No quibbles here -- this was my assumption, and the reason I didn't include this stuff.
I beg to disagree. If you know latin and basics of Artes Liberales, then MT 3 requires just one season of study with a commonplace primer.
Good points here, but I think I'd allow Exposure for at least some of these, so you'd be pretty much bound to have at least 1 in most of these
without actually spending a season.
Cheers,
--d
Remember that magic theory is an ability and they take more work than arts to increase...
level--exp
1--5
2--15
3--30
since you need a high ability level to write a good book, the 5/15 style books (as you can find in arts) will be less available, so you'll need more time...
so:
is correct (assuming that isn't started before opening the arts)
My bad, I misread the table in a rush. In any case, L 3 Q 15 book is still a vain book, and gets you to 2 in one season and 3 in two.
Cheers,
--d
Also, remember that there are penalties to a character's Attributes, including Intellegence, based on their age. It is very likely that for the first few years that the negative modifier along with a low Magic Theory can make an apprentice a hinderance rather than a benefit in the laboratory.
I have also considered a house rule to apply the age modifier to study totals (for reading and maybe teaching) to prevent seven year olds from getting huge advancements from reading books.
Something I wanted to point out with respect to the Roots of the Arts is that, if one is using the book rules from Covenants, part of the points of the Roots is that they are generally quickly copied. Part of what I take from that is that copies of the roots practically never use resonant materials (e.g. are ex libris); as a result, even with proficient book workers, they would be based on Com + bonuses + 3, not + 6. We might even conclude that they are closer to juvenilia, and thus would not get the illumination nor binder bonuses, and could be Com + bonuses + 0/1.
Q15, L8 is an interesting breakpoint, because at that stage, two seasons of study is efficient (assuming not reader bonuses). If we assume all the above, and that Quality can only be doubled via level reduction (even though it's not in the online errata, I have always figured the Covenants "double bonus" phrasing was a mistake), that implies that Com + bonus is at least 7, so we'd be talking about a naturally impressive writer, in addition to having the art in question at around level 30.
So, based on that thought, I've made the roots in my covenant all hang around the Q15, L8 range. I varied it slightly... one or two are L9, one is L7, I think I gave one Q16...
Q15, L5 felt a little too silly to me, in part due to the fact that fast readers would find such a book under-fulfilling, and in part because the +5 Com Good Writer who writes stuff like this probably has at least one Art he's got a 20 in. 
As for which Arts are covered... I think the natural side effect of the division between forms and techniques is that techniques are more valued in the order... the vis exchange rules imply that this isn't just a meta-game analysis... this is how the order views it, as well. As a result, I assume that all five of the Techniques are both Rooted and Branched. From there, I think about which Techniques are likely to have had a specialist author who was a good communicator. Vi, Ig, Im strike me as likely. (Everybody needs a Vi artist for the Aegis, Flambeau builds fire specialists, and the 5th ed Jerbiton seem the most likely to be great communicators, and they seem to have a taste for Im.) Of course, given how rare such a great writer is (YMMV depending on how common you think +5 scores ought to be), what they happened to specialize in could be just about anything.
I wanted to toss in my two shillings about min-maxing apprentices.
There's a general tendency to assume that would-be apprentices get trained in useful skills before starting their apprenticeship. And there is RAW support stating that magi do often do this sort of thing. On the other hand, on p.63, under Academic (and Arcane) Abilities, it's stated that without a virtue allowing otherwise, such skills can only be bought "during or after apprenticeship". That, combined with the fact that one isn't an apprentice until their arts are opened, could certainly be interpreted by a SG in a strict way, which would slightly curtail apprentice power-gaming.
