Advice on university preparation.

[Dissonance in E]

Hey, I finished the IB diploma in 2007, with a 6 in Physics HL, and I am hoping to get into engineering eventually.
However during my high school years i really didnt have much direction to my studies and ended up taking math studies (for those who don't know, it is a really pathetically weak math course...) ,passed with ease and regretted not taking more demapnding math classes.
I have 18 months before i finish army service and other commitments i have i would love to catch up a bit with the whole math thing during this time. So my question is this, does anyone have any good self study resources to prepare for 1st yr university math stuff.
Or more importantly would it be possible to get some kind of guidance as to what I should learn topic wise? Is a solid precacalculus foundation enough at this stage or is calculus a required base skill at uni 1. ?

Thanks.

 

[Howers]

Learn proof techniques. Engineers take middle steam math that is usually a blend of linear algebra and calculus. Calculus will cover transcendal functions (trig), limits, differentiation, integration, series and sequences, and a bunch of application. Linear algebra will cover algebra of multi variables, matrices, vectors, vector spaces, and diagonalization. Getting a solid precalc is only good if you learned the theorems and how to prove them. Computational skills won't prepare you for the rigor. In terms of background, you would need atleast a working knowledge of basic differentiation and vectors.

The only thing I can emphasize for uni is proofs. Geometry is a good way to build up these skills. A good book on math in general is "Principles of Mathematics by
Allendoerfer". Pretty old but it has pretty much everything you need and more.

 

[chroot]

I have to disagree with Howers; engineering is usually quite light on proofs and proof techniques, even graduate programs at prestigious universities. You can pretty much skip proof techniques entirely, and you won't miss it. (In case anyone is wondering, I'm a senior IC designer for a NASDAQ 100 corporation, and a part-time graduate student at the #2 ranked university in the world -- I've seen pretty much the entire gamut of EE education.)

You should instead focus on calculus, both single-variable and vector formulations. You will use basic single-variable calculus in almost every class you'll take, from introductory physics and circuit analysis, up through signals and systems and so on. Linear algebra would be next in line in terms of importance.

- Warren

 

[Dissonance in E]

K thanks for the replies! What about matrices? should i be pretty solid with them before entering uni? what kind of applications do they have and to what extent should i have them covered?

 

[nicktacik]

K thanks for the replies! What about matrices? should i be pretty solid with them before entering uni? what kind of applications do they have and to what extent should i have them covered?

From my experience, introductory linear algebra courses are taught assuming no prior knowledge (other than basic arithmetic).

 

[mathwonk]

Warren, I was going to give the same aevice as Howers, and was aurprized to see your more knowledgeable remarks.

Is it possible though that you are already strong on the logical reasoning side of things and do not need training in it, such as a good proofs course can give?

I am not talking about formal proofs, but problem solving and making logical connections betwen different but related phenomena. Is this useful in practice?

 

[mgb_phys]

chroot is correct that you aren't going to need proofs for any classes/exams in engineering (you barely need them in physics) but as a way of deeply understanding a topic and as a 'mental toolbox' to apply techniques they are a good exercise.

(He says as the least mathematically skilled physics PhD he knows ;-)

 

[chroot]

Is it possible though that you are already strong on the logical reasoning side of things and do not need training in it, such as a good proofs course can give?

I took a proofs class because I wanted a math minor, but the proofs class was neither required nor relevant to anything else I did in my undergraduate program. The most rigorously mathematical subjects you're going to touch in an engineering curriculum are:

• Fourier and Laplace transforms in a signals and systems class.
• Proof by mathematical induction in a discrete math class.
• Differential equations and boundary-value problems in higher-level physics class.

Most of these topics are presented as tools, used for a specific computational end, rather than as subjects for study all by themselves. The induction proofs were probably the only proofs I was ever required to do in undergraduate school, and they're extremely easy. I've been required to do some much more difficult proofs in graduate school, but still nowhere near the level required for a graduate class in mathematical analysis.

Basic single-variable calculus, however, is used all over the place, as are vectors. Thus, my advice is to study those much more precient topics first.

I am not talking about formal proofs, but problem solving and making logical connections betwen different but related phenomena. Is this useful in practice?

Certainly, an intuition is very valuable. You look at a circuit and write down a relevant equation. If you can immediately see the form of the solution by inspection, then you'll have the upper hand over most of the rest of the class. However, I just don't see any situation where proofs, in particular, will be valuable to a first-year engineering student. Maybe some other engineers here with different backgrounds can share their opinions.

- Warren

 

[Dissonance in E]

K, thanks again.
Whatabout chemistry? would i need somekind of a basis in that before entering?
If so what do you recommend to learn before hitting the lectures.

 

[chroot]

If you're doing chemical engineering, sure. If you're doing electrical engineering, not at all.

- Warren

 

[Dissonance in E]

Ok, thanks a lot. youre answer have come very handy!