How can I improve my mathematical skills and avoid careless mistakes?

[mathsciguy]

This is my first post and I've decided to make a thread right away. I just want to ask about how should I work on my maths?

Not so long ago I flunked one mathematics quiz, I don't know if it's because I'm not studying hard enough or if it's because of my careless mistakes or if it's plain stupidity. Either way, it's still kind of frustrating.

I'm only taking freshman level math courses, so I'm yet to experience the more rigorous maths in my curriculum (I'm a physics major). Now, after flunking that one quiz I've studied and reviewed my stuff and also I've picked on the habit of working on as many problem sets as I can everyday. Now my question is, is this enough? And also, general advice regarding math.

Sorry if I have a bad english.

 

[micromass]

We can't really know if it's enough. Only you will be able to know this.
Try to get hold of some practice quizzes and try to solve them within the time limit. If you do good, then you're doing ok.

 

[mathsciguy]

I guess there's no helping it, I'd really appreciate it if you guys could link me to practice quizzes online (lower level courses from trig to calculus) though.

 

[chiro]

I guess there's no helping it, I'd really appreciate it if you guys could link me to practice quizzes online (lower level courses from trig to calculus) though.

Hello mathsciguy and welcome to the forums.

One piece of advice I can give you is to figure out what the big picture is and then use your homework/assignments to clarify the specifics.

With calculus (differential and integral, standard Riemann type) the real understanding is knowing what is changing (differential) and what that actually means. The computation is also important, but it comes after formulating the specific model that you intend to look at.

A lot of the rules used in applications of calculus pop straight up from the definition. Some of these definitions might require a few innovative tricks, but many results are no more than using the machinery of algebra to derive some specific result.

If you can derive the model and then use algebra/other tools to solve a problem then that's great. If you can not really understand what you are doing, then focus on that first. Algebra is important also, but my opinion is that it is more important to know the big picture about what is really going on, because the algebra is a lot easier to learn than the higher level concepts.

 

[mathsciguy]

With calculus (differential and integral, standard Riemann type) the real understanding is knowing what is changing (differential) and what that actually means. The computation is also important, but it comes after formulating the specific model that you intend to look at.

A lot of the rules used in applications of calculus pop straight up from the definition. Some of these definitions might require a few innovative tricks, but many results are no more than using the machinery of algebra to derive some specific result.

If you can derive the model and then use algebra/other tools to solve a problem then that's great. If you can not really understand what you are doing, then focus on that first. Algebra is important also, but my opinion is that it is more important to know the big picture about what is really going on, because the algebra is a lot easier to learn than the higher level concepts.

Thank you sir, that's what I actually do first. I study the concepts and proofs as in depth as I could then I go straight to practicing with the problem sets that I have. One of my problems though is that I tend to get really messy when I'm doing calculations and solutions. That's why I usually end up missing signs or doing wrong arithmetic along the way when I'm solving. Though I suppose I just need more practice in actual problem solving.