Use selection function with a certain parameter and without parameter

I have a system to register students to projects that have a university (projects table), which should not be in another project.

This system allows me to see a list of students who have the ability to be registered to enroll them, before it even showed those who were already in projects, so I got the following function

function bd_alumno_opciones($proy_id_seleccionado){
$sql = "SELECT cedu_alum,";
$sql .= " CONCAT(nom1_alum,' ',nom2_alum,' ',ape1_alum,' ',ape2_alum,' ',cedu_alum) ";
 $sql .= " FROM alumno LEFT JOIN proyecto_alumno ON cedu_alum = alum_id ";
 $sql .= " WHERE proy_id = $proy_id_seleccionado OR proy_id is null ORDER BY cedu_alum ASC"; 
$res = sql2options( $sql ); 
return $res; }

This allows you to show those that are not enrolled in another project, the problem is that it only works when you want to modify a project to add or delete students, but when I want to register them I get an error, because there is no variable that compares them

MYSQL USE

I would like to have a function that shows those that are not with projects to register them, and that also helps me to modify a project taking that ID of the project

PUPILS TABLE

CREATE TABLE 'alumno' (
'cedu_alum' int(9) UNSIGNED NOT NULL COMMENT 'Cédula',
'ape1_alum' varchar(50) COLLATE utf8_unicode_ci NOT NULL,
'ape2_alum' varchar(50) COLLATE utf8_unicode_ci NOT NULL,
'nom1_alum' varchar(50) COLLATE utf8_unicode_ci NOT NULL,
'nom2_alum' varchar(50) COLLATE utf8_unicode_ci DEFAULT NULL,
'fech_naci' date NOT NULL,
'telf_resi_alum' varchar(11) COLLATE utf8_unicode_ci NOT NULL,
'telf_celu_alum' varchar(11) COLLATE utf8_unicode_ci DEFAULT NULL,
'emai_alum' varchar(100) COLLATE utf8_unicode_ci DEFAULT NULL,
'carr_id' int(2) NOT NULL,
'seme_id' int(2) NOT NULL,
'pera_id' int(1) NOT NULL,
'peri_id' int(1) NOT NULL,
'capa_id' int(1) NOT NULL

PROJECT TABLE

CREATE TABLE 'proyecto' (
'proy_id' int(4) UNSIGNED NOT NULL,
'proy_deno' varchar(100) COLLATE utf8_unicode_ci NOT NULL,
'plan_proy' varchar(100) COLLATE utf8_unicode_ci NOT NULL,
'objg_proy' varchar(100) COLLATE utf8_unicode_ci NOT NULL,
'obje_proy' varchar(100) COLLATE utf8_unicode_ci NOT NULL,
'fech_insc' date NOT NULL,
'nomb_comu' varchar(50) COLLATE utf8_unicode_ci NOT NULL,
'resp_comu' varchar(50) COLLATE utf8_unicode_ci NOT NULL,
'parr_id' int(4) NOT NULL,
'deta' varchar(100) COLLATE utf8_unicode_ci NOT NULL,
'esta_proy_id' int(1) NOT NULL,
'telf_inst' varchar(11) COLLATE utf8_unicode_ci NOT NULL,
'telf_resp' varchar(11) COLLATE utf8_unicode_ci NOT NULL,
'obsv_proy' varchar(255) COLLATE utf8_unicode_ci NOT NULL,
'proy_carr_id' int(2) NOT NULL

TABLE PROJECT_ALUMNO

CREATE TABLE 'proyecto_alumno' (
'proy_alum_id' int(4) UNSIGNED NOT NULL,
'proy_id' int(5) UNSIGNED NOT NULL,
'alum_id' int(9) NOT NULL

RESULT OF CONSULTATION IN ENROLLING STUDENT

Warning: Missing argument 1 for bd_alumno_opciones(), called in     C:\xampp\htdocs\Sistema Automatizado de Registro y Control 2016\registro4.php on     line 37 and defined in C:\xampp\htdocs\Sistema Automatizado de Registro y     Control 2016\conexion.php on line 342
Notice: Undefined variable: proy_id_seleccionado in C:\xampp\htdocs\Sistema    Automatizado de Registro y Control 2016\conexion.php on line 347

DESIRED RESULT

BY CERTAIN APPLY THE FUNCTION OF: Eduardo Fuentes and now it shows what I want but keeps saying that a variable is missing.

The line of code that gives error is the function that is above

REGISTRATION FORM:

<?php
include 'conexion.php';
$proy_id_seleccionado= 0;
$alumno = bd_alumno_opciones();
$proyecto = bd_proyecto_opciones();
<form id="frmIns" class="form-horizontal" method="POST"   action="proc_inscripcion4.php" role="form">



        <select class="form-control" name="proyecto" id="proyectos">

        <?php foreach($proyecto as $i=>$proyecto_temp):?>
            <option value="<?=$i?>"><?=$proyecto_temp?></option>
        <?php endforeach; ?>
        </select>

    </div>
</div>

<div class="form-group">
    <div class="control-label col-lg-2"></div>
    <div class="col-lg-5">

        <input type="hidden" name="proy_id" id="proy_id" readonly  value="" />

    </div>
</div>



   <div class="form-group">
    <label for="alumno" class="col-lg-2 control-label"><font size=3 color="red">*</font>Alumnos:</label>
    <div class="col-lg-5">
        <?php foreach($alumno as $i=>$alumno_temp): ?>
        <div class="checkbox"><label>
        <input type="checkbox" name="alum[]" id="alum_<?=$i?>" value="<?=$i?>"> <?=$alumno_temp?></label></div>
        <?php endforeach; ?>
    </div>
</div>




<div class="form-group">
    <div class="col-lg-2"></div>
    <div class="col-lg-5">
        <button type="submit" class="btn btn-default">Guardar</button>
    </div>
</div>