Lecture 22
4/1/04 18:21
Lecture 22
Read S&G ch. 12
(Computer Networks)
for next week
Databases
Numeric & Symbolic Computing
(S&G, §§11.3
–11.4)
§§11.3–
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Data Organization
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Example File “Employee”
• 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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CS 100 - Lecture 22
PayRate
Hours
Pay
86
Janet Kay
51
16.50
94
1560.40
123
Francine Perreira
18
8.50
185
1572.50
149
Fred Takasano
43
12.35
250
3087.50
71
John Kay
53
17.80
245
4361.00
165
Butch Honou
17
6.70
53
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355.10
Field
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• 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”
– think of IRS databases, Wal-Mart employee &
inventory databases
• Each instance of the entity is represented by a tuple
• Therefore efficiency is critical:
– e.g., the data for a particular employee
– efficiency of data storage
– efficiency of retrieval
• Each tuple has a number of attributes
– which characterize the instance (e.g., a particular
employee’s attributes)
• The data in a database is usually static
– updated manually, not automatically
CS 100
Age
Relational Database Model
• Databases are typically oriented toward
very large amounts of data
CS 100 - Lecture 22
Name
Record
3
How is this different from a
spreadsheet?
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ID
• Primary key: attribute(s) that uniquely identify a tuple
5
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1
Lecture 22
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A Table for the “Employee” Entity
Query Languages
• A query language allows users to:
ID
Name
Age
PayRate
Hours
Pay
86
Janet Kay
51
16.50
94
1560.40
123
Francine Perreira
18
8.50
185
1572.50
149
Fred Takasano
43
12.35
250
3087.50
71
John Kay
53
17.80
245
4361.00
165
Butch Honou
17
6.70
53
355.10
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Primary
Key
Tuple
–
–
–
–
• SQL (Structured Query Language)
– a standard query language
– a textual language
– sometimes used behind a graphical “front end”
Attribute
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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
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Example Query
Example Query (2)
>SELECT ID, NAME, AGE, PAYRATE,
HOURS, PAY
>FROM EMPLOYEE
>WHERE ID = 123;
>SELECT ID, NAME, AGE, PAYRATE,
HOURS, PAY
>FROM EMPLOYEE
>WHERE NAME = ’John Kay’;
123 Francine Perreira
$8.50 185 $1572.50
18
71 John Kay
$4361.00
>
53
$17.80
245
>
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CS 100 - Lecture 22
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ID Name
$4361.00
>
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>SELECT *
>FROM EMPLOYEE
>ORDER BY PAYRATE;
>SELECT NAME, PAY
>FROM EMPLOYEE
>WHERE NAME = ’John Kay’;
John Kay
CS 100 - Lecture 22
Example Query (4)
Example Query (3)
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Age
PayRate
165 Butch Honou
123 Francine Perreira
17
18
$6.70
$8.50
Hours
53
$355.10
185 $1572.50
Pay
149 Fred Takasano
250 $3087.50
43
$12.35
86 Janet Kay
51
$16.50
94 $1560.40
71 John Kay
53
$17.80
245 $4361.00
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CS 100 - Lecture 22
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2
Lecture 22
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Example Query (5)
Modifying Databases
>SELECT *
>FROM EMPLOYEE
>WHERE AGE > 21;
ID Name
86 Janet Kay
149 Fred Takasano
71 John Kay
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Age
PayRate
51
$16.50
94 $1560.40
43
$12.35
250 $3087.50
53
$17.80
245 $4361.00
CS 100 - Lecture 22
Hours
Pay
13
• 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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Another Table
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Foreign Key
Primary Key
InsuredID PlanType
DateIssued
86
A4
02/23/78
123
B2
12/03/91
149
A1
06/11/85
71
A4
10/01/72
149
B2
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• 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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NAME
Fred Takasano
Fred Takasano
PLANTYPE
A1
B2
• 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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Computer Science Issues
Example Query of Joined Tables
>SELECT EMPLOYEE.NAME,
INSURANCE.PLANTYPE
>FROM EMPLOYEE, INSURANCE
>WHERE EMPLOYEE.NAME = ’Fred Takasano’
AND EMPLOYEE.ID = INSURANCE.INSUREDID;
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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
Numeric and Symbolic
Computing
 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)
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Computer Science Issues
• Manipulate mathematical formulas,
equations, etc. much the way a
mathematician would
better algorithms
accessing of data in memory hierarchies
parallel computation
data communication in networks
– automate processes that are mechanical,
tedious, and error-prone
• Mathematical software libraries
• Accuracy and stability of numerical
approximations
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• Examples: Macsyma, Mathematica, Maple,
MatLab
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Example: Simplification
( x −1)
2
+ ( x + 2) + (2x − 3) + x
(1+ x + 3y )
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4
• Expand[(1 + x + 3y)^4]
• 1 + 4x + 6x2 + 4x3 + x4 + 12y
€
+ 36xy + 36x2y + 12x3y + 54y2
+ 108xy2 + 54x2y2 + 108y3
+108xy3 + 81y4
• 12 - 12x + 5x2
CS 100 - Lecture 22
CS 100 - Lecture 22
Example: Expansion
2
• Simplify[(x-1)^2 + (x+2) +
(2x-3)^2 + x]
€
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Symbolic Computing
• Performance:
–
–
–
–
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Lecture 22
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Typical Expansion Rules
Example: Solving Equations
Expand[ X × (Y + Z )] ⇒ X × Y + X × Z
2x + y = 11
6x − 2y = 8
Expand[( X + Y ) × Z ] ⇒ X × Z + Y × Z
Expand[ X 2 ] ⇒ X × X
Hence,
Expand[(n + 1)2]
€ ⇒Expand[(n + 1)(n + 1)]
⇒Expand[(n + 1)n + (n + 1)1]
⇒Expand[(n + 1)n + (n + 1)1]
⇒Expand[n×n + 1×n + n×1 + 1×1]
• Solve[ {2x + y == 11,
6x - 2y == 8},
{x,
€ y}]
• {{x -> 3, y -> 5}}
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Computer Science Issues
Digression
• Symbolic computation systems are:
• 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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CS 100
CS 100 - Lecture 22
– 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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5