Ignoring 1), I think it's often ignored how many points go into the covenants assumed in the earlier apprentice examples. Having a Q15, L5 book in each art costs 300 build points. You need a trainer to do that initial pre-apprentice Latin training , unless you've got some generous fellow magi... let's min-max and have him know both Latin and Artes Liberales at 5, since then we don't have to pay points for the AL... that's still an 11 point teacher. Another 24 goes into that Q15, L3 MT book. So now we've got 335 build points stashed away in stuff that is pretty much only useful to apprentices (since, if you're training 'em, you've moved past Latin 4, MT 3, and Arts < 6). In other words, you've definitely not a low-powered covenant, and if that's just your apprentice stuff, before counting vis stocks, "real" books, laboratories, I'm willing to bet you're not a medium-powered covenant, either.
If you use your apprentice in the lab for half the year, he reads an arts book one season each year to get each art to 5, he uses 2 of the remaining 15 seasons to get MT 3... 1 season for PM, and gets his spell levels from the other 12 seasons:
a) Your apprentice has zilch in arcane abilities. (And even if we assume you can teach your apprentice Academic abilities before their arts are opened, I'd be way harder to convince that you can teach them Penetration before you've opened their arts.)
b) Your apprentice has no scribal skills. Oh, you had your impressive trainer teach him that, too? Just how many years did you keep this kid sitting around in the classroom before you opened him, and how many tutors does your covenant keep around?
c) You're just not using your apprentice right, in my view. On those seasons when I, as a magus, am not doing lab work and am not training my apprentice, that doesn't mean he gets to go read whatever he wants. Pshaw! I've got lab texts I've borrowed from some magus... someone needs to translate them from the owning magus' chicken scratch, and that's not something you can hand off to the covenant scribe. And, if I'm not using my lab, and my apprentice is familiar with it, this sounds like the perfect time for him/her to increase the covenant's vim vis stocks. And, speaking of vis, guess who's learning those various vis-finding and vis-moving spells so that I don't have to go deal with that darn vis source that requires sucking small amounts of vis out over the course of a week? No more wasting my time with such minutae!
To conclude, while I agree that the rules allow an apprentice to end up far more powerful if run manually rather than using the fast generation rules, I'd argue that such apprentices tend to require access to a relatively powerful covenant, in terms of books, tutors, and/or magi generous with their time, and a parens who allows their apprentice an unexpected amount of free time.
We have used Int mod as a per year modifier to XP gain, with the placing forced to be as flat as possible, ie a PC with +4 would get +1XP per season, a +5 would get +1 3 seasons and +2 a single season. Negative values working the same.
Applying it per season was tried shortly and totally rejected because it was just waaaaay to powerful or terrible depending on positive or negative score. Per year however works nicely.
Well, in the campaign that stayed closest to RAW, we still had several magi with art scores in the 70s even a few higher still.
In short meaning that the restrictions on books during creation was totally whacked at the end, try figuring a Com+5 PC with lets be nasty and say an art score of 85 together with a +6 bonus and a +3 bonus from Good Teacher... 
Now think of the "primer" that can be written by such a PC in just a couple of seasons.
Oh and Edit, since i almost forgot, due to it simply being impossible to end up with art scores like those you often get by creating a PC rather than playing the PC into being(you simple wont EVER get even a single score of "1" and scores of "2" is almost as difficult to get), we use a simple D6-1 roll for each art when the arts are opened, or you can choose to give 2 each of score 0,1,2,3,4,5 and another 1 each of 1,2,3 totalling 80 XP and ending up slightly below the expected average from rolling the die and allowing specialisation before training any arts meaning even an apprentice can start out being better or worse in different arts.
We have found this method to be VERY good and not really unbalancing since 80XP can be gained in just a year or two with barely decent to good sources. And also producing those darned low art scores that you simply cannot get if you playcreate apprentices, either they had a zero or they had 4 or better(rarely a 3 and usually 5 or better).
