Preventing my Math skills from becoming rusty

[Bogrune]

Hey everyone!

I'm deciding whether to major in Economics, Business Finance, or Chemical Engineering, and what I know about the three is that they all require plenty of knowledge in mathematics (Chem. Engineering especially). I wanted to take Calculus 1 next semester, but my couselor suggested that I take it easy next semester because of my problems with stress, and told me to take a course in Critical Thinking instead.

My question is: to prevent my skills in Precalculus from becoming rusty, would it help if I buy myself both a used Trigonometry and Precalculus textbook? Or what else could prevent my preparations for Calculus from fading?

 

[chiro]

Hey everyone!

I'm deciding whether to major in Economics, Business Finance, or Chemical Engineering, and what I know about the three is that they all require plenty of knowledge in mathematics (Chem. Engineering especially). I wanted to take Calculus 1 next semester, but my couselor suggested that I take it easy next semester because of my problems with stress, and told me to take a course in Critical Thinking instead.

My question is: to prevent my skills in Precalculus from becoming rusty, would it help if I buy myself both a used Trigonometry and Precalculus textbook? Or what else could prevent my preparations for Calculus from fading?

Hey Bogrune.

I think the most important thing in mathematics is to understand the key ideas.

In most mathematics courses there are a few main key ideas that set the foundation for the rest of the course.

Take for example calculus. Calculus is the study of change. One main idea in calculus is that you can calculate different measures like area, volume, length, flux and so on analytically for large classes of objects. The key thing though is not the actual equation, what it represents. When you are able to understand how things are actually changing with respect to whatever else, it becomes a lot easier to not only realize what an existing integral/differential equation etc represents, but also how to construct various formulas for things like length, volume, area and so on.

Again, if you understand what the differentials, derivatives and integrals are referring to, that is the most important thing. You will probably not remember all of the substitutions and tricks off by heart, but then again many people don't unless they use it on a semi-regular or regular basis.

Also with regard to the critical thinking class, I don't know if its a waste of time or not, but in terms of critical thinking, be critical of everything you hear no matter who tells you, but keep an open mind and consider all that is out there. It sounds paradoxical but its hard to find any absolute truth in the world no matter what field we are talking about, so you need to be open to new ideas as well as on your guard for not blindly accepting them.

Maybe you do the class you could also critically assess your teacher and give them a run for their money.

Also remember that everything won't make sense all at once. Sometimes it comes instantly and sometimes it doesn't.

 

[Bogrune]

Also with regard to the critical thinking class, I don't know if its a waste of time or not, but in terms of critical thinking, be critical of everything you hear no matter who tells you, but keep an open mind and consider all that is out there. It sounds paradoxical but its hard to find any absolute truth in the world no matter what field we are talking about, so you need to be open to new ideas as well as on your guard for not blindly accepting them.

It's not that I'm taking the class because I want to, but because it's a general ed. requirement. I'm still deciding whether to take it as Literature or as Philosophy.

Still, thanks for the advice. I'm just concerned about my skills in Trigonometry and wtih Matrices because I kept hearing that both topics will be crucial in Calculus III and Linear Algebra.

 

[mege]

How long ago did you have Trig and Precalc, and how well did you do?

While tutoring calculus the biggest issue I see with calculus students that have taken a small break is they just forget algebra stuff more than some of the specifics in precalc. Do you remember your properties of logs/exponents/roots? Can you factor a binomial and use the quadradic formula? The specific things you covered in precalc like finding limits and asymptotes likely is covered again, with a different mindset, in Calc I (so having a basic knowledge of the concepts from earlier is all you need).

I would say that even semester-to-semester most students lose the trig-identities (which is OK, since most calc books have a table in the covers/appendex to reference double angle and squares when neccessary), but it would be important to know the trig functions themselves.

 

[Dembadon]

Have you ever considered tutoring? It's another option for consideration.

 

[Highway]

trig and precalc have nothing to do with what you cover in calc, and the things you might have seen from there, they will go over again.

just make sure to review your algebra/fractions/logs/exponents a few days before class starts.

 

[Brandon_R]

Have you tried viewing Khanacademy? I think it might fit your needs (more intuition than solving problems) and it even has calculus explained at a high school level so you could get a head start.

 

[Danton]

Or you could just check out a calculus book from your library and start studying that during your free time

 

[Bogrune]

Or you could just check out a calculus book from your library and start studying that during your free time

You know, that's just what I kept thinking to myself over the past few weeks! All I know about Calculus so far is the basics of limits (i.e. (f(x)= 1/x) y=0 as x→∞).

trig and precalc have nothing to do with what you cover in calc, and the things you might have seen from there, they will go over again.

just make sure to review your algebra/fractions/logs/exponents a few days before class starts.

Guess that means I should review polynomial factoring and division some more then. Should I also review partial fractions as well?

 

[mege]

Guess that means I should review polynomial factoring and division some more then. Should I also review partial fractions as well?

Partial fraction decomposition should be 'retaught' enough for you to catch on. It has more integrations usage, so you probably don't need to worry about it as much until you get to Calc II.

But polynomial factoring and your 'basic' algebra operators (log, exponents) should be second nature, if you're going to be successful. Don't worry about synthetic division of polynomials. Anything of order > 2 will be easilly factorable (eg: x^5-16x can be very easilly factored by chaining difference of squares a few times).

 

[Danton]

I would agree with that. The most common problem I see when I tutor freshman in calc 1 classes is that they have completely forgotten basic algebra.

Basically you want these skills to be second nature so that you can focus all your attention on the problem at hand.

As far as trig goes, it is useful to know the properties of the functions as well as the common identities, both of which can be found in most standard calculus books.

Finally, in regards to matrices you should just know how to add, multiply and take the determinant, everything else should be covered in your linear algebra course