[Mowicz]

I'm doing this in response to a request for a review of Math 1B03. I gave it a perfect score, but for reasons to be explained in this review...This course leads to higher level algebra courses:

->Math 2R03 (Linear Algebra II),
->Math 2S03 (Linear Algebra III),
->Math 3E03 (Group Theory),
->Math 3EE3 (Ring Theory and Field Theory)
->Math 4E03 (Galois Theory)

But I've only listed the Algebra courses...It is required for almost every single Math course, 2nd year and above.

Is this course easy?

I'd like to open by saying that this math in my opinion, was the easiest math course I've taken in all my four years at Mac. Some ideas however, such as a determinant, are kind of abstract. Not everyone is meant for math so you may not completely wrap your head around all the ideas of this course, but it's ok! Those of you who aren't in math can do the practice problems and probably ace the tests...and those of you who are, may not get it in this course but by the time you graduate these concepts will be fundamental. In my opinion, the material is interesting and practical, which is why I have given it a score of 10 in Interest and Easiness. There aren't very many 'tricky questions' that could be asked!

What can I expect from this course?

The course opens by introducing you to the concept of '2 equations and 2 unknowns.' If x + y = 2, and x + 2y = 3, can we solve for x and y uniquely? That is, are there infinitely many solutions, exactly one solution, or no solutions? You begin by loosely defining the idea of 'linear independence' and a 'parameter' or dummy variable...big fancy talk for "You'll learn how to see the answer."

You then proceed to define what's called a matrix...a square (or rectangular) array, or grid of numbers. Every matrix can be interpreted as a system of equations, and every system can be put into matrix form. Matrices, as mathematical objects, have a unique addition and multiplication defined on them, which you will learn. Every matrix has a special number associated to it called its determinant...you will figure out how to compute a determinant, and what a determinant of 0 means (as opposed to a determinant not equal to 0). You will then learn that "Multiplying" matrices can be viewed as something called a Linear Transformation. This is slightly abstract and will make a lot more sense in Linear Algebra II (Math 2R03).

Then you define what's called a vector...which is really just a line segment that sits in Euclidean Space (such as the xy-plane). You can specify vectors in a variety of ways, which you will learn about in great detail. You will define the notion of Linear Independence further...which 'basically' means the vectors are not parallel, but in higher dimensions (such as 3-D space) this is no longer necessarily true. You will learn operations which are like addition and multiplication of vectors (but not really multiplication, though it can be thought of as similar) called the dot and cross products. The dot product is a measure of 'how parallel' two vectors are, while the cross product produces a vector which is perpendicular to both of the previous ones (usually in 3-D space). Nothing too difficult here.

Then you will define the notion of a Vector space. It's just a set of points which satisfy a bunch of rules. You won't deal with this too much, it's just kind of filler material at the end, and instead you deal with it a lot more in Linear Algebra II (Math 2R03). A little more abstract, but definitely doable.

Was your professor effective?

I took this course several years ago and had Dr. Lozinski. Dr. Lozinski is one of my favourite profs. He had excellent pacing of the material (which really is kind of light), and threw in some very interesting remarks. I don't believe Dr. Lozinski is teaching 1B03 in 2009/2010, so this isn't particularly relevant...but I felt he deserved a 10/10 also.

And of course for Overall Rating, I simply averaged my other 3, and also gave a 10.

Can I contact you in regards to help/private tutoring for this course?

Absolutely. This course was one of my favourites, and I know the material like the back of my hand (and infact, I'm trying to become the TA for this course, it's my first priority).

Good luck!

[veena_vd]

Some of the topics you talked about, like cross and dot product, we covered vaguely in grade 12 calc. and vectors. Is it somewhat reviewed material?
Does anyone know how the course has been in more recent years?
any advice on prof. Kovarik, ZV?

[Mowicz]

The course make up has not changed since I've taken it...they are even using the same textbook, to my knowledge.

Infact, when I went to highschool we had an entire course dedicated to linear algebra (and various other topics such as Euclidean Geometry) which has since been removed, so people are entering university with less knowledge of the subject matter than before.

It is designed to have some overlap with highschool, for the simple reason that different highschools and different grade 12 classes with different teachers means 1 thing: Students come into university knowing different things.

Most, if not all, of the introductory level science courses are meant as like 80% review material simply so that all of the students know all of the material. Think of how devastating it would be if someone took say, a physics course and their highschool class ran short and didn't cover a certain unit...they would be forced to learn this unit on their own, while learning more advanced "new" material that may escape them...That's what first year's all about in the sciences, bringing everyone up to speed.

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So in answering, yes, if you're familiar with the cross and dot products then that will be review...but not everyone entering university is familiar with them.

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Kovarik is a brilliant guy, he's one of those Math Olympiad contest writer guys who always excels at problem solving.

