Initial commit: Mathe-App Phase 1-3

- React+Vite Frontend mit Routing, eigenem fetch-Client (kein axios)
- Express Backend: Auth (JWT), Topics, Tasks, Leaderboard
- PostgreSQL Schema + Seed: 7 Kategorien, 21 Topics, ~25 Aufgaben
- Gamification: XP, Level (100×n^1.5), tägliche Streaks
- docker-compose auf Port 3100 für DS1621
- Alltagsaufgaben: Finanzen, Geometrie, Physik, Informatik, Verkehr, Shopping

backend/src/routes/topics.js

@@ -0,0 +1,60 @@
+import { Router } from 'express';
+import { requireAuth } from '../middleware/auth.js';
+import pool from '../db/index.js';
+
+const router = Router();
+
+// GET /api/topics — alle Kategorien mit Topics
+router.get('/', requireAuth, async (req, res) => {
+  try {
+    const cats = await pool.query(
+      'SELECT id, slug, title, icon FROM categories ORDER BY sort_order'
+    );
+    const topics = await pool.query(
+      `SELECT t.id, t.category_id, t.slug, t.title, t.description, t.difficulty, t.is_premium,
+              COUNT(tk.id) AS task_count
+       FROM topics t
+       LEFT JOIN tasks tk ON tk.topic_id = t.id
+       GROUP BY t.id
+       ORDER BY t.sort_order`
+    );
+
+    const result = cats.rows.map(cat => ({
+      ...cat,
+      topics: topics.rows.filter(t => t.category_id === cat.id),
+    }));
+
+    res.json(result);
+  } catch (err) {
+    console.error(err);
+    res.status(500).json({ message: 'Serverfehler' });
+  }
+});
+
+// GET /api/topics/:slug/tasks — Aufgaben eines Topics (mit Fortschritt)
+router.get('/:slug/tasks', requireAuth, async (req, res) => {
+  try {
+    const topic = await pool.query(
+      'SELECT * FROM topics WHERE slug = $1', [req.params.slug]
+    );
+    if (!topic.rows[0]) return res.status(404).json({ message: 'Topic nicht gefunden' });
+
+    const tasks = await pool.query(
+      `SELECT tk.id, tk.title, tk.question, tk.answer_type, tk.choices,
+              tk.unit, tk.xp_reward, tk.difficulty,
+              up.correct AS solved, up.solved_at
+       FROM tasks tk
+       LEFT JOIN user_progress up ON up.task_id = tk.id AND up.user_id = $1
+       WHERE tk.topic_id = $2
+       ORDER BY tk.difficulty, tk.id`,
+      [req.user.id, topic.rows[0].id]
+    );
+
+    res.json({ topic: topic.rows[0], tasks: tasks.rows });
+  } catch (err) {
+    console.error(err);
+    res.status(500).json({ message: 'Serverfehler' });
+  }
+});
+
+export default router;