Number Theory Advice: Struggling with Proofs in Course

[only_huce]

I am an undergrad taking my first course in number theory. For some reason, this is the hardest course I have ever taken in my life. It puts Calculus and Differential Equations to shame in my honest opinion.

My question is, am I the only one who thinks so? I mean, I go over the chapters, attend every class, and I can do any problem or apply any theorem when it involves actual numbers. However, when I have to do proofs (which is 70% of the coursework) I still find myself struggling. It's half-way through the semester and constructing proofs still hasn't clicked for me. When doing the HW, I find myself spending over 2 hours on a problem only to prove it half way.

Am I doing something wrong? Any advice is greatly appreciated.

 

[Office_Shredder]

Did you have to do proofs in your other courses?

 

[only_huce]

No, I'm an engineering major deciding to pursue a math minor therefore this is the first class I've ever taken involving proofs.

I mean I did some proofs in calculas 2, however they were more computational and involved integrating a formula rather than logical which is what I am encountering in this course.

 

[HallsofIvy]

Definitions, definitions, definitions.

In mathematics, definitions are "working" definitions. You use the exact wording of definitions in proofs. The absolute best thing you can do is learn definitions by heart and understand what they mean.

 

[yasiru89]

I'd beg to differ on that matter of semantics; definitions in mathematics are absolute definitions for the given theory. To grasp a proof what's required is not committing them to memory, but following from the foundations they establish.

Considering the definitions you're working with in different ways and combining them is what leads to proofs of propositions most easily.