diff --git a/ods/notes/chapter2.txt b/ods/notes/chapter2.txt
index 6152937..3f2afe0 100644
--- a/ods/notes/chapter2.txt
+++ b/ods/notes/chapter2.txt
@@ -28,6 +28,32 @@ resizing isn't too bad.
 * The analysis of add and remove didn't consider cost of resize.
 * An amortised analysis is done instead that considers the cost of all calls
   to add and remove, given a sequence of *m* calls to either.
-* Lemma: if an empty ArrayStack is created and any sequence of *m* >= 1 calls
-  to add and remove are performed, the total time spent in calls to resize is 
-  O(m).
+* **Lemma**: if an empty ArrayStack is created and any sequence of *m* >= 1
+  calls to add and remove are performed, the total time spent in calls to 
+  resize is O(m).
+* Optimisations (FastArrayStack): using memcpy or std::copy to copy blocks of
+  data, not one element at a time.
+
+## ArrayQueue
+
+* ArrayStack is a bad implementation for a FIFO queue; either add or remove
+  must work from the head with index = 0, which means all calls to that
+  method will result in running time of O(n).
+* We could do this with an infinite array, using an index into the head (*j*)
+  and the size of the backing array. We don't have an infinite array, so we'll
+  have to use modular arithmetic with a finite stack.
+* **Theorem**: Ignoring the cost of calls to resize, an ArrayQueue supports the
+  operations add and remove in O(1) per operation. Beginning with an empty
+  ArrayQueue, any sequence of m add/remove operations will result in a total
+  of O(m) time resizing.
+
+## ArrayDeque
+
+* Implementation of adding and removing from both ends using the same circular
+  buffer technique.
+* add/remove check whether their index is before or after the halfway point and
+  shift from there as a performance benefit.
+* **Theorem**: Ignoring the cost of calls to resize, an ArrayDeque supports
+  set/get in time O(1) time per operation, and add/remove in O(1+min(i, n-1))
+  time per operation. Beginning with an empty ArrayDeque, performing any 
+  sequence of m operations results in a total of O(m) time resizing.
diff --git a/ods/src/array_test.cc b/ods/src/array_test.cc
index a184dbf..bf900eb 100644
--- a/ods/src/array_test.cc
+++ b/ods/src/array_test.cc
@@ -1,3 +1,4 @@
+#include <cassert>
 #include <iostream>
 #include <ods/array.h>
 #include <ods/array_stack.h>
@@ -51,16 +52,30 @@ main(void)
 	cout << "=== ArrayDeque ===" << endl;
 	ArrayDeque<int>	ad(1);
 	for (int i = 0; i < 5; i++) {
-		ad.add(0, i);
+		ad.add(0, 4-i);
 	}
 	cout << "size: " << ad.size() << ", cap: " << ad.cap() << endl;
 
 	for (int i = 0; i < 5; i++) {
-		ad.add(ad.size() - 1, i);
+		ad.add(ad.size(), i);
 	}
 	cout << "size: " << ad.size() << ", cap: " << ad.cap() << endl;
 
 	for (int i = 0; i < ad.size(); i++) {
 		cout << i << "\t" << ad.get(i) << endl;
 	}
+
+	auto x = ad.remove(1);
+	assert(x == 1);
+	x = ad.remove(7);
+	assert(x == 3);
+	cout << "size: " << ad.size() << ", cap: " << ad.cap() << endl;
+
+	for (int i = 0; i < ad.size(); i++) {
+		cout << i << "\t" << ad.get(i) << endl;
+	}
+	ad.remove(2);
+	ad.remove(3);
+	ad.remove(4);
+	cout << "size: " << ad.size() << ", cap: " << ad.cap() << endl;
 }
diff --git a/ods/src/ods/array_deque.h b/ods/src/ods/array_deque.h
index d4830fc..acd110e 100644
--- a/ods/src/ods/array_deque.h
+++ b/ods/src/ods/array_deque.h
@@ -55,6 +55,28 @@ public:
 		n++;
 	}
 
+	T remove(int i) {
+		T x = a[index(i)];
+		if (i < (n/2)) {
+			for (int k = i; k > 0; k--) {
+				a[index(k)] = a[index(k-1)];
+			}
+			j = index(1);
+		}
+		else {
+			for (int k = i; k < n-1; k++) {
+				a[index(k)] = a[index(k+1)];
+			}
+		}
+		n--;
+
+		if (a.length > 3 * n) {
+			resize();
+		}
+
+		return x;
+	}
+
 	void resize(void) {
 		Array<T> b(max(2 * n, 1));
 		for (int k = 0; k < n; k++) {