Originally Posted by Mowicz

As for the "Tips for Success" I meant specifically as it would pertain to that course, or math in general. The welcome week events are more general if I understand correctly.

(Would you find it weird if I turned out to be TAing 1X03 or 1B03? Haha)

OH. okay. I guess it couldn't hurt to learn more 'tips to success'.

It wouldn't be weird! It would be kind of cool! I'll look out for you and come say hello if I get ya!

I would reiterate that a light and fluffy first class with info about you a little to help the class connect and feel more relaxed.

I'll also suggest this option, you may want to run it by your class and it depends on time but in my physics class the TA had us e-mail any questions we wanted to go over to him at least a day ahead.
this is good cause it lets you see if the class is having issues with one particular area, prepare ahead of time (thereby appearing more on top and cutting time taken) and time manage for how many questions you can cover during the time you have.
I found that more helpful than re lecturing but that is dependent on the Prof and the class.

The best TA I ever had also really used WebCT to connect with the students so that may or may not work with math but its worth a thought.

In my last semester of highschool, I had an amazing Physics teacher who wrote part of the Grade 12 Physics textbook and I was hardpressed to find even one student who didn't like him or absorbed what he taught. I'll relay some of the strategies he used and answer your questions one by one

Even though this is university math and we could say that "If you can't do it, you wouldn't be here", this is not necessarily true. Several students who didn't anticipate taking math have been thrust into it due to their program choices and not all of us are brilliant.

He made it quite clear at the beginning of our Physics course that we didn't know what Physics was and we hadn't begun breaching the surface to understanding Math. This sounds devastating and as though it would take a real shot of self esteem off us but it did the opposite. This was because, while on one hand he was informing us that we knew nothing, he was also telling us that we didn't need to know everything to do well...we had to work hard and listen, ask questions and do the assigned problems and challenge ourselves.

He never babied us.

The effect of this tactic was wonderful. It instantly pegged down those students who breathe math and consider their peers inferior for asking uncommon questions, while giving students like myself who enjoy math but struggle with it a boost of confidence that we were all in the same boat and I could do well.

He was very upfront and honest about the realities of our knowledge, explaining everything over and over again and answering even the so called "dumb questions".

The way he taught was to assign several difficult problems, and he explained that homework was not to reiterate our strengths but to challenge us and that if he assigned the hardest questions we would think more and we'd all be forced to come back and ask him good questions; even the geniuses.
Then he'd go over the problems slowly and while I'm sure it wasn't his intent to spend 50% of class time going through even the simplest problem, that's what happened.
It was a bit redundant at times but in terms of academics, it was great because it reinforced the foundations of the topic he was teaching us and I think that's a wonderful occurence.

He would also make up "tricky" problems and show us how they were really simple and pick questions that he felt he'd put on tests and walk us through how to navigate them.
He changed them for tests but we still weren't caught off guard


Question 1: Would it be beneficial for me to set aside the entire first tutorial to give some tips for success? I was thinking of discussing relevant strategies for test writing, studying, and the 'attitude' one should have toward their practice problems. And of course, perhaps some comforting stories of my own struggles.

I like Danielle's idea of a handout here You could also suggest that people email you (love the idea of an email but please respond I did Calculus and Vectors online and my teacher would take 2 days to answer his emails. 2 days was like 4 due to the intense pace we were proceeding at) if they want more ideas for how to succeed. If you wanted to have a 5 minute introduction on how to succeed in Math specifically, that would be better because it would be tailored to the tutorial and people wouldn't tune out if they'd been to previous "First Year Success" sessions.
Your proposal sounds great because it is relevant to Math and not just "go to class. Talk to the professor." but you may want to pack in more during your first day so again, email, handout and a brief overview should be spectacular


Question 2a: Should I allow some tutorial time for homework problems?

Yes.

Question 2b: If you answered "Yes" to 2a, should I answer students' specific homework problems (up on the board) during this 'homework time?'

Again I would suggest like Maryanne before me that you ask students who have "easier" questions to email you and take up the most difficult questions or the easier questions that incorporate challenging or tricky concepts.

Question 3: Would you like to have your TA reiterate the lecture ideas? What I did in my past tutorials, was teach a little mini-lecture, quickly covering the ideas presented in the past week (or two sometimes) of lectures.

You could always email this to them and just have a summary up on the board with the key topics.

Let's say the lecture covered addition, subtraction, multiplication, you could email a brief:
Addition is the sum of two or more parts.


