Mastodawn

**Combinations:** Ways to choose items from a set where ORDER *doesn't* matter.
Ex: Picking 2 from {A,B,C} is {A,B}, {A,C}, {B,C} (3 ways). Formula: C(n,k)=n!/(k!(n-k)!)
Pro-Tip: Think groups or subsets – the sequence you pick them in doesn't change the group!
#Combinatorics #DiscreteMath #STEM #StudyNotes

kipriyanovich 4d ago

Alright, future engineers!

**Permutations:** Ways to arrange items from a set where ORDER MATTERS.
Ex: Arranging 3 distinct books on a shelf: 3! = 6 ways.
Pro-Tip: Use when position or sequence is crucial! Think passwords or schedules.
#Combinatorics #DiscreteMath #STEM #StudyNotes

kipriyanovich Jun 13

Alright, future engineers!
**Permutation (nPr):** An arrangement of items where the order *matters*.
Ex: Arranging 3 distinct books from 5 on a shelf: P(5,3) = 60 ways.
Pro-Tip: Think 'P' for 'Position' – a different order means a different outcome!
#Probability #Combinatorics #STEM #StudyNotes

kipriyanovich Jun 12

Alright, future engineers!
**Combination:** A selection of items where the order of selection *doesn't matter*.
Ex: Choosing 3 people from 10 for a committee: C(10,3) = 120.
Pro-Tip: Think 'C' for 'Committee' – selecting a group where roles aren't specified.
#Combinatorics #DiscreteMath #STEM #StudyNotes

kipriyanovich Jun 10

**Permutation:** An arrangement of items where order *matters*.
Ex: Ways to pick 1st, 2nd, 3rd place from 10 runners: P(10,3) = 10*9*8 = 720.
Pro-Tip: 'P' for 'Position' – sequence makes each arrangement unique!

#Combinatorics #StatsProb #STEM #StudyNotes

kipriyanovich Jun 8

Alright, future engineers!
**Combination:** Selecting items where order *doesn't* matter.
Ex: Choosing 3 toppings from 10. C(10,3) = 120.
Pro-Tip: 'C' for 'Choice' – order isn't relevant to the selection itself!
#Combinatorics #DiscreteMath #STEM #StudyNotes

Ross Kang Jun 4

The past two months, I helped coordinate the "Phase Transitions..." research semester programme at CWI (https://www.cwi.nl/en/events/research-semester-programmes/phasecap-phase-transitions-in-combinatorics-algorithms-probability/). It ended last Friday, and still I feel "hungover" from the intensive blur of activities/developments/ideas. Very grateful to my team --Feri, Jop, Serte, Carla, Noela, Guus-- we did it!

In parallel, during the same two months, after the dawn of recognition of what has arrived (after a tip from Jeroen), I underwent a kind of phase transition myself. Avowed refusenik in March (see https://mathstodon.xyz/@kangmeister/115252549665766971); an "anti-Gemini" research working group in April; compulsive button-pressing in May. (And yes, I *know* it is easy to set it up for pressing fewer buttons...)

That poetic part of me (or whatever remains of it) is allured by the term, "cognitive surrender", if only to help in my search for the right words to describe the sharp changes underway in various facets of mathematical life/growth.

#CWI #combinatorics #algorithms #probability #conferences #generativeAI #formalization #lean #scientificpublishing

PhaseCAP: Phase Transitions in Combinatorics, Algorithms, Probability

Combinatorics, Algorithms, Probability

kipriyanovich Jun 3

Alright, future engineers!
**Permutations:** Ways to arrange items where order *matters*.
Ex: Arranging 3 distinct books on a shelf: 3! = 6 ways.
Pro-Tip: Think 'P' for 'Position' – each arrangement is unique!
#StatsProb #Combinatorics #STEM #StudyNotes

kipriyanovich May 31

Alright, future engineers!
**Combinations:** Ways to select items where order *doesn't* matter.
Formula: C(n, k) = n! / (k! * (n-k)!)
Pro-Tip: Think 'C' for 'Committee' - the order you pick members doesn't change the committee!
#Combinatorics #DiscreteMath #STEM #StudyNotes

kipriyanovich May 31

Alright, future engineers!
**Permutations:** Ways to arrange items where order *DOES* matter.
Ex: Arranging 3 books from 5 on a shelf: P(5,3) = 60 ways.
Pro-Tip: Think 'P' for 'Position'! Order matters for unique arrangements.
#StatsProb #Combinatorics #STEM #StudyNotes