Thursday, August 17, 2006

My Semester

Classes start Monday - woo! Exciting!

I have two classes, as is typical for the spring & fall semesters for me. I'm taking Calc 3 and Intro to Proofs. Both of them are on Monday & Wednesday nights. Calc 3 is 5:00-6:50, and Proofs is 7:00-8:15 (shorter because it's a 3-hour class).

I'll be coming to work at 8 AM every day. I only take half an hour for lunch most days, so leaving at 4:30 on Mondays & Wednesdays shouldn't be a big deal. The other days, I'll stay until 5.

As school schedules go, this is a pretty easy one. I'll have two hard nights, but the rest of the week is normal. Then of course, I also have my grant project to work on. So it might be a semester with a lot of work. But I think neither of my math classes will have projects or anything like that. Math seems like such a straightforward subject to take classes in.

Then there's the question of whether I'm ready for Calc 3, given that I basically didn't do much calculus this summer at all. (I got through about half of Calc 1 in review before I quit.) Hopefully I can pick up or quickly relearn anything I need to know. I think it will be OK. I'm looking forward to the semester.

sally said...

Does Calc 3 = differential equations?

Tam said...

No, it's not. Here are the descriptions for Calc 1, 2, 3, and Diff EQ, from the course catalog:

MTH 1410-4 Calculus I (4 + 0)
This is a first course in calculus for science and engineering. The topics covered include derivatives of polynomials, trigonometric, exponential and logarithmic functions, applications of
the derivative, the definite integral, and the fundamental theorem of calculus.

MTH 2410-4 Calculus II (4 + 0)
This is a second course in calculus. The topics covered include techniques of integration,
applications of the integral, introductory differential equations, and infinite series, including Taylor’s series.

MTH 2420-4 Calculus III (4 + 0)
This course in the calculus of functions of more than one variable includes the following topics: partial derivatives, definite integrals over plane and solid regions, vectors and their applications, and Green’s Theorem and its generalizations.

MTH 3420-4 Differential Equations (4 + 0)
This course includes a study of first, second, and higher order differential equations and systems giving solutions in closed form, by numerical approximations, and through Laplace Transforms. These techniques are applied to problems in the physical sciences and engineering.

sally said...

Ah, OK. I think schools must differ in whether they offer the pre-diff equations stuff in 2 or 3 classes. The stats program at CSU requires 3 semesters of calculus plus linear algebra, but they must mean calc 3 = diff e because diff e is a prerequisite for the first class in the MS program. I think Metro's calc 1-3 series was also covered in 2 semesters at Rice.

Tam said...

That's kind of been my working hypothesis over the years too. I seem to recall that Diff EQ was the third in the sequence at Rice.

I'm not taking Diff EQ, though. Nothing in the Calculus progression beyond Calc 2 is required for any of my remaining classes. (Intro to Proofs is the gateway for everything else I'm taking.)

Tam's momm said...

What is Intro to Proofs? I loved solving proofs in the logic courses I took but this is probably not the same thing. I vaguely remember doing proofs in a geometry class too.

Tam said...

I don't really know what will be in the Proofs class. I know the book is called "A Transition to Advanced Mathematics" (Smith et al, you can look it up, Momm).

My 9th grade Geometry class was basically all proofs. The kind we used there were the kind where you draw a vertical line and on one side you put statements, and on the other side you put a reason (a theorem or justification for the statement). Those are formal and we also did them in my logic class at Rice. I like them too.

There are also proofs by contradiction, where if you want to prove A, you show that "not A" leads to something that is not true (like 0 = 1, for instance), so then you know A must be true. There is something called "proof by contrapositive" which I think must be the same thing, since that's what a contrapositive is.

In math there are also proofs by induction, where (based on my vague memories from high school), you show first that if A (the thing you want to prove) is true for N (some number), it must be true for N + 1. Then you show that A is true for 1 (or 0 or something) and now you've shown that it's true for all the numbers from there up, at least.

I'm guessing there might be other types of proofs too.

My understanding is that all of math (theoretical math, which precedes figuring out how to use math to solve problems) proceeds by means of proofs. I mean, that's how it's developed.

But I'll let you know later in the semester if everything I said here was completely nonsense. Or maybe someone else can weigh in - Robin, you were a math major, right?

Tam's momm said...

I looked it up and the subject heading is Mathematics--Textbooks. Not very helpful. The call number is QA37.2 which is the general number for mathematics textbooks. Also not very helpful. We do have a copy here but with all the remodelling I have no idea where the Q's are. I'm afraid to leave the comfort of the basement. I might never find my way back.