diff --git a/.obsidian/plugins/obsidian-icon-folder/data.json b/.obsidian/plugins/obsidian-icon-folder/data.json index 8fcf229..2b4fd7a 100644 --- a/.obsidian/plugins/obsidian-icon-folder/data.json +++ b/.obsidian/plugins/obsidian-icon-folder/data.json @@ -80,7 +80,7 @@ "iconColor": "#5773ff" }, "Statistics and Probability/R": "📊", - "Discrete Structures/Midterm prep.md": { + "Discrete Structures/Midterm/Midterm prep.md": { "iconName": "LiBookOpenCheck", "iconColor": "#ffbb00" } diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index f245054..5c98b37 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -10,15 +10,27 @@ { "id": "25537c3876ede1e3", "type": "leaf", + "state": { + "type": "excalidraw", + "state": { + "file": "Discrete Structures/Midterm/ex 1.md" + }, + "icon": "excalidraw-icon", + "title": "ex 1" + } + }, + { + "id": "91554391c16f6712", + "type": "leaf", "state": { "type": "markdown", "state": { - "file": "Discrete Structures/Midterm prep.md", + "file": "Discrete Structures/Counting.md", "mode": "source", "source": false }, "icon": "lucide-file", - "title": "Midterm prep" + "title": "Counting" } } ] @@ -200,15 +212,17 @@ }, "active": "25537c3876ede1e3", "lastOpenFiles": [ + "Discrete Structures/Recurrence relations.md", + "Discrete Structures/Counting.md", + "Discrete Structures/Midterm/ex 1.md", + "Discrete Structures/Midterm/Midterm prep.md", + "Discrete Structures/Midterm", "Extracurricular/CANSAT/img/Pasted image 20241206134156.png", "Extracurricular/CANSAT/Parts Proposal.md", "Untitled.md", "Untitled.canvas", - "Discrete Structures/Midterm prep.md", - "Discrete Structures/Counting.md", "Discrete Structures/Mathematical Data Structures.md", "Discrete Structures/Relations and Digraphs.md", - "Discrete Structures/Recurrence relations.md", "Discrete Structures/Mathematical Proofs (Induction).md", "Advanced Algorithms/Graphs.md", "Advanced Algorithms/P vs. NP.md", @@ -245,7 +259,6 @@ "Discrete Structures/img", "Algorithmic Programming Contests", "Functional Programming/assets", - "Extracurricular/CANSAT", "Web Engineering/canvae/server_client.canvas", "Advanced Programming/projects/second/Refactoring.canvas", "Advanced Programming/assets/assignment/assignment_organization.canvas", diff --git a/Discrete Structures/Counting.md b/Discrete Structures/Counting.md index 1b8edc0..bb69ef6 100644 --- a/Discrete Structures/Counting.md +++ b/Discrete Structures/Counting.md @@ -9,7 +9,8 @@ type: theoretical A permutation is an arrangement of objects in a specific order. - Without Repetition[^1]: The number of permutations of $n$ distinct objects taken $r$ at a time is denoted by $nP_r$ and calculated as: - $$ + Let f (n) = 7n + 3n2 + n2n and g(n) = 3n +n . Prove that f (n) = O(g(n))$$ nP_r = \frac{n!}{(n - r)!} $$ diff --git a/Discrete Structures/Midterm prep.md b/Discrete Structures/Midterm/Midterm prep.md similarity index 100% rename from Discrete Structures/Midterm prep.md rename to Discrete Structures/Midterm/Midterm prep.md diff --git a/Discrete Structures/Midterm/ex 1.md b/Discrete Structures/Midterm/ex 1.md new file mode 100644 index 0000000..29a2202 --- /dev/null +++ b/Discrete Structures/Midterm/ex 1.md @@ -0,0 +1,8889 @@ +--- + +excalidraw-plugin: parsed +tags: [excalidraw] + +--- +==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving' + + +# Excalidraw Data +## Text Elements +%% +## Drawing +```compressed-json +N4KAkARALgngDgUwgLgAQQQDwMYEMA2AlgCYBOuA7hADTgQBuCpAzoQPYB2KqATLZMzYBXUtiRoIACyhQ4zZAHoFAc0JRJQgEYA6bGwC2CgF7N6hbEcK4OCtptbErHALRY8RMpWdx8Q1TdIEfARcZgRmBShcZQUebQAWbQBGGjoghH0EDihmbgBtcDBQMBLoeHF0ADNAhE8qflLGFnYuNB4+Qsgm1k4AOU4xbgBmJIB2AFZR0YBOUYAOBshCDmIs + +bghcAAZUkqXmABF0qFruSoIwxYgSdYAFXs2ASVIkgHFRhElCUgArfAB9GC4ABSQ0IAAkdqVKoR8PgAMqwYLrQQeSECKCkNgAawQAHUSOpuElLswMdiEAiYEiJCjrpdMX5JBxwrk0MTOhA2HBcNg1DAiZtNpdrMpqaghRzMNxnElptNLvy0PEeHMEtMeEk5hMSWScQBhNj4NikdYAYiSCAtFrREE0PKxygZKwNRpNEgx1mY3MC2RtFAJkm47W040u + +kgQhGU0m4ADZRiGSQgTmgRjxpoLlZdHcI4A9iKzUHkALqXaq4TJ57gcISw+nCFbM5gF6u1jmaevEACiwUy2QLxcuQjgxFwx2IRNGQ3im3i8TmMfTY0uRA4WKrNfwy7Y2Bx47QZ3wFw5cDYyxy+U6YAKuxKEpvYE2l5Ll+vN6S2h4ocvD6fiyv37iL970fG9nxvV9diGbRtW/GUP3GX8X2/VUYPvZwY3gxDwO/JJ30/P8wGcFCENAv8IJKJJAIImV + 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b/Discrete Structures/Recurrence relations.md @@ -37,7 +37,7 @@ A recurrence relation is an equation that defines a sequence based on its earlie x^k - a_1 x^{k-1} - a_2 x^{k-2} - \ldots - a_k = 0 $$ - - The roots of the characteristic equation determine the explicit formula for the sequence. The sources focus on degree-2 relations, but the method generalizes to any degree. + - The roots of the characteristic equation determine the explicit formula for the sequence. ---