1. Lecture 22 Databases Numeric & Symbolic Computing (S&G, §§11.3–11.4)
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Lecture 22
Databases Numeric & Symbolic Computing
(S&G, §§11.3–11.4)
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CS 100

2. Read S&G ch. 12 (Computer Networks) for next week
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3. Data Organization A database is a collection of related files
analogy: all the file cabinets in a business
A file is a collection of related records
analogy: all the folders in one drawer (holding, say, the personnel records)
A record is composed of fields
analogy: the folder for a particular employee, containing, for example their name, employment history, pay rate, insurance information, evaluations
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4. Example File “Employee”
Field ID
Name
Age
PayRate
Hours
Pay 86
Janet Kay 51
16.50 94
123
Francine Perreira 18
8.50
185
149
Fred Takasano 43
12.35
250 71
John Kay 53
17.80
245
165
Butch Honou 17
6.70
355.10
Record
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5. How is this different from a spreadsheet?
Databases are typically oriented toward very large amounts of data
think of IRS databases, Wal-Mart employee & inventory databases
Therefore efficiency is critical:
efficiency of data storage
efficiency of retrieval
The data in a database is usually static
updated manually, not automatically
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6. Relational Database Model
A file is viewed as a table
Each table contains information about a number of instances of some entity
an entity is a fundamental distinguishable object, such as “employee”
Each instance of the entity is represented by a tuple
e.g., the data for a particular employee
Each tuple has a number of attributes
which characterize the instance (e.g., a particular employee’s attributes)
Primary key: attribute(s) that uniquely identify a tuple
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7. A Table for the “Employee” Entity
Attribute
Primary
Key ID
Name
Age
PayRate
Hours
Pay 86
Janet Kay 51
16.50 94
123
Francine Perreira 18
8.50
185
149
Fred Takasano 43
12.35
250 71
John Kay 53
17.80
245
165
Butch Honou 17
6.70
355.10
Tuple
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8. Query Languages A query language allows users to:
retrieve information from a database
relate information in different files in a database
update information in a database
perform statistical and other data processing operations on selected information
SQL (Structured Query Language)
a standard query language
a textual language
sometimes used behind a graphical “front end”
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9. Example Query >SELECT ID, NAME, AGE, PAYRATE, HOURS, PAY
>FROM EMPLOYEE
>WHERE ID = 123;
123 Francine Perreira 18 $ $
>
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10. Example Query (2) >SELECT ID, NAME, AGE, PAYRATE, HOURS, PAY
>FROM EMPLOYEE
>WHERE NAME = ’John Kay’;
71 John Kay 53 $ $
>
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11. Example Query (3) >SELECT NAME, PAY >FROM EMPLOYEE
>WHERE NAME = ’John Kay’;
John Kay $
>
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12. Example Query (4) >SELECT * >FROM EMPLOYEE >ORDER BY PAYRATE;ID
Name
Age
PayRate
Hours
Pay
165
Butch Honou 17
$6.70 53
$355.10
123
Francine Perreira 18
$8.50
185 $
149
Fred Takasano 43
$12.35
250 $ 86
Janet Kay 51
$16.50 94 $ 71
John Kay
$17.80
245 $
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13. Example Query (5) >SELECT * >FROM EMPLOYEE
>WHERE AGE > 21; ID
Name
Age
PayRate
Hours
Pay 86
Janet Kay 51
$16.50 94 $
149
Fred Takasano 43
$12.35
250 $ 71
John Kay 53
$17.80
245 $
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14. Modifying Databases DELETE * FROM EMPLOYEE WHERE AGE < 21;
UPDATE EMPLOYEE SET PAYRATE = 8.75 WHERE ID = 123;
INSERT INTO EMPLOYEE VALUES (456, ’Sandy Beech’, 13.25, 0, 0);
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15. Another Table InsuredID PlanType DateIssued 86 A4 02/23/78 123 B2
Primary Key
InsuredID
PlanType
DateIssued 86 A4
02/23/78
123 B2
12/03/91
149 A1
06/11/85 71
10/01/72
04/23/90
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16. Foreign Key
The “InsuredID” attribute is a foreign key because it is a primary key into a different table (EMPLOYEE)
Foreign keys establish relationships between tables
E.g., between the employee (with all his/her attributes) and the insurance plan (with all its attributes)
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17. Example Query of Joined Tables
>SELECT EMPLOYEE.NAME, INSURANCE.PLANTYPE
>FROM EMPLOYEE, INSURANCE
>WHERE EMPLOYEE.NAME = ’Fred Takasano’ AND EMPLOYEE.ID = INSURANCE.INSUREDID;
NAME PLANTYPE Fred Takasano A1 Fred Takasano B2
>
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18. Computer Science Issues
SQL is a very high-level language
nonprocedural
problem-specific
Performance in a major issue
Consistency issues with simultaneous updates
Distributed databases (files stored in many locations)
access time & consistency problems
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19. Numeric and Symbolic Computing
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20. Lecture 22
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Numeric Computation
Applications that make heavy use of real arithmetic
Especially used in science, engineering, economics, statistics, animation
The motivation for the first computers
Still drives the development of supercomputers and parallel computers
a teraflop machine performs at least 1012 (a trillion) floating-point operations per second
36 Tflops already achieved (Japan’s Earth Simulator, which cost $350–500M)
Data from Washington Technology V.18 No.21 (02/09/04).
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21. Computer Science Issues
Performance:
better algorithms
accessing of data in memory hierarchies
parallel computation
data communication in networks
Mathematical software libraries
Accuracy and stability of numerical approximations
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22. Symbolic Computing
Manipulate mathematical formulas, equations, etc. much the way a mathematician would
automate processes that are mechanical, tedious, and error-prone
Examples: Macsyma, Mathematica, Maple, MatLab
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23. Example: Simplification
Simplify[(x-1)^2 + (x+2) + (2x-3)^2 + x]
x + 5x2
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24. Example: Expansion Expand[(1 + x + 3y)^4]
1 + 4x + 6x2 + 4x3 + x4 + 12y + 36xy + 36x2y + 12x3y + 54y xy2 + 54x2y y3 +108xy3 + 81y4
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25. Example: Solving Equations
Solve[ {2x + y == 11, 6x - 2y == 8}, {x, y}]
{{x -> 3, y -> 5}}
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26. Typical Expansion Rules
Lecture 22
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Typical Expansion Rules
Hence,
Expand[(n + 1)2]
Expand[(n + 1)(n + 1)]
Expand[(n + 1)n + (n + 1)1]
Expand[nn + 1n + n1 + 11]
Note need for simplification in result.
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CS 100

27. Digression
Recall our discussion of formalized mathematics, and the idea of reducing mathematics to the mechanical application of formal rules
Formal rules: depend on the form of expressions, not their meaning
Symbolic computation is an application of the idea of a calculus
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28. Computer Science Issues
Symbolic computation systems are:
very high-level languages
problem-specific
nonprocedural
Depend on many algorithms, e.g.:
pattern matching
efficient management of complex data structures representing formulas
Results should be presented in a form familiar and useful to the mathematically literate
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