Update all notes, update introduction

docs/index.md → index.md

-# Math for Quantum
+# Mathematics for Quantum Physics
 
-!!! summary "Learning goals"
+*Mathematics for Quantum Mechanics* gives you a compact introduction and review
+of the basic mathematical tools commonly used in quantum mechanics. Throughout
+the course, we keep quantum mechanics applications in mind, but at the
+core, this is still a mathematics course. For this reason, applying what you learned
+to examples and exercises is **crucial**!
+
+!!! tip "Learning goals"
 
     After following this course you will be able to:
 
@@ -8,20 +14,15 @@
     - solve mathematical problems encountered in the follow-up courses of the minor.
     - explain Hilbert spaces of (in)finite dimension. 
 
-*Mathematics for Quantum Mechanics* gives you a compact introduction and review
-of the basic mathematical tools commonly used in quantum mechanics. Throughout
-the course, we keep quantum mechanics applications in mind, but at the
-core, this is still a math course. For this reason, applying what you learned
-to examples and exercises is **crucial**!
 
-Each lecture note comes with an extensive set of exercises, and each exercise is labeled
-according to its difficulty:
+!!! note "Exercises"
+    Each lecture note comes with an extensive set of exercises, and each exercise is labeled according to its difficulty:
 
-- [:grinning:] easy
-- [:smirk:] intermediate
-- [:sweat:] difficult
+    - [:grinning:] easy
+    - [:smirk:] intermediate
+    - [:sweat:] difficult
 
-In these notes, our aim is to provide learning materials which are:
+With these notes, our aim is to provide learning materials which are:
 
 - self-contained
 - easy to modify and remix, so we provide the full source, including the code