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/package.json

@@ -0,0 +1,22 @@
+{
+  "name": "backend",
+  "version": "1.0.0",
+  "description": "",
+  "main": "src/index.js",
+  "type": "module",
+  "scripts": {
+    "start": "node src/index.js",
+    "dev": "node --watch src/index.js"
+  },
+  "keywords": [],
+  "author": "",
+  "license": "ISC",
+  "dependencies": {
+    "bcryptjs": "^3.0.3",
+    "cors": "^2.8.6",
+    "dotenv": "^17.4.1",
+    "express": "^5.2.1",
+    "jsonwebtoken": "^9.0.3",
+    "pg": "^8.20.0"
+  }
+}