School of Battle

Wizards who enter the School of Battle value value the power that comes with combining a brilliant mind with a honed body. Wizards of this school learn how to merge these two features together like no one else, augmenting their spellcasting with physical might and vice versa. The individuals who follow this school often come from veteran spellcasters who have learned how to utilize their experience and martial prowess to augment their spellcasting ability.

This school of wizardry has been developed by individuals who fought in the front lines for long periods of time, observing the rhythm of battle and learning from experience. Over the years they developed a unique style of fighting that combines all of their skills in devastating waves of magical energy that consume their foes. They are a match not only to the knights and opposing martial combatants, but can easily stand their own against other spellcasters and obliterate them with equal magical prowess.

Brains and Brawn

Starting at 2nd level when you choose this school, you learn how to augment your physical prowess with your spellcasting and vice versa. Your unarmed strikes count as a sufficient component for [spell]Green-Flame Blade[spell] and similar spells.
Additionally, when you expend a spell slot as a part of your action, you can make an unarmed strike as a bonus action.

Martial Resilience

Starting at 2nd level, years of battle experience have made you tougher and harder to take down. Your hit point maximum increases by 4 and increases by 1 again whenever you gain a wizard level.
In addition, you gain proficiency with light and medium armor.

Empowered Strikes

At 6th level, you learn how to fuel your physical strikes with magical energy. Your unarmed strikes count as magical for the purposes of overcoming resistance and immunity to non-magical attacks. Before you make an attack with your unarmed strike, you can choose to also expend a spell slot. If you do and you hit, your unarmed strike deals extra acid, cold, fire, lightning, or thunder damage. The extra damage is 1d6 for a 1-st level spell slot, plus an additional 1d6 for each spell level beyond the first.
When you use your this feature, if you use a 6th level spell slot or higher, roll an additional die per original die rolled(for a total of two dice per spell slot level), and increase the size of the area to 30 feet if you choose to use this feature. If you use a 9th level of spell slot, roll an additional die per original die rolled(for a total of three dice per spell slot level), and increase the size of the area to 60 feet.

Wizard's Riposte

Starting at 10th level, you learn how to utilize the force of your spells to fuel your speed and strength. Whenever you use your reaction to cast a spell, you can make a single unarmed strike as a part of the same reaction. You can use your Empowered Strikes feature with this unarmed strike as if you expended the spell slot used for the spell you cast with your reaction.

Mage Fist

From 14th level onwards, the unity of your martial and spellcasting proficiencies has reached its peak. Before you would make an unarmed strike using your Empowered Strikes feature, you can choose to release a powerful magical pulse. Instead of making an attack roll, all creatures in a 15ft cone make a Dexterity saving throw. On a failure, they take the full damage of your Empowered Strikes feature, on success, they take half damage. Additionally, if you use a 6th level spell slot or higher, roll  increase the size of the area to 30 feet if you choose to use this feature. If you use a 9th level of spell slot to 60 feet.
You can release a pulse a number of times equal to your intelligence modifier, and regain all uses upon finishing a long rest.