Question 4: Do you enjoy hearing about the TA during the first lecture? Like, what they're studying, where they attended school, etc.

Yes More humanizing I'm sure they'll like hearing you were an undergrad at Mac (unless I'm wrong; I think you were) and realise that the university offers a great deal of potential and entices people to stay

(My teacher btw was Charles Stewart who graduated from McMaster )

PLEASE TA Stats 1L03 and Math 1A03

I found that in my previous math tutorials (1A03 and 1AA3...I'm taking 1B03 correspondence from Laurentian, so there are no tutorials for it), it seemed to basically involve me speedcopying notes from the board. Yes, examples are useful, but for me, I gained nothing from speedcopying. I think that examples are an excellent tool, but they should be used to demonstrate specific concepts, and instead of speedwriting 30 questions in an hour, it would be much better to do 10 questions and have them fully explained. And in this, you can do the minilecture thing, either by minilecturing first and then doing a handful of questions that emphasize certain points from the minilecture, or by incorporating examples into the minilecture.
And explaining concepts is key. Sometimes students need to hear something more than one way before they are able to understand it.

And mowicz, this is unrelated, but I was wondering if you could tell me anything about MATH 2C03, and Dr. Yazdani (I'm assuming it's Dr.)

Originally Posted by Kareko

I'll also suggest this option, you may want to run it by your class and it depends on time but in my physics class the TA had us e-mail any questions we wanted to go over to him at least a day ahead.

It's funny because that's kind of a 'sneaky move' in my opinion. xD

In math (I'd imagine physics is similar enough) we're supposed to prepare by doing the same homework assignments that the students do beforehand, to make sure we're ready to answer it 'on the spot.' It strikes me that this is a way to get out of doing the easier, redundant work, haha.

But no, maybe I'm just cynical. I can see a number of positive things about the email approach...the students feel more connected to the TA, they're more inclined to do their homework before the tutorial, and I can 'plan a strategy' for which questions to do and how to comment on them. It's also good to avoid some of the unnecessary work should there ever be time pressures on my schedule...but I'd hate to get into a bad habit or something.

Thanks for the suggestion (:

EDIT: For everyone else, I'll respond to your posts in an hour or so, I have to grab some dinner. Thanks in advance!

If you're my TA I can loudly yell that I know you from MacInsiders and feel really cool

Originally Posted by Mowicz

As a student, I noticed most people who found it redundant wouldn't show up...but anyway, the beauty part of math is that you can explain in any number of ways, and it very well may be something even the best and brightest haven't thought of. I'd imagine teaching math is more like a humanities-style course than one might think.

I think the most important part of 'teaching the mini-lessons' is that they would be feedback oriented, whereas lectures are not...Or rather, the lectures could be but let's face it, first years in particular won't want to disrupt the lectures ask questions. So essentially, my goal would be creating a 'highschool-like environment' as opposed to just re-teaching the lessons.

Does that sound any better, or more worthwhile? Or do you still feel it'd be a waste of time?

I feel that might be a bit better...but some students go to all classes because they feel there may be a little tidbit that they can use and find a lot of other material redundant.

Although this is specific to me, going over what and how to reference things in essays in second year classes drove me nuts since I'd been using MLA format since ninth grade. So I was irritated during most of my tutorials as I didn't need things to be re-iterated.

My experiences with learning math, however were much different. But my Math 1M03 TA was terrible...maybe it was the way he tried to teach us mini lectures...but I ended up more confused. So I stopped going and thus missed out on the homework help.

And I do agree with what Kareko said; that way you can get a better feel if you need to teach concepts or if you can just do one problem.

Originally Posted by jade177

And explaining concepts is key. Sometimes students need to hear something more than one way before they are able to understand it.

And mowicz, this is unrelated, but I was wondering if you could tell me anything about MATH 2C03, and Dr. Yazdani (I'm assuming it's Dr.)

That's precisely was I was thinking, thanks (:

Math 2C03 is considered to be a very easy math course by many people. It's what's called a 'methods' course, and I'll explain what that means momentarily.

The course starts off by introducing you to what's known as an Ordinary Differential Equation or O.D.E. (which you may have seen before). It's basically a fancy name for an equation involving Derivatives. y - y' = 0 is a differential equation for instance (where y' = dy/dx is the derivative of y with respect to a dummy variable x).

