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  3. University Of Surrey (UNIS)
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  5. Foundations of Computer Science (COM1026)

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Summary and Flashcards - Foundations of Computer Science
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In-depth coverage going over mathematics for computer scientists. Probability, permutations, bionomial and pascals triangle. Axioms, logic and proofs, regular languages and finite automata, sets and venn diagrams and their relationships. In depth coverage of number theory. Strings, concatenation an...

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  • June 25, 2024
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  • 2023/2024
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Foundations of Computing (COM1026)


https://www.cl.cam.ac.uk/teaching/1213/RLFA/reglfa-notes.pdf
(Regular Languages
and Finite Automata)
https://www.cl.cam.ac.uk/teaching/2122/DiscMath/materials.html]
(Discrete Mathematics)
https://www.cl.cam.ac.uk/teaching/2122/LogicProof/logic-notes.pdf
(Logic and Proof)
https://github.com/EasyCrypt/easycrypt
(EasyCrypt)
http://mfleck.cs.illinois.edu/building-blocks/version-1.0/proofs.pdf
(Direct Proofs)
https://courses.engr.illinois.edu/cs173/fa2009/lectures/lect_07.pdf
(Proofs by contrapositive and by contradiction)
http://mfleck.cs.illinois.edu/building-blocks/version-1.3/contradiction.pdf
http://www.oxfordmathcenter.com/drupal7/node/317
http://www.personal.kent.edu/~rmuhamma/Philosophy/Logic/ProofTheory/proo
f_by_contradictionExamples.htm
(Proofs by contradiction)
http://mfleck.cs.illinois.edu/building-blocks/version-1.3/induction.pdf
http://www.oxfordmathcenter.com/drupal7/node/114
http://www.oxfordmathcenter.com/drupal7/node/117
(Proofs by induction)

,1) What is a set? “A set is a collection of objects called
elements”

2) How do we describe a set in • An enumeration of elements
mathematics? A={1,2,3,4,5,6}
• Give a verbal description:
A is the set of all integers from 1 to 6,
inclusive
• Give a mathematical inclusion rule:
A={ Integers x | 1 ≤ x ≤ 6}

3) What is the Abstraction Axiom? Given a property P, there exists the set S of
objects that satisfy this property P.

(whatever property P, there exists a set S
containing the objects that satisfy P and only
these objects).

4) What is the empty set? The empty set is a set with no elements.

,5) What are the basic operations on sets? Membership:
– `x is in A’ 𝒙 ∈ 𝑨
– `x is not in A’ 𝒙 ∉ 𝑨
– `A is a subset of B, but A can be equal to
B’ 𝑨 ⊆ 𝑩
– `A is a proper subset of B, i.e., A cannot be equal
to B’ 𝑨 ⊂ 𝑩
or, specifically, 𝑨 ⊊ 𝑩

Operations:
– Union: putting sets together. 𝑨 ∪ 𝑩
– Intersection: what’s in both. 𝑨 ∩ 𝑩
– Set difference: what’s in the first but not in the
2nd. 𝑨 ∖ 𝑩

6) What are some examples of basic A = {alice, ben, cora}
operations on sets? B = {ben, dan, fran}
Membership:




Operations:
– Union:
– Intersection:
– Set difference:

, 7) How do we use Venn Diagrams in Set
Theory?




8) What are the basic operations of Venn
Diagrams?




9) What are subsets? Set A is a subset of set B if every element of A
is an element of B.
" A is a subset of B" is
denoted A ⊆ B

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