I think the "pre training of apprentices" thing is vastly overstated, as suggested by others above. The most important thing to realize is that the Gifted child is simply NOT yours until you open his arts. Any other magus who wants an apprentice more than they want to be friends with you can just take the child and train him or her and you are SOL. Isn't there an example ruling about a maga who lost her biological child to someone else this way? I can't recall if that was in a rule book or someone's saga notes 
Secondly, its potentially very expensive to maintain the wide range of scholars needed to properly pre-train a Hermetic apprentice. Learning to speak and read Latin is a definite chore. What are these scholars doing during all the years the covenant doesn't have any apprentices needing tutoring?
Perhaps most importantly, most magi are probably not specifically interested in maximizing their apprentices' stats as a primary goal. There also seems to be an assumption the apprentice is a highly motivated student who can be left to his own devices and will actually study if so. Or does the covenant also have 'apprentice minders' to make sure they are studying properly and not running with the grogs' kids or getting 'lost in the barn' with a serving maid or dashing warrior, as appropriate?
The rule on training of one season per year is in place specifically because less training than that was proving to be unduly common. There's just too many useful things for an apprentice to be doing besides 'getting a free education'. Its all about work-study. There aren't many free rides. A senior magus usually has a pretty specific reason why he's throwing a quarter of his research time away on training some snot nosed brat. In a few cases it will be some sort of self sacrificing paternal instinct, but generally its blatant self interest.
I just want to comment on the repeated idea that a Parens might lose his apprentice to another person if he has not opened the arts but has the apprentice learning latin, etc.
I dont see it as a serious problem. I assume that aside from the occasional redcap, most covenants are not brimming with hermetic guests. Most magi will not have any idea what your are teaching your apprentice let alone whether or not his arts have been opened. this is especially true if you dont bring your apprentice out to tribunals or other covenants prior to opening the arts.
Well that leaves outsiders irrelevant. thus the real threat to losing your apprentice seems most likely to be from others in your covenant. I would assume that most covenants are cordial enough such that they dont go stealing one anothers apprentices prior to the opening of arts. Sure some will be like that, but I doubt most would be.
Anyway, if your a bonisagus then the only person you have to fear taking your apprentice is a more powerful bonisagus.
No, its not a very likely occurence. But it is a risk you are taking unnecessarily. Its obviously something that has happened, because there are tribunal rulings on it. So I suspect that most wizards are not going to risk losing "their" apprentice to a surprise guest or a rival magus just to give the kid a head start on Latin.
Maybe if its a covenant that schools all the children or is in some way involved with a cathedral school or other educational endeavor. But I don't see very many magi or covenants over all taking on that expense and risk without a more compelling reason than has been provided.
Erm... tries to fathom Assuming they started at L20, no summae is likely to help them. I suppose if they had a friend who also happen to have Com 5 who liked the same art, they could share tractatus at Q10... but that only gets them 10 tractati between L20 and L70, a period in which they require 2275XP. Assuming they spent 3 seasons a year (so, no going and finding a familiar, no apprentice, no adventuring, no writing, no spell learning, etc, etc) and average that Q10 each season, they'd need almost 76 years of nothing but working that art to manage that level. And, if they do vis studying for it, they'll need more than a half-rook each season after the first few. So some combination of queens of vis and dozens upon dozens of high-quality tractati... well, suffice to say that, to my sensibilities, this sounds like a highly overpowered game.... via vis alone we'd be talking approximately 2275 pawns (I won't do the rigorous math right now, since it'd have to take into account the stress die and the interaction of low/high rolls on overall vis needed at any point, but it should be approximately a roll of 10 with approximately 10 pawns needed per level), which is 455 covenant build points; with tractati alone, it'd need 227.5 Q10 tractati, which is 2,275 build points. (Yes, I'm ignoring the handy virtues right now, because it's late. Cut those numbers in half and I'd still call them high, especially if you had different magi each with a 70 in a different art, thus meaning you need multiple piles of vis/books.)
