the complexities of a real-world object or event • It represents data structures and their: • Characteristics • Relations • Constrains • Transformations

  10. Module 2:1 1 Building blocks of data models

  11. Histories of Database Designs • 1950s and early 1960s: • Data processing using magnetic tapes for storage • Tapes provide only sequential access • Punched cards for input • Late 1960s and 1970s: • Hard disks allow direct access to data • Network and hierarchical data models in widespread use • Ted Codd defines the relational data model • Would win the ACM Turing Award for this work • IBM Research begins System R prototype • UC Berkeley begins Ingres prototype • High-performance (for the era) transaction processing

  12. Histories of Database Designs • 1980s: • Research relational prototypes evolve into commercial systems • SQL becomes industry standard • Parallel and distributed database systems • Object-oriented database systems • 1990s: • Large decision support and data-mining applications • Large multi-terabyte data warehouses • Emergence of Web commerce • 2000s: • XML and XQuery standards • Automated database administration • Increasing use of highly parallel database systems • Web-scale distributed data storage systems

  13. Data Modeling • A collection of tools for describing • Data entities • Data attributes • Data relationships • Data constraints

  14. Data entities • Anything! Person, Place or thing, or events which data are to be collected and stored • An entity represents a particular type of object in a real world • Physical objects • customers • Products

  15. Data Attributes • Characteristics of an entity • Example: the Attributes of a Customer are: • Firstname • Lastname • Course • Year

  16. Data Relationships • Association among entities • Example: • The relationship between customers and an agent • Types of Relationship • One to Many (1:M) relationship • Many to Many (M:N) relationship • One to One (1:1) relationship

  17. Data Relationships • 1:Many (1:M) • Store  Employees • Many:Many (M:N) • Employees  Skills • 1:1 (1:1) • Employee  Store

  18. Entity Relationship Model • Models an enterprise as a collection of entities and relationships • Entity: a “thing” or “object” in the enterprise that is distinguishable from other objects • Described by a set of attributes • Relationship: an association among several entities • Represented diagrammatically by an entity-relationship diagram:

  19. Diagraming using Ched’s Entity Relational Diagram Painter Employee Employee M 1 1 paints learns manages N M 1 Painting skills store

  20. Example of Data Relationships • Example of tabular data in the relational model

  21. Data Constrains • Restrictions placed on the data • This ensures data integrity • Usually in a form of rulews • Examples • QPI: Not less than 0.00 not more than 4.00 • A class should only have a maximum of 45 students • A teacher should only have 21 units or 7 subjects • An uyab should have one and only one uyab.

  22. Data Abstraction • Physical level: describes how a record (e.g., customer) is stored. • Logical level: describes data stored in database, and the relationships among the data. type customer = record customer_id : string; customer_name : string;customer_street : string;customer_city : string; end; • View level: application programs hide details of data types. Views can also hide information (such as an employee’s salary) for security purposes.

  23. View of Data • An architecture for a database system

  24. At a larger scale…

  25. Module 2:1 2 Business Rules

  26. Understanding the Organization • Before database designers start designing databases (entities, attributes and relationships), they understand first the business rules.

  27. Business Rules • A business rule is • Brief • Precise • And unambiguous • Description of • Policies • Procedures • And principles • Of a specific organization

  28. Enforces order • Business rules help to create and enforce action within that organization’s environment • It is rendered in writing and updated to reflect any changes in the organization’s operational environment

  29. Examples of Business rules and procedures • A customer may generate many invoices • An invoice is generated by one customer • A training session cannot be scheduled for fewer that 10 employees or for more than 30 employees.

  30. Examples of Business rules and procedures • A customer may generate many invoices(1:M relationship) • An invoice is generated by one customer(1:M relationship) • A training session cannot be scheduled for fewer that 10 employees or for more than 30 employees.(1:M relationship with a constrain)

  31. Module 2:1 3 Translating business rules into data model components

  32. Things to consider • What are the Business Rules? Site all of it. • In every business rule, look for its entities and attributes • Are there relationships from it? • From the business rules, identify possible constrains.

  33. Case Discussion • Enrolling a Subject IM32 • Business Rules • A class should have a maximum of 45 students • A student can’t enroll twice on a class on the same semester. • There should be one teacher per class. • Only 3rd and 4th year IM students are allowed to enroll in the class

  34. Case Discussion • Enrolling a Subject IM32 • Entities • Class • Student • Teacher

  35. Case Discussion • Enrolling a Subject IM32 • Attributes • Class • Seats, Subject Code,SubjectDescription,Schedule • Student • Name, year, course • Teacher • Name, Subject, Schedule

  36. Case Discussion • Enrolling a Subject IM32 • Constrains • Class not exceed 45 students • Teacher not exceed 45 students

  37. Case Discussion • Enrolling a Subject IM32 • Relationships • Class • 1 Class  1 Teacher • 1 Class  45 students • Student • 1 Student  1 Class • Teacher • 1 Teacher  Many students • 1 Teacher 1 Class • 1 Teacher  1 Class schedule

  38. Diagraming Class Teacher Teacher M 1 1 enrols teaches handles N M 1 student skills Class

  39. A Sample ER

  40. Module 2:1 Summary

  41. Point # 1 • Data Model is a (relatively) simple abstraction of complex real-world data environment. Database designers ause data models to communicate with application programmers and end users.

  42. Point #2 • Basic data-modeling components are entities, attributes , relationships and constrains

  43. Point #3 • Business rules are used to identify and define the basic modeling components within a specific real-world environment

  44. Module 2:1 End

More Related