<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<script>
$(document).ready(function(){
var form=$("#myForm");
$("#smt").click(function(){
$.ajax({
        type:"POST",
        url:form.attr("action"),
        data:form.serialize(),
        success: function(response){
            console.log(response);
        }
    });
});
});
</script>

<form action="check.php" method="post" name="myForm" id="myForm">
<input type="text" name="user" id="user" />
<input type="text" name="pass" id="pass" />
<input type="button" name="smt" value="Submit" id="smt" />
</form>
<div id="err"></div>

$user=$_POST['user'];
$pass=$_POST['pass'];

if($user=="tony")
{
    echo "HI ".$user;
}
else
{
    echo "I dont know you.";
}

$(document).ready(function(){
    var form=$("#myForm");
    $("#smt").click(function(){
    $.ajax({
            type:"POST",
            url:form.attr("action"),
            data:$("#myForm input").serialize(),//only input
            success: function(response){
                console.log(response);
            }
        });
    });
    });

<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<script>
$(document).ready(function(){
var form=$("#myForm");
$("#smt").click(function(){
$.ajax({
        type:"POST",
        url:form.attr("action"),
        data:form.serialize(),

        success: function(response){
        if(response === 1){
            //load chech.php file
        }  else {
            //show error
        }
        }
    });
});
});

parse_str($_POST["data"], $_POST);

<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<script>
$(document).ready(function(){
var form=$("#myForm");
$("#smt").click(function(){
$.ajax({
        type:"POST",
        url:form.attr("action"),
        data:form.serialize(),

        success: function(response){
        if(response == 1){
              $("#err").html("Hi Tony");//updated
        }  else {
            $("#err").html("I dont know you.");//updated
        }
        }
    });
});
});
</script>

<?php
$user=$_POST['user'];
$pass=$_POST['pass'];

if($user=="tony")
{
    echo 1;
}
else
{
    echo 0;
}
?>

Try this its working

    <script>
      $(function () {
      $('form').on('submit', function (e) {

        e.preventDefault();
        $.ajax({
            type: 'post',
            url: '<?php echo base_url();?>student_ajax/insert',
            data: $('form').serialize(),
            success: function (response) {
            alert('form was submitted');
            }
            error:function()
            {
            alert('fail');
            }
      });
      });
          });
    </script>