diff --git a/lectures/functions.md b/lectures/functions.md
index cdc88059..9152f15d 100644
--- a/lectures/functions.md
+++ b/lectures/functions.md
@@ -447,11 +447,11 @@ def x(t):
         return 2 * x(t-1)
 ```
 
-What happens here is that each successive call uses it's own *frame* in the *stack*
+What happens here is that each successive call uses its own *frame* in the *stack*
 
 * a frame is where the local variables of a given function call are held
 * stack is memory used to process function calls
-  * a First In Last Out (FILO) queue
+  * a last-in, first-out (LIFO) data structure
 
 This example is somewhat contrived, since the first (iterative) solution would usually be preferred to the recursive solution.
 
diff --git a/lectures/numpy.md b/lectures/numpy.md
index 653ca0fc..1d247cc0 100644
--- a/lectures/numpy.md
+++ b/lectures/numpy.md
@@ -215,7 +215,7 @@ z
 See also `np.asarray`, which performs a similar function, but does not make
 a distinct copy of data already in a NumPy array.
 
-To read in the array data from a text file containing numeric data use `np.loadtxt` ---see [the documentation](https://numpy.org/doc/stable/reference/routines.io.html) for details.
+To read in the array data from a text file containing numeric data use `np.loadtxt` --- see [the documentation](https://numpy.org/doc/stable/reference/routines.io.html) for details.
 
 
 
@@ -1271,7 +1271,7 @@ you will understand.
 
 There is a problem here, however.
 
-Suppose that `q` is altered after an instance of `discreteRV` is
+Suppose that `q` is altered after an instance of `DiscreteRV` is
 created, for example by
 
 ```{code-cell} python3
@@ -1406,11 +1406,11 @@ F.plot(ax)
 :label: np_ex4
 ```
 
-Recall that [broadcasting](broadcasting) in Numpy can help us conduct element-wise operations on arrays with different number of dimensions without using `for` loops.
+Recall that [broadcasting](broadcasting) in NumPy can help us conduct element-wise operations on arrays with different number of dimensions without using `for` loops.
 
 In this exercise, try to use `for` loops to replicate the result of the following broadcasting operations.
 
-**Part1**: Try to replicate this simple example using `for` loops and compare your results with the broadcasting operation below.
+**Part 1**: Try to replicate this simple example using `for` loops and compare your results with the broadcasting operation below.
 
 ```{code-cell} python3
 
@@ -1429,7 +1429,7 @@ tags: [hide-output]
 print(A)
 ```
 
-**Part2**: Move on to replicate the result of the following broadcasting operation. Meanwhile, compare the speeds of broadcasting and the `for` loop you implement.
+**Part 2**: Move on to replicate the result of the following broadcasting operation. Meanwhile, compare the speeds of broadcasting and the `for` loop you implement.
 
 For this part of the exercise you can use the `tic`/`toc` functions from the `quantecon` library to time the execution. 
 
diff --git a/lectures/pandas.md b/lectures/pandas.md
index 8218f44d..fac1f41b 100644
--- a/lectures/pandas.md
+++ b/lectures/pandas.md
@@ -380,7 +380,7 @@ df.apply(update_row, axis=1)
 
 ```{code-cell} ipython3
 # Round all decimal numbers to 2 decimal places
-df.map(lambda x : round(x,2) if type(x)!=str else x)
+df.map(lambda x : round(x,2) if not isinstance(x, str) else x)
 ```
 
 **Application: Missing Value Imputation**
@@ -403,8 +403,8 @@ We can use the `.map()` method again to replace all missing values with 0
 ```{code-cell} ipython3
 # replace all NaN values by 0
 def replace_nan(x):
-    if type(x)!=str:
-        return  0 if np.isnan(x) else x
+    if not isinstance(x, str):
+        return  0 if pd.isna(x) else x
     else:
         return x
 
@@ -536,7 +536,7 @@ In the second case, you can either
 * switch to another machine
 * solve your proxy problem by reading [the documentation](https://requests.readthedocs.io/en/latest/)
 
-Assuming that all is working, you can now proceed to use the `source` object returned by the call `requests.get('https://research.stlouisfed.org/fred2/series/UNRATE/downloaddata/UNRATE.csv')`
+Assuming that all is working, you can now proceed to build the `source` object from the data returned by the call `requests.get(url)`
 
 ```{code-cell} ipython3
 url = 'https://fred.stlouisfed.org/graph/fredgraph.csv?bgcolor=%23e1e9f0&chart_type=line&drp=0&fo=open%20sans&graph_bgcolor=%23ffffff&height=450&mode=fred&recession_bars=on&txtcolor=%23444444&ts=12&tts=12&width=1318&nt=0&thu=0&trc=0&show_legend=yes&show_axis_titles=yes&show_tooltip=yes&id=UNRATE&scale=left&cosd=1948-01-01&coed=2024-06-01&line_color=%234572a7&link_values=false&line_style=solid&mark_type=none&mw=3&lw=2&ost=-99999&oet=99999&mma=0&fml=a&fq=Monthly&fam=avg&fgst=lin&fgsnd=2020-02-01&line_index=1&transformation=lin&vintage_date=2024-07-29&revision_date=2024-07-29&nd=1948-01-01'
diff --git a/lectures/python_by_example.md b/lectures/python_by_example.md
index f89c87f5..919770ad 100644
--- a/lectures/python_by_example.md
+++ b/lectures/python_by_example.md
@@ -380,9 +380,9 @@ plt.plot(ϵ_values)
 plt.show()
 ```
 
-A while loop will keep executing the code block delimited by indentation until the condition (```i < ts_length```) is satisfied.
+A while loop will keep executing the code block delimited by indentation as long as the condition (`i < ts_length`) is satisfied.
 
-In this case, the program will keep adding values to the list ```ϵ_values``` until ```i``` equals ```ts_length```:
+In this case, the program will keep adding values to the list `ϵ_values` until `i` equals `ts_length`:
 
 ```{code-cell} python3
 i == ts_length #the ending condition for the while loop