Ajax form submission with Jquery validation plugin is not working

I am using Jquery validation plugin to validate form, I need to display success/error message after submission without reloading page. But everytime I submit form, page reloads. Also even when data appears on database, "error" alert keeps coming.

index.php

    <?php

    function register(){ 
    $name = $_POST['name']; 
    $mail = $_POST['email']; 
    $query = "INSERT INTO table_name (name,email) VALUES ('$name','$email')"; 
    $data = mysql_query($query)or die(mysql_error()); 
    echo json_encode($data);
    }   
    if(isset($_POST['submit'])){ 
    register();
    }
    ?>

Javascript code:

       $("#myform").validate({
       //rules, messages go here

       submitHandler: function(event) {
                    $.ajax({
                         url: "index.php",
                         type: "POST",
                         data: $(#myform).serialize(),
                         dataType: 'json',
                         success: function() {
                               alert("Thank you!");
                         },
                         error: function() {
                               alert("Error. Try again please!");
                         }
                         });

                    event.preventDefault();
         } 

     });