In any case, most of those levels are gratuitous for purposes of writing a summae primer. Let's say your Com +5, Good Teacher, Art 85 PC wants to write the best Lvl 5 summae he can according to the basic 5th ed core rules. His base quality is 14; he can get it to 22 by subtracting 8 levels. Ergo, he needs to start at a Lvl 13 book, which means he needs an art score of 26. Yes, your overpowered magus can write a Q22 L34 summa (in a year), but he and Smooth Talking Specialist ex Jerbiton can both bang out a primer in a season even though you can spont spells in the topic without fatiguing yourself that he has to have a lab text to even think about. (I suppose the existence of a Q22, L34 summa in your saga would then allow your magi to get to their level 85 state faster. But, of course, that means that last generation, there was another Com +5 Good Teaching Art 85 magus with the same specialty as him, who either had the impressive resources listed above, or a slightly smaller resource pile and a preceeding Com +5 Good Te... well, you get the idea.)
But, certainly, in a campaign where +5 Com, Good Teaching magi with arts in the 70s-80s who then stop to write books in their twilight years cannot be counted on zero hands, you end up with an Order of Hermes that simply doesn't make much sense given the character creation and covenant creation guidelines as present in the RAW.
That's a reasonable house rule, but I would argue your assumption. My current Bonisagus gets 1XP in his arts all the time. Exposure, secondary insight, story experience, elemetnalist... these are all things that tend to lead to smaller arts bumps than your stereotypical "read a Q15 book". Given the power levels you appear to be playing at, I am not surprised that your characters tend not to be in situations where they would have any desire or reason to invest small amounts of experience into their arts.
EDIT: I'd also note that this is one of the reasons I like the Covenants rules; instead of just automatically getting those nice bonuses to quality to your writing, they are half a matter of covenant investment (in handy book employees), and half a matter of interesting story (for resonant materials, not to mention the potential for implanting vis in the book and then fearing it ever leaving a magical aura).
I think one of the (unfortunate) tendencies in AM sagas, which is really just an example of role-playing general tendencies, is that parties (in this case, covenants) are preternaturally cooperative. The majority of canonical covenants involve internal strife. The general description of Winter covenants tends to involve old, half-insane wizards and the put-upon, shut-off-from-power new blood.
Apprentices are a resource that is dwindling in Mythic Europe. Gifted individuals are becoming harder to find. If someone in my covenant finds one, and then decides to sit on him/her for five years because they don't want to teach the child how to use magic until he can spout Virgil and make his own laboratory, that's just greedy hording of resources. And their house is funny, anyhow. The child would obviously be better trained by me. And I could use an extra hand around here, and if my soldales wants to be overly-perfectionistic... well, the law's on my side if I open the kid's arts now.
At the least, the threat of that should be in a potential parens head. If it isn't, then, in my view, you have a hippie commune, rather than a covenant. 
Ok, I have to admit, I was definitely ignoring autumn and winter covenants which can be hyper political. Really, I was assuming the situation in the context of a weak and new sprin covenant. I think that in situation magi must be fairly cooperative: at least for a while. 4-6 hermetic newbs all alone in big scary ME are not likely to screw each other over apprentices. But in oterwise older and more stable covenants magi may not have external pressures to keep them friendly an cooperative and hence screw each other and apprentices.
Yes, weak spring covenants tend to be more cooperative (or they don't survive). But then they don't have the resources to keep professional scribes, teachers, librarians, and all the rest that goes along with "pre training" apprentices.
In our game, set in Stonehenge, the ranking Bonisagus in the area is a woman who is interested in the development of the Gift in apprentices. She has trained something like 20ish magi, and has that "Granny-bear" reputation. However, her covenant is a pack of bloodthirsty psychopaths, (Ungulus) and so when she shows up for a "visit," you don't leave her waiting outside, and you don't give her a hard time when she asks why you think you should be training an apprentice.
An apprentice is the hermetic equivalent of a child...there's something to be said about taking an apprentice either too early or before you've made the appropriate preparations for that apprentice's education. Personally, I think probably 10 years out of Gauntlet is the earliest one should consider taking an apprentice.
-Ben.
