diff --git a/00_intro_numerical_methods.ipynb b/00_intro_numerical_methods.ipynb
index 49dcbaee..e55ac35b 100644
--- a/00_intro_numerical_methods.ipynb
+++ b/00_intro_numerical_methods.ipynb
@@ -702,7 +702,7 @@
     "\n",
     "Topics Covered: (see Syllabus on [Courseworks](https://courseworks2.columbia.edu/courses/107701/assignments/syllabus))\n",
     "\n",
-    "1. Quick <font color=red>*Review*</font> of computational Tools (Python,numpy,matplotlib,scipy,git)\n",
+    "- Quick <font color=red>*Review*</font> of Computational Tools (Python,numpy,matplotlib,scipy,git)\n",
     "- Sources of Error and Error Analysis\n",
     "- Rootfinding/Optimization of non-linear functions $f(x)$ \n",
     "- Interpolation\n",
@@ -723,11 +723,11 @@
    "source": [
     "### Topics Not Covered: \n",
     "\n",
-    "1. Optimization -- linear programming, constrained optimization\n",
+    "- Optimization -- linear programming, constrained optimization\n",
     "- Numerical Solution of PDE's (APMA E4301)\n",
     "- Mathematical Modeling (maybe a little)\n",
     "- Machine Learning/Data Science (APMA 4990 Intro Math of Data Science)\n",
-    "- Lot's of things that would be fun...\n"
+    "- Lots of things that would be fun...\n"
    ]
   },
   {
diff --git a/06_interpolation.ipynb b/06_interpolation.ipynb
index 304cd353..a2a1dd46 100644
--- a/06_interpolation.ipynb
+++ b/06_interpolation.ipynb
@@ -397,7 +397,7 @@
     }
    },
    "source": [
-    "But more fundamentally. A set of functions is **linearly independent** if the only linear combination that add to form the zero function, e.g.\n",
+    "But more fundamentally. A set of functions is **linearly independent** if the only linear combination that adds to form the zero function, e.g.\n",
     "\n",
     "$$\n",
     "    P_N(x) = p_0 1 + p_1 x + p_2 x^2 + \\ldots + p_n x^n = 0\n",
@@ -1274,7 +1274,7 @@
     "axes.plot(x, f(x), 'k', label=\"True $f(x)$\")\n",
     "axes.plot(data[:, 0], data[:, 1], 'ro', label=\"data\")\n",
     "          \n",
-    "axes.set_title(\"Interpolation of Runge's function\")\n",
+    "axes.set_title(\"Interpolation of the Weierstrass function\")\n",
     "axes.set_xlabel(\"x\")\n",
     "axes.set_ylabel(\"y\")\n",
     "axes.legend(loc=1)\n",
@@ -2013,7 +2013,7 @@
    "source": [
     "### Transformation of intervals\n",
     "\n",
-    "The previous algorithms are quite direct but can look a bit messy because every interval (or set of points) appears different...An important trick that is used in finite-element analysis is to to transform each interval (or element) \n",
+    "The previous algorithms are quite direct but can look a bit messy because every interval (or set of points) appears different... An important trick that is used in finite-element analysis is to to transform each interval (or element) \n",
     "\n",
     "$$\n",
     "    x \\in[x_k, x_{k+1}]\n",
@@ -2762,5 +2762,5 @@
   }
  },
  "nbformat": 4,
- "nbformat_minor": 1
+ "nbformat_minor": 4
 }
diff --git a/09_ODE_ivp_part1.ipynb b/09_ODE_ivp_part1.ipynb
index b5bfde54..58a82029 100644
--- a/09_ODE_ivp_part1.ipynb
+++ b/09_ODE_ivp_part1.ipynb
@@ -1604,7 +1604,7 @@
     "\n",
     "$$\\begin{aligned}\n",
     "    K_1 &= \\Delta t f(U_n, t_n) \\\\\n",
-    "    K_2 &= \\Delta t f(U_n + K1, t_n + \\Delta t )\\\\\n",
+    "    K_2 &= \\Delta t f(U_n + K_1, t_n + \\Delta t )\\\\\n",
     "    U_{n+1} &= U_n + \\frac{1}{2}\\left[K_1 +K_2\\right] \\\\    \n",
     "\\end{aligned}$$\n",
     "\n",