For this reason, he teaches the third year problem solving course extremely well (which I can attest to), but other courses he may go a bit too quickly and assume a lot of knowledge because it seems so obvious to him.

In Math 1B03 however, I seriously doubt this will be an issue. You could probably ace the class without attending a lecture (I only attended once every 2 weeks).

[Shananaghens]

I'm taking this course now, and I really love it. I came from a math background with only grade 12 advanced functions (no vector background, no calculus) and I've gotten 100% on the past two tests, now the exam is coming up. My prof is Nicas, and I must say, I dislike his teaching style very much. He shows us the concepts in very complicated detail and improper wording, and then explains how "this is how we'd do it in third year - but oh, here's the way you guys will be doing it." It confused me a lot, and it was really intimidating at first, but tutorials are really where the main part of my learning came from. Overall, easy concepts, easier math, and an easy 12 if you like math.

[faytless]

I can attest that this course is very easy.
If you go to class, it would be a very easy 12 - because most of the test is just applying formulas. For me, I haven't been to many classes, but I'm still pulling 11-12 (12 before exam at least, we'll see after).

It'd be a nice easy math elective to take for the most part.
Dr. Nicas is funny, and he's great - you do get a lot from class.
The concepts are pretty interesting - simple, but interesting.

[erinterpol]

one of my favourite courses during the year. i didn't think i'd do too well in this course, but i think think the tutorials helped a lot. definitely continuing in upper years.

[Biochem47]

What semester would you recommend taking it? I also am taking MATH1LS3. I was thinking MATH1LS3 first semester, and MATH1B03 second semester, or does it not make a difference?

[jhan523]

Originally Posted by Biochem47

What semester would you recommend taking it? I also am taking MATH1LS3. I was thinking MATH1LS3 first semester, and MATH1B03 second semester, or does it not make a difference?

It doesn't matter, one's calculus the other's linear algebra.

[faytless]

I think it matters, as getting Nicas greatly improves your mark. Nicas's tests are like assignment questions.

[Mowicz]

^^Actually assignment questions are, generally speaking, more difficult than test questions since you have time to think about them. So I think you want to say the opposite...that the tests are actually even easier than the assignments. Haha.

Yes, Dr. Nicas is a very reasonable test-giver...even at the graduate level.

[ruby101]

Thanks every one ! I will choose Math 1B03 as my first elective.

[Mahratta]

I took Math 1B03 in the summer with Dr. Ryan, who's a professor emeritus of math and computer science. Having sat in on lectures during the year, I can attest that the course in the summer was definitely more 'theoretical' (more interesting!) and the tests had some unexpectedly interesting questions on them. Concepts were more often than not proved (somewhat) rigorously, and we experienced quite a few students dropping the class because it wasn't the bird course that everyone expected it to be...if you're interested in math, though, don't let this scare you away, because it wasn't hard at all, and there was really not much work you needed to do.

I thoroughly enjoyed the course, with my only qualms being the order in which we were taught certain concepts - for example, the idea of a determinant was pretty meaningless when we first learned it, as we learned about the concept before we learned about matrices as linear transformations. The same goes for the first mention of eigenvectors, which had a pretty hollow meaning at first (but this was further elaborated on later in the course). The second issue I had was the manner in which certain concepts, for example vector spaces, were described and taught - it was somewhat 'hollow' and not as concretely proven as the rest of the ideas in the course.

Dr. Ryan was an excellent lecturer, and class was interesting. We had 5 assignments worth 10% of the mark in total. This made the textbook basically worthless for me, since the professor explained the concepts in a much more interesting manner, and I didn't end up doing practice problems at all, since the assignments usually had a few problems on them.

The midterms were fair - each one had a few 'plug-and-chug'-type questions and a few questions with a bit more thinking required. There was usually at least one question which amounted to a proof by another name. I had more trouble with the 'plug-and-chug' type questions (terrible arithmetic on my part), but even if you don't care much for "proofs", you can easily do well enough on the midterms (and final) by doing problems and getting the non-proof questions right.

Overall, I'd definitely recommend the course as I took it, and I'd also definitely recommend supplementing the course with Axler's "Linear algebra done right" (if you care at all about the material you're working on, or are interested in math), which I thought was much, much, much better at explaining and defining concepts than the book we had to purchase.

[RodrigoNarro]

Does anyone know if Derek Krepski is a good professor ?
I was hoping Nicas would be teaching all 1B03 classes but it appears Derek is teaching term 1

[ruby101]

I really want to take Math 1B03, Math 1C03 but they were full . I kept checking solar all the time but they're always full. If anyone are dropping these courses, Please, let me know. I would be very appreciated.

[strawbrryjam]

how does this schedule look like?
bio1a03
chem1a03
psych1a03
econ1b03
math1a03

bio1m03
chem1aa3
math1b03
math1aa3
physics1b03