To give an idea of how to solve it:

y - y' = 0 =>
y = y'

So which function do you know that is equal to its (first) derivative? It's clearly some form of e^x right? It is infact Ce^x, for any constant C.

Easy stuff right? Well unfortunately it does get a bit harder than that, but you spend the entire semester learning to recognize 'types' of differential equations, and the way to solve them. (Some techniques are rather sophisticated...but if all else fails, you don't need to understand the methods (though that's always a good thing :p) you just need to recognize cases, and use the method). This is why it's often called a methods or methodology course.

There are some finer details you need to learn, you'll get sick of the words "Existence and Uniqueness" which basically mean, does a solution exist for a given O.D.E.? And is it the only possible solution? (You will learn, not every differential equation is actually solvable, which is why this is an area with a lot of research potential)


Hope that gives an idea of what to expect. (:

As for Soroosh (Dr. Yazdani prefers to be called by his first name, because he claims, fewer people pronounce it incorrectly haha), I only had him as a professor for one day when he covered for another professor. He did however, coach the Putnam Mathematics Contest with Dr. Kovarik, so I knew him in this extra-curricular sense.

He's a very laidback, informal guy...I'd imagine he'd be a pretty good prof from what I've seen.

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Bushra: Math 1A03 and 1B03 are probably my first picks for courses to TA. If I do get it, make sure you come introduce yourself haha. I was thinking of mentioning macinsiders at some point too, so that'd be awesome.

I'm sure you'll be a great TA, Mike and I'm not saying that just to say it or make you feel better
You're taking a great deal of effort and really responding and considering all the input provided which I think is incredibly impressive and the hallmark of somebody who is not only passionate about the subject but about teaching and helping students, cause you didn't have to do this.
I'm sure you're going to do a great job and even if I don't get you as a TA I wish you all the best

Originally Posted by Mowicz

... with Dr. Kovarik...

How is Dr. Kovarik as a professor? I think I saw that he's one of the professors I could get for math next year.

Originally Posted by Ownaginatios

How is Dr. Kovarik as a professor? I think I saw that he's one of the professors I could get for math next year.

Me too. I'm supposed to get him for 1B03.... lots of mixed reviews. LOTS.

Thanks Bushra (: That's kind of you to say.

Kovarik, the mixed reviews are understandable, since I even have mixed feelings about him...I've had him twice.

First I had him for Math 2A03 (Calculus III), during the summer. He taught the course more like a 'review' than teaching new information in my opinion. I inevitably stopped going to lectures, but did fine in the course. Undoubtedly however, he's a very generous guy, and is lenient with his grading (though you may have a TA doing the grading for you).

Then I had him for Math 3G03 (Problem Solving), and he was the ideal professor. Kovarik is a 'contest writer' he always coaches the Putnam and Squire competitions, and since 3G03 is a 'get ready for contests' kind of course, he runs it perfectly. Again he showed his generosity, since I calculated my final mark to be something like 89.2 and he bumped me up to a 90 to get the 12.

In the end: I like him, but you may find yourself wanting to attend other lecture sections for 1B03 (Like Lozinski, if he's teaching it). I'm pretty sure it's something like, he's so smart that he can't comprehend people not understanding such 'basic material' (from his perspective). So he goes kinda quickly.

His examples are always interesting, and he makes some really corny jokes which is always awesome.

Hey Mike!
Can you provide a few examples of "Existence and Uniqueness" regarding derivative equations? Is it related to complex numbers?

Also I was thinking of taking second year math courses as electives since I never got to take any math at Mac since my GCSE Alevel Math was equal to 1K03/1M03 and Stats 1L03. I've been told that my GCSE syllabus pretty much covered upto 1M03 and maybe beyond :S
I did help out a couple of people with math last year(I think it was 1M03) and they were doing rates of change or double differentiation I think :S
http://www.cie.org.uk/docs/dynamic/5165.pdf Can you please take a look at that syllabus list and tell me If I should be well equipped to take a second year math course(not sure which :S)

And Sorry well I'm pretty blank about any actual T.A recommendations, I've never really benefitted from my Socsci/Humanities Tutorials apart from Facepalming during discussions at some of the ridiculous things people said

Originally Posted by huzaifa47

Hey Mike!
Can you provide a few examples of "Existence and Uniqueness" regarding derivative equations? Is it related to complex numbers?

