Typo fixes in max_sharpe_ratio_optimization.ipynb

docs/source/apps/max_sharpe_ratio_optimization.ipynb

@@ -23,7 +23,7 @@
    "source": [
     "A well-known application of QUBO solving is the Maximum Independent Set (MIS) graph problem - the task of finding the largest independent set in a graph, where an independent set is a set of vertices such that no two vertices are adjacent. Here, we explore a similar method of solving a QUBO, but with a different application.\n",
     "\n",
-    "In this notebook, we will demonstrate an example portfolio optimization problem by looking at Sharpe ratio maximization. To that, we will formulate the problem as a QUBO and try to find optimal weights for assets in a given portoflio. We will get many results using simulated annealing for our QUBO and then classically post-process to find the one that gives the actual highest Sharpe ratio. "
+    "In this notebook, we will demonstrate an example portfolio optimization problem by looking at Sharpe ratio maximization. To that, we will formulate the problem as a QUBO and try to find optimal weights for assets in a given portfolio. We will get many results using simulated annealing for our QUBO and then classically post-process to find the one that gives the actual highest Sharpe ratio. "
    ]
   },
   {
@@ -123,7 +123,7 @@
     "\n",
     "where $\\rho$ is a symmetric matrix that contains the correlation coefficient between an asset $i$ and asset $j$. The product ${\\sigma_{a_i}}{\\sigma_{a_j}}\\rho_{ij}$ = $\\text{Cov}_{ij}$ is also called the covariance of the assets $a_{i}$ and $a_{j}$. \n",
     "\n",
-    "In general, for $N$ assets = {$a_1,a_2,...,a_N$} in a portfolio $P$, the square of the portfolio standard deviation, in other words the variance, is given by the following formula:\n",
+    "In general, for $N$ assets = {$a_1,a_2,...,a_N$} in a portfolio $P$, the square of the portfolio standard deviation, in other words, the variance, is given by the following formula:\n",
     "\n",
     "$$ \n",
     "\\begin{align}\n",
@@ -165,7 +165,7 @@
    "id": "4e612676",
    "metadata": {},
    "source": [
-    "Given that understanding we will go through an example Sharpe ratio optimization. As an example dataset, we can use stocks from the S \\& P 500 Companies (available on Wikipedia) for our portfolio:"
+    "Given that understanding, we will go through an example of Sharpe ratio optimization. As an example dataset, we can use stocks from the S \\& P 500 Companies (available on Wikipedia) for our portfolio:"
    ]
   },
   {
@@ -431,7 +431,7 @@
    "id": "761572e7",
    "metadata": {},
    "source": [
-    "Given the selection of assets, we can then get the correlation matrix, $\\rho_{ij}$, between the choosen assets. In this case, we take a list of stock tickers as input and return the matrix for the monthly data in the last 2000 days: "
+    "Given the selection of assets, we can then get the correlation matrix, $\\rho_{ij}$, between the chosen assets. In this case, we take a list of stock tickers as input and return the matrix for the monthly data in the last 2000 days: "
    ]
   },
   {
@@ -1020,7 +1020,7 @@
    "id": "a4a521e0",
    "metadata": {},
    "source": [
-    "Finally, we utilize the functionality in our `submit_qubo()` function to solve the optimization problem of our objective function as a QUBO using multiple techniques. In this case, we employ Superstaq's internal simulator (which uses the simulated annealing technique) by specifying `target=\"ss_unconstrained_simulator\". Use `client.get_targets(supports_submit_qubo=True)` to see a complete list of available targets supporting QUBO submission."
+    "Finally, we utilize the functionality in our `submit_qubo()` function to solve the optimization problem of our objective function as a QUBO using multiple techniques. In this case, we employ Superstaq's internal simulator (which uses the simulated annealing technique) by specifying `target=\"ss_unconstrained_simulator\"`. Use `client.get_targets(supports_submit_qubo=True)` to see a complete list of available targets supporting QUBO submission."
    ]
   },
   {