Step 1: Why transition metals vary.
Transition metals can show many oxidation states. This is because they can use both their outer s electrons and their inner d electrons in bonding.
Step 2: Find the highest state idea.
The highest oxidation state usually equals the total of the s and d valence electrons that can take part. So we count those electrons for each metal.
Step 3: Count for each metal.
Titanium has $4s^2 3d^2$, so up to 4 electrons, giving $+4$. Chromium has $4s^1 3d^5$, so up to 6 electrons, giving $+6$. Iron has $4s^2 3d^6$, but commonly reaches only about $+6$.
Step 4: Count for manganese.
Manganese has $4s^2 3d^5$. That is $2 + 5 = 7$ electrons that can take part, so it can reach $+7$.
Step 5: Compare the totals.
The highest values are Ti +4, Fe up to +6, Cr +6 and Mn +7. So manganese has the biggest value.
Step 6: Final choice.
Manganese reaches $+7$, as in $\text{KMnO}_4$. So it shows the highest oxidation state.\[ \boxed{\text{Mn } (+7)} \]