Also I was thinking of taking second year math courses as electives since I never got to take any math at Mac since my GCSE Alevel Math was equal to 1K03/1M03 and Stats 1L03. I've been told that my GCSE syllabus pretty much covered upto 1M03 and maybe beyond :S
I did help out a couple of people with math last year(I think it was 1M03) and they were doing rates of change or double differentiation I think :S
http://www.cie.org.uk/docs/dynamic/5165.pdf Can you please take a look at that syllabus list and tell me If I should be well equipped to take a second year math course(not sure which :S)

And Sorry well I'm pretty blank about any actual T.A recommendations, I've never really benefitted from my Socsci/Humanities Tutorials apart from Facepalming during discussions at some of the ridiculous things people said

So many :S,

Haha, you should have seen the surprised look on my face when I read the word gradient...then I realized that it's refering to what I, and probably most people here, would know as the slope of a line. (This is what I know as the 'gradient' of a vector field http://en.wikipedia.org/wiki/Gradient)

So are you saying you've taken all of the courses in that syllabus? From the looks of it, you've 'touched' Math 1A03, and 1AA3. I would definitely say with confidence that you could skip 1A and go straight to 1AA.

But the question is whether or not you could jump right to 2A or 2C, I'm not quite so sure. It isn't necessarily that you are missing some knowledge, it just seems as though you haven't gone into as much depth in your GCSE courses. You could probably pull off taking 2A03 (Calculus III), or 2C03 (Intro to Differential Equations), but they might be a huge burden and occupy more time than they're worth, since most of it is practice.

What I would recommend, if you're interested, is take Math 1AA3 next year, and consider 2A03 and/or 2C03 the following year. I have full confidence that you could do it if you took that course first. Or if you don't really want to waste a year, and/or a first year elective (remember you can take a maximum of 48 level I credits), then you could take the risk and gamble a bit. Make sure you can handle the other 4 courses you'll be taking at the same time, ask for lots of help from your TA/professor and you could probably pull it off too.

Originally Posted by huzaifa47

Hey Mike!
Can you provide a few examples of "Existence and Uniqueness" regarding derivative equations? Is it related to complex numbers?

Is it related? Yes and no. Differential equations become more 'screwy' if you will, when Complex Numbers are thrown into the mix...infact, some differential equations involve matrices 0: and that's when complex numbers start floating around. You get some really pretty graphs, like spirals.

http://tutorial.math.lamar.e du/Cla...nvalues.as px

Don't worry about the math too much, but scroll down and take a look at the graphs. (:

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But that doesn't mean Complex Numbers must be around, for questions of existence and uniqueness to play a role. So what do we mean?

I'll try to explain without doing any of the rigorous details. This would be a proof done by the instructor, and you wouldn't be expected to do it by yourself anyway (on a test at least).


EXAMPLE: I gave the example of y - y' = 0 (*).

Existence: Well, we know a solution exists, because in my earlier post, I suggested y = Ce^x. Taking a derivative, y' = Ce^x. So y - y' = 0, as required.


Uniqueness: Suppose we had another solution, bolded y. Then our solution y = Ce^x is 'unique' if y = d*y ... namely, it only differs by a constant factor.

Since y is also a solution, then it must satisfy the differential equation. So y - y' = 0 (**).

So what you do is compute y / y, using some tricks like cross-multiplying, and applying (**) and you'll find it does indeed come out to some constant, let's call it d.

But then y / y = d, and y = Ce^x...

Then that means y = (C*d)e^x. But C*d is just a constant...so it doesn't really matter. It's 'the same' as y.

So this solution exists and is unique. (This also shows e^x is the ONLY function that equals its derivative).


[**EDIT** Someone might suggest that 0 is a function which equals its derivative. This is certainly true...but 0 = Ce^x for C = 0. So e^x is still the 'only' such function.]



EXAMPLE: Now recall the 2nd derivative y''. Consider the equation y - y'' = 0.


Existence: What functions are equal to their second derivatives? Well, there's e^x...sin(x)...cos(x) . So a solution exists.


Uniqueness: Is there only one? Sin and Cosine are kind of like the same thing, since you can 'shift' and turn sin into cosine. But is e^x the same? Not over the real numbers...but *gasp* over the complex numbers...it is!

Because of the following identity, called Euler's Identity:

e^(ix) = cos(x) + i*sin(x), where i is the square root of -1. (This can be proven very easily using a Taylor Series expansion for e^x, cos(x) and sin(x), which you usually do in Math 1AA3) Strange things indeed, these differential equations... (: