vault backup: 2024-12-13 01:56:36

.obsidian/plugins/obsidian-icon-folder/data.json

@@ -80,7 +80,7 @@
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@@ -10,15 +10,27 @@
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+              },
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+              "title": "ex 1"
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-              "title": "Midterm prep"
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@@ -200,15 +212,17 @@
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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)!}
   $$
   

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.
 
 ---