I'm a first year math and stat major and I'm contemplating whether to take Math 1C03 in the second term. Is the class useful?

If it isn't, I'll take Comp Sci 1FC3 instead.

Take both (not necessarily both this year though).

Comp Sci 1FC3 covers some stuff you won't see for a while as a math major (third year or later), such as combinatorics and tree theory, and gives a firm grounding in proof (It's the only place I have ever "formally" learned about mathematical induction. While it's not exactly rocket science, it quickly becomes assumed knowledge). It presents things at a manageable pace.

Math 1C03 is ultimately a course that prepares you for what math actually is. I've heard mixed reviews about the course, largely depending on who the instructor is, but the course covers a variety of topics generally selected from 'real math' (loosely speaking).

You know, you could have asked the same question in the thread you made yesterday.

But yeah, I'd say take math 1C03, what do you have to loose?

Originally Posted by Incognitus

Take both (not necessarily both this year though).

Comp Sci 1FC3 covers some stuff you won't see for a while as a math major (third year or later), such as combinatorics and tree theory, and gives a firm grounding in proof (It's the only place I have ever "formally" learned about mathematical induction. While it's not exactly rocket science, it quickly becomes assumed knowledge). It presents things at a manageable pace.

Math 1C03 is ultimately a course that prepares you for what math actually is. I've heard mixed reviews about the course, largely depending on who the instructor is, but the course covers a variety of topics generally selected from 'real math' (loosely speaking).

Are you sure I'll learn the math used in Comp Sci 1FC3 during third year or later? Because then, I won't bother taking Comp Sci 1FC3 as many people have said that it is too difficult.

Originally Posted by Alexmahone

Are you sure I'll learn the math used in Comp Sci 1FC3 during third year or later? Because then, I won't bother taking Comp Sci 1FC3 as many people have said that it is too difficult.

I didn't say that, I meant that you won't see much of it in the first two years. It will become in large part expected knowledge by third year, much of it 'slips through the cracks' in the natural Math progression. Or rather, a lot of the methods used will be advantageous to keep in your mind while you take courses. But no, you will not learn combinatorics in any math course besides "Combinatorics (3U03)**" so if you never take that you never get to experience how valuable it is.

Knowing what a set is, or how a function acts on a discrete set will be invaluable should you enter say, Topology. (You're taught the relevant material hyper-speed in about 2 lectures during Math 3T03, since it's necessary)

While the tree theory let's say, that you cover in CS 1FC3 will not directly apply to something in say, Real Analysis(Math 3A03), it can stimulate the right type of thought process. Perhaps you can prove something is true by exhausting all possible cases. Taking 'too much math' is an impossibility, it all helps and it all leads you toward new levels of mathematical sophistication.

**EDIT: Note: Some other courses do use combinatorial methods of proof. I meant this as a sweeping generalization.

Yes. Take it--it teaches a lot of notation and stuff that you will see in your courses. It also teaches you the basics of how to look at proofs.

There's also the question of how much you're willing to learn by yourself.

I never took 1C03 or (CS) 1FC3 and am glad I didn't, since (i) most of that stuff is easy to learn online, and (ii) I would have lost two courses I took from other disciplines.

If you can wrap your head around the mathematical way of thinking and have the interest, then there isn't a need to take either course. Plus, when learning online, there are no artificial restrictions on what is or isn't covered; you can learn at your own pace and find all sorts of interesting connections. For example, I was first introduced to trees via linguistics rather than via mathematics, lattices (a type of poset) via chemistry, and so on. I think that, having learned the mathematics this way, that I've gained a lot of intuition that I may not have gained otherwise.

Learning on your own is very important, especially in mathematics -- by third year, you won't be doing "plug and chug" work any more, and the provided examples in the textbook may not motivate the concepts sufficiently. Additionally, looking stuff up yourself may help you see "the big picture", and connect the disparate stuff you'll see in 3rd year.

Also, as Incognitus said, you will cover most of the material somewhere in first/second year. In most cases, when you cover the material in a dedicated math class, it will have more motivation than in, say, CS 1FC3.

Additionally, I don't think that the notation should be a big deal, as you're introduced to it very gradually; they're not going to throw natural deduction style proofs at you in first-year. Rather, you will be gradually eased in to the formalism.

However, learning things yourself means that you'll have to do some extra work. So taking 1FC3 and 1C03 can save you some time, but again, it's very helpful to start looking at math on your own as soon as possible.

What Mahratta said is a very interesting way to look at it. So the big question is, are you willing to learn this on your own (and use those unites towards other courses), or would you rather learn it in a course (and possible save some time)?

Originally Posted by Eternal Fire

What Mahratta said is a very interesting way to look at it. So the big question is, are you willing to learn this on your own (and use those unites towards other courses), or would you rather learn it in a course (and possible save some time)?

Indeed, that's a succinct way to put it -- this also brings up another point: this technique makes more sense in first year than in later years for a couple of reasons.

Firstly, courses in upper-years obviously cover far more material at a far quicker pace, and the majority of the material can be seen as "harder" as well.

Second, many upper-year courses are required by graduate schools as yardsticks -- for example, a pure math grad school would like to see grades in real analysis and group theory, but wouldn't care about something like 1FC3.

Third, if you do learn stuff by yourself and free up the space (in first year), you can take first-year courses in other disciplines -- of course you can do this later too, but I think it would feel like a waste of time to take a first-year course in year 2-4 (in most cases), because you'll be used to a particular pace, and then have to go to a class which crawls along at a relatively slow pace.