Establishing PHP connection with localhost server

Question

I am having trouble connecting my PHP script to the database on my localhost server. 

The errors in  browser console:

Failed to load resource: the server responded with a status of 404 (Not Found) 

ReferenceError: Can't find variable: $

The UNIX socket code from MAMP:

$user = 'root';
$password = 'root';
$db = 'inventory';
$socket = 'localhost:/Applications/MAMP/tmp/mysql/mysql.sock';

$link = mysql_connect(
   $socket, 
   $user, 
   $password
);
$db_selected = mysql_select_db(
   $db, 
   $link
);

The PHP code:

    //connect to database
    $db = mysql_connect("localhost", "root", "", "authentication");

    if (isset($_POST['register_btn'])) {
        session_start();
        $username =mysql_real_escape_string($_post['username']);
        $email =mysql_real_escape_string($_post['email']);
        $password =mysql_real_escape_string($_post['password']);
        $password2 =mysql_real_escape_string($_post['password2']);


        if ($password == $password2) {
            //create user
            $password = md5($password); //hash password before storing for security 
            $sql = "INSERT INTO users(username, email, password) VALUES('$username', '$email', '$password')";
            mysql_query($db, $sql);
            $_SESSION['message'] = "Find a Table";
            $_SESSION['username'] = $username;
            header("location: HomePage.html"); //redirect to homepage 
        }else{
            $_SESSION['message'] = "Your passwords must match to proceed";

        }


    }


?>

Can someone help me solve this?