Its the only game sofar going THAT high for sure. But it was also quite exceptional and nonstandard.
Thing is it started out with a number of apprentices to a less than liked faction of old magi of a really BIG old autumn covenant(biggest we ever played sofar), to cut things short, to forestall a "civil war" within the covenant the player faction leaves and uses the mundane connection of one of the apprentices to get themselves a nice comfy "little" fortress, and in doing so, one of their parens also brings his sizeable private share of the old covenants library with him.
So, the covenant starts out with 4 old magi with no art below 20 and several above 30 and some above 40, and IIRC 8 young magi, with many PCs having the "Good Teacher", "Apt Student" or "Book Learner" virtues, several with 4 or 5 in Com and a vauge goal of getting uber powerful(due to vauge and inadequate visions of the mongol hordes incoming, merely making sure everyone knows a bigtime military threat is enroute) with perfect cooperation and with one of the PCs being the lady of the castle making certain that mundane problems wasnt a too big deal(250 grogs(and if really needed the village militia adding to that) can solve alot of problems very well, especially when supported by a magi or 2 )...
And it was more like a hundred years of powerplaying.
All magi was constantly involved in correspondence of course, that alone makes for around 400XP if we say it was 100 years exactly. Also dont forget the usefulness of Commentaries or Florilegia made by masters or the fact that they brought a "small" library with them from the start(and "small" in this case is only compared to the huge covenant they originated from, as it included a huge collection, much of which had been assembled or written during the previous play where the 4 current parens were the main PCs) and with the "librarian" also having IIRC a score of 11 in Teaching from the start.
I think there was at least 6-10 Tractatus on every art even from the start...
As the new covenant was created through play, no accounting was ever tried.
Only needs to be one of those writing the book ONCE, ever. After that its going to be one of those "to die for" items (literally most likely since this involves trying to get it from magi not interested in letting it go)...
The point being that the RAW restrictions are very questionable and especially the "Exceptional Book" boon from Covenants becomes ridiculous to pick as a Major Boon, because really, its not THAT terribly hard to achieve something better if you really try.
So even if they´re likely to be rare, really SUPERB books will be in existance.
Indeed yes.
Which is why rules tends to get bent.
Oh no, the above one was an exception, its not unheard of with 70+ art levels in the other campaigns we have played, but its also not something normal, or even uncommon, although 40+ tend to be fairly common and 50+ are not that really impossible as long as there is some decent cooperation within a covenant.
Hmm? Of course they want those extra XP! 
lets say a magi has Int 4, that combined with constant correspondence means getting 8XP extra per year, it makes a difference for sure.
Certainly, but having run some "internal fighting"/politicking games(too a large extent the "parent game" of the above highpowered one was a very infighting one) it usually ends up either with cooperation by force, a split(like the powergame began) or total annihilation.
Okaaaaay...
Methinks that here lies the "problem" 
But, well, as long as you all had fun
Dont forget, or if you missed it, that those 4 old magi were all previous main PCs, we basically continued the earlier campaign by letting them step back and just be "supporting characters".
That combined with the "new generation" having played through their apprenticeships, well you know how much better chars you can get from that even with fairly lowend playing, and here we had a really nasty and powerful covenant and with parens all hypersupportive about getting the best possible apprentices they ever could(and the rest of the covenant totally hating them for it)... 8)
However you might want to realise one "little thing", and that is that their leaving the old covenant only avoided open fullscale warfare, the old grudges were still there and the old covenant still wanted to erase these noobs and their parens from the face of the earth, piss on their graves and then annihilate every last piece or memory of them ever existing.
The occasional feuding that followed(whenever enough magi in the old place remembered about it... ) might be called "epic" in scale.
We have tried to keep things a LITTLE less extreme since, while it was certainly a fun game, it got a BIT crazy sometimes.
Being able of doing non-fatigueing spontaneous spells above lvl 20 and fatigueing at up to the limit for non-ritual spells, i guess you can figure out that caused some problems for SGs?