How can I improve my ability to work with proofs?

[Arnoldjavs3]

I'm a CS student and I'm about to take discrete mathematics next two semesters. My proofs are very weak and I want to change this. (I'm told discrete math is a lot of proofs.)

Are there any books/courses/resources to help me work my way up? I have a summer to prepare for.

 

[haruspex]

I'm a CS student and I'm about to take discrete mathematics next two semesters. My proofs are very weak and I want to change this. (I'm told discrete math is a lot of proofs.)

Are there any books/courses/resources to help me work my way up? I have a summer to prepare for.

In what way are you weak on proofs? Are there gaps in the logic? Are you unable to see how to prove something? Do you confuse sufficiency with necessity? Or...?

 

[Mark44]

Here are a couple of books I have that might be helpful to you.
"How to Read and Do Proofs, 2nd Ed." -- Daniel Solow, ISBN 0-471-51004-1
"The Nuts and Bolts of Proofs" -- Antonella Cupillari, ISBN 0-534-10320-0

 

[Arnoldjavs3]

In what way are you weak on proofs? Are there gaps in the logic? Are you unable to see how to prove something? Do you confuse sufficiency with necessity? Or...?

Not knowing where to begin. How to make proper use of information that they already give me.

Here are a couple of books I have that might be helpful to you.
"How to Read and Do Proofs, 2nd Ed." -- Daniel Solow, ISBN 0-471-51004-1
"The Nuts and Bolts of Proofs" -- Antonella Cupillari, ISBN 0-534-10320-0

Thanks, I'll look into it.

 

[haruspex]

Not knowing where to begin. How to make proper use of information that they already give me.

A method I often used to was to try to construct a counterexample, i.e. disprove the thing to be proved. It can shed light on why the given facts prevent such a counterexample.

Sometimes it is easier to work back from what is to be proved, but generally that only works for if-and-only-if.

In a formula to be proved, the structure of the formula can give hints. E.g. if the answer has arcsin in it, it suggests a trig substitution in the method.

 

[UsableThought]

My proofs are very weak and I want to change this. (I'm told discrete math is a lot of proofs.) Are there any books/courses/resources to help me work my way up?

You haven't said what you've actually studied in this area. If you can be specific, that might help people give you more precise recommendations.

For example, I recently took a popular introductory-level MOOC on predicate logic & proofs, via Stanford University - Introduction to Mathematical Thinking - and enjoyed it. But I can't tell from what you've said so far if this would be appropriate for you, or whether it would be too elementary.

 

[Arnoldjavs3]

You haven't said what you've actually studied in this area. If you can be specific, that might help people give you more precise recommendations.

For example, I recently took a popular introductory-level MOOC on predicate logic & proofs, via Stanford University - Introduction to Mathematical Thinking - and enjoyed it. But I can't tell from what you've said so far if this would be appropriate for you, or whether it would be too elementary.

Aside from calculus 1, linear algebra i haven't taken any maths. Or atleast not anymore that I can recall.