Things to do

Montréal is a wonderful city to visit (and also in which to live). The weather in October might not be the best, but don't let that get in the way. For those who are staying more than a week, here are some ideas to keep you occupied during those very rare moments when mathematics just isn't enough.

Visit l'Oratoire Saint-Joseph du Mont-Royal. It's very close to the CRM, makes for impressive photographs and, with a bit of climbing, you'll get some pretty good views.
Take some time to climb to the Parc du Mont-Royal. Early October is a great time to catch the changing colours and there are literally thousands of (often unmarked) paths to explore through the lush maple forests.
A standard tourist outing involves the Biosphere, a giant environmental museum enclosed in a great big buckyball structure. Even if you don't want to pay to see the exhibits, it still makes for great photos. This shouldn't be confused with the Biodome, which is a bit like a zoo and a bit like an aquarium featuring canadian fauna... and penguins (because everyone loves penguins). Excellent, especially for penguin lovers. The otters are great fun too, as I recall.
In the north-east, just next to the Biodome, stands the Parc Olympique, testament to how holding an olympic games can bankrupt your city. I believe that it took the Montréalais 30 years of special taxes to pay off the debt. Anyway, the stadium isn't my cup of tea, but the story is eye-opening. There's a botanical garden nearby too, though you have to pay!, and an insectorium if you like that kind of thing!
And of course, there is the Vieux Port. Very touristic, but very photogenic. Worth a gander... once.
Are there museums and art galleries? Mais, oui! I'm not much for art, but my favourite is le Musée des Beaux-Arts. Let me know if you find something even better!
Montréal has two main markets, one in Atwater and one in Jean Talon, both very close to metro stations. I personally prefer the latter, though it contracts significantly in the colder months. But, there should still be plenty of locally grown apples, tomatoes, pumpkins (of course) and maybe even the last of the truly excellent corn. You might find some quality local cheeses (le migneron and pied de vent are worth your time), plenty of excellent meats and even some awesome mexican food. And little Italy is next to Jean Talon (and little Portugal isn't too far away either).
More importantly, you might get some maple syrup vendors at the markets --- Québec produces 90% of the world's supply and what you buy here is infinitely better than what you'll find elsewhere, even in Anglo-Canada. But, avoid the tourist stuff in glass: the real stuff comes in a round pint tin. My advice is to get the ambré or (if you can find it) foncé grades (the lower grades are much tastier). You can also buy it cheaply in supermarkets and pharmacies, but the markets have the really good stuff.
In Montréal, the coolest parts are generally where the french and english communities overlap. One such is Le Plateau, easily accessible by metro. Full of places to eat, drink and generally have fun. Another interesting area is Mile End / Outremont which also features jewish communities. Be on the lookout for street art whenever strolling around the suburbs of Montréal.
Try the infamous smoked meat sandwiches at Schwarz's or (Leonard Cohen's favourite) the Main Deli Steakhouse (or indeed many other establishments). You may have to queue up at the more famous ones...
Buy bagels fresh from the wood-fired ovens at Fairmount or St Viateur, both in Mile End. Which are better? That's asking for trouble. The only thing that's certain is that they're both better than anything you can find in New York (yuk!). Fact of the day: William Shatner was born in Mile End...
For the chocaholics among you (you know who you are!), camp out at Juliette et Chocolat. You'll probably see my wife there... Another excellent place for sweet pastries (and excellent baguettes) is Mamie Clafoutis. Try an "oh mon dieu" if you dare.
I can confirm that Bilboquet hasn't closed for the winter. It's a great place for top-quality ice cream and ice cream cakes. And it's never too cold for excellent ice cream!
How could I wax lyrical about Montréal food without mentioning Québec's favourite heart-attack-inducing snack: poutine. There are so many varieties these days and you can find it pretty much everywhere (with extraordinarily variable quality). The classique is chips, chicken gravy and a terrible local curd cheese that tastes like elastic bands... appetising no? But, you gotta try it!
For those not afraid of driving, an easy day trip will take you to Parc National du Mont-Tremblant. There won't be earthquakes, just lots of pretty forests with (hopefully) awesome autumn colours. There may also be rivers and a waterfall or two; sometimes you will see some animals (go early and be quiet!).
Apples are a big thing in the countryside around Montréal. If you have a car, October is a great time to pick your own. More importantly, many of those apples are destined to become delicious cidres and most cidreries have a "cellar door" where you can buy (and sometimes try before you buy). Around Rougemont, there is Michel Jodoin and Cidrerie Milton (but there are many many others). A speciality of Québec is cidre de glace (ice cidre) in which the apples are left on the tree all winter long to slowly concentrate the juice and the flavour. These sweet dessert liqueurs may be bought at the cidreries, at the markets or at SAQ stores. If you happen to find a bottle of Michel Jodoin's rose "Fine Caroline" or "Nos pommes tombées dans le vermouth", feel free to buy it for me!
Finally, if you're staying for a while, I strongly recommend a weekend in Québec City, aka Québec. Around three hours by car or bus, and a little longer by train, it is an extremely beautiful city with its original city wall still intact. From the Gare du Palais to the Château Frontenac, from les Plaines d'Abraham to l'Île d'Orléans, from la Chute Montmorency to les Chutes-de-la-Chaudière, you'll have a lot to see and do. Even Vieux-Québec is beautiful in its own touristic way! And then there's the Parc National de la Jacques-Cartier (see photo above) and all the other amazing nature around. Moi, je l'aime... l'adore!