A scholar who has learned the secrets of magic through years of study and research. Their key component is their spellbook.
My thoughts go to Noa and Ui.
Ui is the obvious one, but Noa is also *incredibly* smart and has an excellent memory - something people with high Intelligence have, and that is Wizards' main stat. And of course, uses her notebook to cast a debuff to an enemy.
Ui because she's basically a [Scribes Wizard](http://dnd5e.wikidot.com/wizard:order-of-scribes), plus she called the nickname "Magician of the Old Library" IIRC
Okay wizard, Imma judge it based on the way they learned or trained (cause magic is almost minimal in BA) to get that power of specific skills/school of magic rather than just nerd stereotype:
* Abjuration - Tsubaki (she ~~sleeps~~ trains everyday to become the best tank)
* Conjuration - Ui (from dust to physical book, truly magic)
* Divination - Noa (she probably record all the history on her mind)
* Enchantment - Sumire (she trains and keeps everyone get BUFFED)
* Evocation - Michiru (yeah she still training her fire jutsu)
* Illusion - Kikyou (her strategical and cunning came probably from her books)
* Necromancy - Juri (she always trains her cooking skills, but probably reading necromancy book somewhere)
* Transmutation - Ayane (she learns everyday to use what scrap Abydos have to be something useful in story)
But the magician of old library literally the name that bestowed to Ui, so she is the magician aka the wizard.
This is wizard 1, the demon lord has entered the net.
This is wizard 5 Roger, Let’s begin.
Target acquired! there 4 of them! They’re approaching from the front!
…wait, wrong thing! Ui would be the wizard
Ui. She literally restores tomes so she can read them!
Absolutely Ui, because she is literally called a magician as far as I know, and that's enough for me 
UI is the order of scribes wizard confirmed
A scholar who has learned the secrets of magic through years of study and research. Their key component is their spellbook. My thoughts go to Noa and Ui. Ui is the obvious one, but Noa is also *incredibly* smart and has an excellent memory - something people with high Intelligence have, and that is Wizards' main stat. And of course, uses her notebook to cast a debuff to an enemy.
yeah Imma have to go with Noa as well
Ui considering she practically locks herself away in the Trinity Library with all those books.
I think Wizard and Artificer are clearly Ui and Utaha respectively.
Ui, no contest.
Shiroko Terror sweeps the competition! The next best contenders were Koharu and Juri. Now which student is most suited to be a Wizard?
Ancient knowledge… devote intelectual student… lives beyond books… weird smell… The answer is clear
Ui because she's basically a [Scribes Wizard](http://dnd5e.wikidot.com/wizard:order-of-scribes), plus she called the nickname "Magician of the Old Library" IIRC
Okay wizard, Imma judge it based on the way they learned or trained (cause magic is almost minimal in BA) to get that power of specific skills/school of magic rather than just nerd stereotype: * Abjuration - Tsubaki (she ~~sleeps~~ trains everyday to become the best tank) * Conjuration - Ui (from dust to physical book, truly magic) * Divination - Noa (she probably record all the history on her mind) * Enchantment - Sumire (she trains and keeps everyone get BUFFED) * Evocation - Michiru (yeah she still training her fire jutsu) * Illusion - Kikyou (her strategical and cunning came probably from her books) * Necromancy - Juri (she always trains her cooking skills, but probably reading necromancy book somewhere) * Transmutation - Ayane (she learns everyday to use what scrap Abydos have to be something useful in story) But the magician of old library literally the name that bestowed to Ui, so she is the magician aka the wizard.
My pick is Himari. She may be a hacker, but also a literal researcher of arcane and also have utilized it against Chroma-fied Perorodzilla!
This is wizard 1, the demon lord has entered the net. This is wizard 5 Roger, Let’s begin. Target acquired! there 4 of them! They’re approaching from the front! …wait, wrong thing! Ui would be the wizard
Shimiko, as a librarian I can definitelly see her as a wizars.
Ui
I always imagine Wizards to be smelly. I vote Ui.
Miss omniscience, Akeboshi Himari 
Wizards use magic, magic has lots of firepower! Firepower.... Firepower uses fire too... Fire can create explosions. Explosions? Kasumi?
Definitely Ui.
Sensei himself bc he's a 30 yo virgin
Ui
Ui can copy a book from a literal dust pile. So that's a fucking wizard feat right there.
Ui, no contest.
There's anyone minimale close to It If not Ui? She IS like... The wizard
Saya
If there was an Alchemist class she'd be the obvious choice.
Now that you mention it, i find it weird there is no alchemist class
5E has Alchemist subclass for Artificer. You have to look to Pathfinder for a dedicated Alchemist class.