add class 21

Author: jkbren

notebooks/class_16/class_16_dynamics1.ipynb

@@ -1488,10 +1488,10 @@
     "* The mean first passage time from node $i$ to node $j$ is the expected number of time–steps for reaching the node $j$ for the first time, given that initially the walker starts from node $i$.\n",
     "\n",
     "* Let us define the probability of reaching a node $j$ after $n$ steps starting from any other node:\n",
-    "$$p(j, n) = p_j (1-p_j)^{n-1}$$\n",
+    "$p(j, n) = p_j (1-p_j)^{n-1}$\n",
     "\n",
     "* Approximately,\n",
-    "$$T_j = \\sum_n^{\\infty}\\Delta t \\times n \\times p(j,n) \\propto \\frac{1}{p_j} = \\frac{\\sum_i k_i}{k_j}$$\n",
+    "$T_j = \\sum_n^{\\infty}\\Delta t \\times n \\times p(j,n) \\propto \\frac{1}{p_j} = \\frac{\\sum_i k_i}{k_j}$\n",
     "\n",
     "* More mathematically,\n",
     "\n",