#discretemath — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #discretemath, aggregated by home.social.
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Alright, future engineers!
**Modular Arithmetic:** `a === b (mod n)` means `a` & `b` have the same remainder when divided by `n`.
Ex: `17 === 5 (mod 12)` since `17 % 12 = 5` & `5 % 12 = 5`.
Pro-Tip: Think 'clock arithmetic'! It's key for cryptography & hashing. -
Alright, future engineers!
**Pigeonhole Principle:** If `n` items are put into `m` containers, and `n > m`, then at least one container must contain more than one item.
Ex: 7 emails into 6 folders means one folder has >1 email.
Pro-Tip: A powerful proof technique for existence!
#DiscreteMath #Logic #STEM #StudyNotes -
Alright, future engineers!
**Combinations:** Ways to *choose* items from a set where the order *doesn't* matter.
Ex: Picking 3 teammates from 5 friends: `C(5,3) = 10` ways.
Pro-Tip: If swapping items doesn't create a new outcome, it's a combination!
#DiscreteMath #Combinatorics #STEM #StudyNotes -
Alright, future engineers!
**Probability Mass Function (PMF)**: Gives the probability for *each specific outcome* of a discrete random variable.
Ex: Fair die `P(X=3) = 1/6`.
Pro-Tip: All `P(X=x)` values must be non-negative & sum to 1.
#Probability #DiscreteMath #STEM #StudyNotes -
Alright, future engineers!
**Modulo Arithmetic** (a mod n) finds the remainder when integer 'a' is divided by integer 'n'.
Ex: 7 mod 3 = 1 (since 7 = 2*3 + 1).
Pro-Tip: Think of clocks! 13:00 is 1:00 (13 mod 12 = 1). Essential for cryptography!
#NumberTheory #DiscreteMath #STEM #StudyNotes -
Alright, future engineers!
The **Union** of sets A & B (A U B) is all elements in A *or* B.
Ex: A={1,2}, B={2,3}. A U B = {1,2,3}.
Pro-Tip: Think 'OR' for Union. It includes everything from either set!
#SetTheory #DiscreteMath #STEM #StudyNotes -
Alright, future engineers!
**Combinations**: ways to choose items where order *doesn't* matter.
Ex: Picking 3 committee members from 5 people: C(5,3) = 10 ways.
Pro-Tip: Think 'selecting ingredients for a soup' – the order you add them doesn't change the final soup! -
Future engineers!
An **Adjacency Matrix** (A) shows graph connections: A[i][j]=1 if vertex i links to j, else 0.
Ex: For a-b, b-c: A[a,b]=1, A[b,a]=1.
Pro-Tip: It's symmetric for undirected graphs!
#GraphTheory #DiscreteMath #STEM #StudyNotes -
Alright, future engineers!
**Permutations** count arrangements where order *matters*.
Ex: Electing a Pres, VP, Sec from 10 people: P(10,3) = 10!/(10-3)!
Pro-Tip: If switching item order creates a *new* distinct outcome, it's a permutation!
#Probability #DiscreteMath #STEM #StudyNotes -
Alright, future engineers!
The **Degree of a Vertex** in a graph is the count of edges connected to it. Ex: If `v` is a person, `deg(v)` is their number of friends. Pro-Tip: The sum of all degrees in any graph is always twice the number of edges!
#GraphTheory #DiscreteMath #STEM #StudyNotes -
Alright, future engineers!
A **Combination** is a selection of items where order *doesn't* matter. Ex: Choosing 3 people for a committee from 10. `C(N,K) = N!/(K!(N-K)!)`. Pro-Tip: Use for groups, not sequences!
#Combinatorics #DiscreteMath #STEM #StudyNotes -
Alright, future engineers!
A **Cartesian Product (A x B)** is the set of all ordered pairs (a,b) where a∈A & b∈B.
Ex: A={1,2}, B={x,y} => A x B = {(1,x),(1,y),(2,x),(2,y)}.
Pro-Tip: It's how you model all possible pairs across two sets! -
Alright, future engineers!
A **Power Set** P(S) is the set of *all* possible subsets of set S. Ex: If `S = {1, 2}`, then `P(S) = {{}, {1}, {2}, {1, 2}}`. Pro-Tip: Its size (cardinality) is always `2^|S|`!
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Alright, future engineers!
**Permutations:** Arrangements where order *does* matter.
Ex: Arranging 3 people for 3 specific roles (Pres, VP, Sec) from 5 options. P(5,3) = 5!/(5-3)! = 60.
Pro-Tip: Think 'ranking' or 'sequence' – position is crucial! -
Alright, future engineers!
**Combinations:** Choosing items from a set where order *doesn't* matter.
Ex: Picking 3 teammates from 10. Formula: C(n,k) = n!/(k!(n-k)!).
Pro-Tip: Think 'committee' selection—roles are identical, order is irrelevant! -
Alright, future engineers! **Cartesian Product (A x B)** creates all ordered pairs (a,b) where 'a' is from set A & 'b' from set B.
Ex: A={1,2}, B={x,y}. A x B = {(1,x), (1,y), (2,x), (2,y)}.
Pro-Tip: Essential for understanding relations and functions – think of it as building a grid of possibilities!
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Alright, future engineers!
The **Power Set** of a set A is the set of *all* possible subsets of A. Ex: For A={1,2}, P(A) = {{}, {1}, {2}, {1,2}}.
Pro-Tip: If a set has 'n' elements, its power set will always have 2^n elements. Handy for combinatorics! -
Vertex Degree: The number of edges connected to a vertex in a graph. Ex: In a social network, your degree is how many friends you have. Pro-Tip: Sum of all degrees is always 2 * (num of edges) – the Handshaking Lemma!
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Set Intersection (A ∩ B) finds elements common to *both* sets A & B. Ex: A={1,2,3}, B={2,3,4} -> A ∩ B = {2,3}. Pro-Tip: Think of it as AND – an element must be in A AND in B to be in the intersection!
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Permutations count arrangements where order matters. Ex: How many ways to arrange 3 books? 3! = 6 ways. Pro-Tip: 'Order matters' is your key phrase. If reordering creates a *new* valid outcome, it's a permutation!
#Combinatorics #DiscreteMath #STEM #StudyNotes -
"Like parsley in Greek food: Elementary set theory and the case for DM1" by Siddharth Bhaskar (https://dblp.org/pid/170/0077.html) got accepted at SIGCSE TS 2026.
#SIGCSE #setTheory #CSEducation #math #discreteMath #computerScience
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I found a good Discrete Mathematics wiki today via a link from Reddit. Check it out below. #math #maths #discretemath #discretemathematics #discretemaths
https://github.com/jongwoojeff/DiscreteMathematics/wiki