diff --git a/concurrency-mapreduce/README.md b/concurrency-mapreduce/README.md
index f937508..b1082a3 100644
--- a/concurrency-mapreduce/README.md
+++ b/concurrency-mapreduce/README.md
@@ -98,19 +98,23 @@ header file that specifies exactly what you must build in your MapReduce library
 #ifndef __mapreduce_h__
 #define __mapreduce_h__
 
-// Various function pointers
-typedef char *(*Getter)(char *key);
+// Different function pointer types used by MR
+typedef char *(*Getter)(char *key, int partition_number);
 typedef void (*Mapper)(char *file_name);
 typedef void (*Reducer)(char *key, Getter get_func, int partition_number);
-typedef unsigned long (*Partitioner)(char *key, int num_buckets);
+typedef unsigned long (*Partitioner)(char *key, int num_partitions);
 
-// Key functions exported by MapReduce
+// External functions: these are what you must define
 void MR_Emit(char *key, char *value);
-unsigned long MR_DefaultHashPartition(char *key, int num_buckets);
-void MR_Run(int argc, char *argv[],
-            Mapper map, int num_mappers,
-            Reducer reduce, int num_reducers,
-            Partitioner partition);
+
+unsigned long MR_DefaultHashPartition(char *key, int num_partitions);
+
+void MR_Run(int argc, char *argv[], 
+	    Mapper map, int num_mappers, 
+	    Reducer reduce, int num_reducers, 
+	    Partitioner partition);
+
+#endif // __mapreduce_h__
 ```
 
 The most important function is `MR_Run`, which takes the command line
@@ -161,7 +165,7 @@ void Map(char *file_name) {
 void Reduce(char *key, Getter get_next, int partition_number) {
     int count = 0;
     char *value;
-    while ((value = get_next(key)) != NULL)
+    while ((value = get_next(key, partition_number)) != NULL)
         count++;
     printf("%s %d\n", key, count);
 }
@@ -195,8 +199,9 @@ invoked once per key, and is passed the key along with a function that enables
 iteration over all of the values that produced that same key. To iterate, the
 code just calls `get_next()` repeatedly until a NULL value is returned;
 `get_next` returns a pointer to the value passed in by the `MR_Emit()`
-function above. The output, in the example, is just a count of how many times
-a given word has appeared.
+function above, or NULL when the key's values have been processed. The output,
+in the example, is just a count of how many times a given word has appeared,
+and is just printed to standard output.
 
 All of this computation is started off by a call to `MR_Run()` in the `main()`
 routine of the user program. This function is passed the `argv` array, and
@@ -209,26 +214,26 @@ partitioning function. In most cases, programs will use the default function
 its implementation:
 
 ```
-unsigned long MR_DefaultHashPartition(char *key, int num_buckets) {
+unsigned long MR_DefaultHashPartition(char *key, int num_partitions) {
     unsigned long hash = 5381;
     int c;
     while ((c = *key++) != '\0')
         hash = hash * 33 + c;
-    return hash % num_buckets;
+    return hash % num_partitions;
 }
 ```
 
 The function's role is to take a given `key` and map it to a number, from `0`
-to `num_buckets - 1`. Its use is internal to the MapReduce library, but
+to `num_partitions - 1`. Its use is internal to the MapReduce library, but
 critical. Specifically, your MR library should use this function to decide
-which Reduce thread gets a particular key/list of values to process.  For some
-applications, which Reducer thread processes a particular key is not
-important (and thus the default function above should be passed in to
-`MR_Run()`); for others, it is, and this is why the user can even pass in
-their own partitioning function as need be.
+which partition (and hence, which reducer thread) gets a particular key/list
+of values to process.  For some applications, which reducer thread processes a
+particular key is not important (and thus the default function above should be
+passed in to `MR_Run()`); for others, it is, and this is why the user can pass
+in their own partitioning function as need be.
 
 One last requirement: For each partition, keys (and the value list associated
-with said keys) should be *sorted* in ascending key order; thus, when a
+with said keys) should be **sorted** in ascending key order; thus, when a
 particular reducer thread (and its associated partition) are working, the
 `Reduce()` function should be called on each key in order for that partition.
 
diff --git a/concurrency-mapreduce/mapreduce.h b/concurrency-mapreduce/mapreduce.h
index ab867cd..24e1aec 100644
--- a/concurrency-mapreduce/mapreduce.h
+++ b/concurrency-mapreduce/mapreduce.h
@@ -1,15 +1,16 @@
 #ifndef __mapreduce_h__
 #define __mapreduce_h__
 
-typedef char *(*Getter)(char *key);
-
+// Different function pointer types used by MR
+typedef char *(*Getter)(char *key, int partition_number);
 typedef void (*Mapper)(char *file_name);
 typedef void (*Reducer)(char *key, Getter get_func, int partition_number);
-typedef unsigned long (*Partitioner)(char *key, int num_buckets);
+typedef unsigned long (*Partitioner)(char *key, int num_partitions);
 
+// External functions: these are what you must define
 void MR_Emit(char *key, char *value);
 
-unsigned long MR_DefaultHashPartition(char *key, int num_buckets);
+unsigned long MR_DefaultHashPartition(char *key, int num_partitions);
 
 void MR_Run(int argc, char *argv[], 
 	    Mapper map, int num_mappers,