CSC165H1 Study Guide - Fall 2018, Comprehensive Midterm Notes - Natural Number, Universal Quantification, Unit Circle
CSC165H1
MIDTERM EXAM
STUDY GUIDE
Fall 2018
CSC165 Lec01 Notes
Why is Math needed for Computer Science?
• Graphics
• Software verification
• Cryptography
• Computational complexity
• Artificial Intelligence
• Numerical analysis
• Scientific computing
• Computer networks
• Databases
Mathematical Preliminaries:
• Sets
• Functions
- Sets:
Define the universe of things being studied.
A set is a collection of distinct objects that we call the elements of the set.
- Functions: Express the relationships between sets.
How to describe a set?
1) List elements in the set between {} (curly brackets).
For e.g., set of all first year CSC courses: F = {CSC104, CSC108, CSC120,
CSC121, CSC148, CSC165}.
G = {(Leafs 91), blue, {afternoon, evening}}
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Number of elements in the set:
Also known as cardinality
Denoted by | |
E.g.: |F| = 6 while |G| = 3 (from the examples above ^)
The different kinds of sets:
- An empty set:
Denoted by Φ Greek sol for phi
|Φ| = 0
- A finite set:
A set that has a finite number of elements / The cardinality of a finite set is a
natural number.
E.g.: A = {5, 4, 900, 40}
- An infinite set:
A set that never ends.
E.g.: natural numbers, integers, rational numbers, real numbers.
Natural uers: N = {, , , , …} (NOTE: 0 IS A NATURAL NUMBER!)
2) Define a set by describing/giving a rule for all elements
E.g.: { x | x ∈ N & <= x < 7 } ould e read as suh that elogs to the set of
atural uers ad is etee ad , ilusie.
Whih traslates to: The set of all atural uers etee ad , ilusie.
E.g.: Set of rational #s:
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CSC165H1 Full Course Notes
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