Lecture 23 4/5/04 23:16
4/5/04
(S&G, §§ 11.3
– 11.4, 12.1
– 12.2)
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CS 100
4/5/04
Numeric and Symbolic
Computing
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Lecture 23
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 10 12 (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
• 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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Lecture 23
CS 100
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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Example: Simplification
( x − 1 )
2
+ ( x + 2 ) + ( 2 x − 3 )
2
+ x
€
• Simplify[(x-1)^2 + (x+2) +
(2x-3)^2 + x]
• 12 - 12x + 5x 2
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Lecture 23
Example: Expansion
( 1 + x + 3 y )
4
• Expand[(1 + x + 3y)^4]
• 1 + 4x + 6x
€
2 + 4x 3 + x 4 + 12y
2 y + 12x 3 y + 54y 2
+ 108xy 2 + 54x
+108xy 3 + 81y 4
2 y 2 + 108y 3
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Example: Solving Equations
2 x + y = 11
6 x − 2 y = 8
• Solve[ {2x + y == 11,
6x - 2y == 8},
€
• {{x -> 3, y -> 5}}
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Lecture 23
Typical Expansion Rules
Expand [ X × ( Y + Z ) ] ⇒ X × Y + X × Z
Hence ,
Expand [ ( X + Y ) × Z ] ⇒ X × Z + Y × Z
Expand [ ] ⇒ X × X
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]
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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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Lecture 23
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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Computer Networks
(S&G ch. 12)
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Lecture 23
Communication Links
• Switched dial-up phone lines
– require modem (modulator-demodulator) to interface between digital interface and analog phone line
• Dedicated links
– wired (wire proper & fiber optic cable)
– wireless
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Kinds of Networks
• Local Area Network (LAN)
– limited range (building, campus)
– typically owned by owners of premises
– example: Ethernet
• Wide Area Network (WAN)
– worldwide (and beyond!)
– typically owned by telecommunications services
– example: Internet
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Lecture 23
Ethernet
• Developed at Xerox PARC in mid-70s
• Communication protocols govern use of the network
• Ethernet uses contention-based distributed control
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Single-Cable Ethernet intended transmission
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Lecture 23
Single-Cable Ethernet
(1) Listen
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Single-Cable Ethernet
(2) Transmit
17
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Lecture 23
Single-Cable Ethernet
(3) Broadcast
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Single-Cable Ethernet
(4) Receive
19
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Lecture 23
Single-Cable Ethernet
(5) Inactive
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Single-Cable Ethernet
(1) Listen
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Lecture 23
Single-Cable Ethernet
(2) Transmit
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Single-Cable Ethernet
(3) Collision
23
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Lecture 23
Single-Cable Ethernet
(4) Wait Randomly
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Single-Cable Ethernet
(5) Listen
25
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Lecture 23
Single-Cable Ethernet
(6) Rebroadcast
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Single-Cable Ethernet
(7) Inactive
27
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Lecture 23
Single-Cable Ethernet
(8) Listen
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Single-Cable Ethernet
(9) Rebroadcast
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Lecture 23
CS 100
A:
B: wait
C: time
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Collision Recovery
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Wide Area Networks (WANs)
• LANs typically broadcast messages
• WANs typically use point-to-point communication
• Typically use store and forward packetswitching
– packet = fixed-size quantity of information
– large messages divided into packets
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Lecture 23
Point-to-point Communication
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Point-to-point Communication:
Node Failure
33
CS 100
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Store-and-Forward Packet-Switching
A
C
ACK
D: packet
D: packet
B
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What We Need
• A way of finding a computer (“server”) on the Internet
• A way of locating a Web page on that computer
• A way of displaying that Web page on my computer (“client”)
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Lecture 23
Locating Computers on the Internet
• TCP/IP (Transmission Control Protocol/Internet
Protocol) – a set of protocols (“rules of the game”) for making transactions
• IP address – standard for identifying a computer
• TCP – describes how packets are sent and retrieved
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IP Format
• Example: 204.202.129.230
• 4 groups of 3 digits
• Range from 0 to 255 (8 bits)
• Total of 256 4 or over 4 billion computers
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Lecture 23
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The Internet and the Web
• The Web sits on top of the Internet and uses its protocols (HTTP, FTP, MAILTO, etc.)
• URL (Uniform Resource Locator) – allows different computers to use the same protocols for Web-based transactions
• HTTP (HyperText Transfer Protocol) format: http: // where / what e.g., http://www.cs.utk.edu/~cs100
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The Internet and the Web
Web
Internet
URL
HTTP, FTP,
MAILTO, ...
TCP
IP
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Lecture 23
CS 100
Named Address ( Domain Name )
• It’s hard to remember 12 digits
• Provide a name and get the computer
(Domain Name Server) to translate it to the IP
address
• e.g, http://160.36.56.64/~cs100 =
http://www.cs.utk.edu/~cs100
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Two Standards for Web Pages
• Standard protocol (URL)
• Standard language for describing Web pages (HTML – HyperText Markup
Language)
• HTML: A set of commands for formatting
Web pages
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Lecture 23
How HTML Works: Client/Server
Server’s disk Network connection
Client’s browser
1. The client sends a request for a page to the server.
2. HTML code is sent as text to the client.
3. HTML code is stored in the client’s cache (temporary memory).
4. The client’s browser interprets the HTML code and formats the page.
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How HTML Works: Client-Side
• The spirit of HTML:
– Content (text, images, videos) + “suggestions” on how to format it
– Hyper-links to other web pages
• Actual formatting (fonts, positions, colors) should be up to client’s browser ( e.g., lynx entirely text-based)
• In practice, web designers want more control (frames, tables, blank spaces)
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Lecture 23
Typical Network Services
• Resource sharing
– print servers, file , compute servers
• Information sharing
– data interchange, information utilities
• Communication
– e-mail, bulletin boards, news groups, chat rooms
• Electronic commerce
• Security issues
– authentication, secrecy, fault tolerance
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Read S&G, ch. 13
(Artificial Intelligence) for next class
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CS 100 23