It is perfectly sensible for a wizard to focus his studies on the traditional schools of magic. After all, the fundamental underpinnings of each of those schools makes it easy to build from one concept to the next. The fundamentals of Necromancy apply all the way through from preserving bodies to raising the dead. The fundamentals of Divination apply whether you're predicting the next few moments or foretelling the doom of a nation. The simple truth however, is that sometimes it is more rewarding to twist and mold the work of those who came before to suit your needs.
Elemental Logicians fiddle with the fundamental nature of spells in many schools to create something that suits their needs. A wizard who lives in a baking desert, surrounded by horrible beasts that are immune to fire has no need for the commonly accepted writings on Fireball. However, with a little forethought and arcane tinkering... well those beasts will react a little differently to a glacial detonation.

Elemental Logic

At 2nd level, when adopting this tradition, choose acid, cold, fire, lightning, poison, or thunder damage. When you prepare your spells each morning you may choose to prepare any number of your spells that deal damage as altered versions using the chosen damage type. You may also make this alteration to spells that are 'always prepared' and cantrips. You may choose to prepare the same spell twice if you would like access to it with multiple damage types.

Acid

You may prepare your damage dealing spells as altered versions that deal Acid damage.

Fire

You may prepare your damage dealing spells as altered versions that deal Fire damage.

Force

You may prepare your damage dealing spells as altered versions that deal Force damage.

Ice

You may prepare your damage dealing spells as altered versions that deal Ice damage.

Lightning

You may prepare your damage dealing spells as altered versions that deal Lightning damage.

Necrotic

You may prepare your damage dealing spells as altered versions that deal Necrotic damage.

Poison

You may prepare your damage dealing spells as altered versions that deal Poison damage.

Psychic

You may prepare your damage dealing spells as altered versions that deal Psychic damage.

Radiant

You may prepare your damage dealing spells as altered versions that deal Radiant damage.

Thunder

You may prepare your damage dealing spells as altered versions that deal Thunder damage.

Elemental Experience

Starting at 2nd level, you gain resistance to the damage type chosen for Elemental Logic.

Potent Cantrips

Starting at 6th level, your damage dealing cantrips deal additional damage of your chosen type equal to your Intelligence modifier.

Elemental Snaring

At 10th level, your understanding of elemental energies allows you to snatch them from the air itself. When a ranged spell attack hits you, you can use your reaction to reduce the damage by 1d10 + your Intelligence modifier, provided that you have a free hand. If you reduce the damage to 0, you can catch and redirect the spell's energy. Make a ranged spell attack against a target within 60 feet, dealing 1d10 damage of your chosen type. If the triggering attack was of your chosen damage type, you instead deal 2d10 damage.
You may use this feature a number of times equal to your Intelligence modifier, you regain all expended uses after a long rest.

Abstract Elemental Theory

At 14th level, you may choose an additional damage type for Elemental Logic. You may choose acid, cold, fire, lightning, poison, thunder, necrotic, radiant, force or psychic damage. When preparing spells you may choose either or both damage types to apply to an altered spell. If both is chosen then damage is calculate as normal then split equally between damage types, rounding down, before determining resistances, immunities and vulnerabilities.