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CS2800
Discrete Structures
Professor George
Professor Chaudhuri
January 21, 2015
What is “discrete structures”?
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Often called “discrete math”
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The mathematical tools that underlie computer science
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Discrete Math : Computer Science :: Calculus : Physics
What is “discrete structures”?
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Formal logic
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Basic probability and statistics
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Sets, functions, relations
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Automata
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Number theory
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Graphs
What is “discrete structures”?
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Formal logic
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Software construction
Algorithm design and analysis
Security
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Basic probability and statistics
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Sets, functions, relations
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Automata
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Number theory
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Graphs
What is “discrete structures”?
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Formal logic
Basic probability and statistics
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“Big data”
Machine learning
Information theory
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Sets, functions, relations
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Automata
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Number theory
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Graphs
What is “discrete structures”?
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Formal logic
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Basic probability and statistics
Sets, functions, relations
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Databases
Functional programming
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Automata
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Number theory
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Graphs
What is “discrete structures”?
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Formal logic
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Basic probability and statistics
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Sets, functions, relations
Automata
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Compilers
Network protocols
Games and animations
Nature of the universe
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Number theory
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Graphs
What is “discrete structures”?
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Formal logic
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Basic probability and statistics
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Sets, functions, relations
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Automata
Number theory
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Cryptography
Geometry
Graphs
What is “discrete structures”?
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Formal logic
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Basic probability and statistics
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Sets, functions, relations
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Automata
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Number theory
Graphs
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Social networks
AI, planning
Networking
What is “discrete structures”?
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Formal logic
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Basic probability and statistics
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Sets, functions, relations
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Automata
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Number theory
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Graphs
Important foundations for computer science
What is this course really about?
Math = Computation?
What is this course really about?
Math = Computation?
Formal, step by step reasoning (proofs)
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Distinguishing good arguments from bad
Clearly stating definitions
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. . . and sticking to them!
Tools for avoiding being wrong
What is this course really about?
Math = Computation?
Formal, step by step reasoning (proofs)
I
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Distinguishing good arguments from bad
Clearly stating definitions
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I
. . . and sticking to them!
Tools for avoiding being wrong
Reasoning abstractly
I Ignore the details of the objects you’re considering; work only
with their properties
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Example: I can add two integers, two real numbers, two
strings, two paths on the surface of a donut.
Example: I can find shortest paths in a social network, a
physical network, the flow of data in a program
What is this course really about?
Math = Computation?
Formal, step by step reasoning (proofs)
I
I
Distinguishing good arguments from bad
Clearly stating definitions
I
I
. . . and sticking to them!
Tools for avoiding being wrong
Reasoning abstractly
I Ignore the details of the objects you’re considering; work only
with their properties
I
I
Example: I can add two integers, two real numbers, two
strings, two paths on the surface of a donut.
Example: I can find shortest paths in a social network, a
physical network, the flow of data in a program
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Avoids getting bogged down in details
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Lets you reuse work
Course logistics
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Lecture
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Designed to be useful
Some from Prof. George, some from Prof. Chaudhuri
Please no laptops.
Course logistics
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Lecture
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Designed to be useful
Some from Prof. George, some from Prof. Chaudhuri
Please no laptops.
Weekly problem sets (∼40%)
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Released Monday, due Monday at noon
Judged on clarity and correctness
Usual rubric:
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3:
2:
1:
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correct and clearly explained
important error
misunderstanding of key concept
blank
Course logistics
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Lecture
I
I
I
I
Designed to be useful
Some from Prof. George, some from Prof. Chaudhuri
Please no laptops.
Weekly problem sets (∼40%)
I
I
I
Released Monday, due Monday at noon
Judged on clarity and correctness
Usual rubric:
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3:
2:
1:
0:
correct and clearly explained
important error
misunderstanding of key concept
blank
Exams
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Two (in class) prelims (∼15% each), on final (∼25%)
Course logistics
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No textbook
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Website, CMS, Piazza
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http://www.cs.cornell.edu/Courses/cs2800
Please use Piazza for all communication with course staff
CMS not populated yet
Lots of office hours!
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But see Rosen or Pass and Tseng (links on website)
Lecture notes and additional readings will be posted
Starting next week.
Schedule posted on Piazza
Study sessions highly encouraged
Collaboration
Expectations:
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You are encouraged to work together, but
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. . . All submitted work must be your own
Encouraged:
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“Let’s work together on problem 3”
Disallowed:
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“What did you write for problem 3?”
Rule of thumb:
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You should be able to reproduce the paper you turned in
without consulting your notes