Proof Laden Semester - Should I?

[sythrox]

Proof Laden Semester -- Should I?

Hello all,

I am trying decide whether or not I should take an intro to proof writing, linear algebra, and an advanced INTRO physics course of which I'm told the latter two have an appreciable emphasis on proofs (at least where I'm at). For someone who hasn't had any exposure to proofs would this be a good idea? I know this is really a question I should be asking myself, but I just wanted to hear other people's opinions on the topic. I plan on getting a PhD in physics so I realize I'll probably take these eventually but due to timing, I can only take the second physics course which allows me to fill my semester with math courses not explicitly required by my major.

 

[xiavatar]

Personally, I had the same predicament last fall as an entering freshman. I had many classes I wanted to take that required proof writing, but I had never had anyone formally go over my proofs from practice work I was doing from math textbooks. Going against my advisers advice, I went into the upper division courses and came out with A's in my courses.

Whether or not you can handle the material will depend on how quickly you can pick up new concepts. I would recommend you do some research on the material you will use in each class, and see if your comfortable doing the problems in the book. As to a good intro to proofs, I recommend the book, How to Read and Do Proofs by Daniel Solow.

After the that the decision is whether or not you want to take a leap of faith and take the classes anyways.

 

[djh101]

Three proof courses will at least be coherent. At my school, linear algebra was the intro proof course. Even if that's not the case at your school, the linear algebra proofs tend to be some of the easier ones in the math department, so I imagine that and intro to proof writing will complement each other nicely. As for the physics course, if it will be expected that you are already familiar with proofs, then you will probably have a difficult time taking that while still learning proofs (imagine if you had taken differential equations while you were taking your first calculus course). Yes, you will have to make final considerations yourself, since only you can accurately judge your own abilities (plus you probably know more about the course content), but it helps to have some perspective.

 

[micromass]

Hello all,

I am trying decide whether or not I should take an intro to proof writing, linear algebra, and an advanced INTRO physics course of which I'm told the latter two have an appreciable emphasis on proofs (at least where I'm at). For someone who hasn't had any exposure to proofs would this be a good idea? I know this is really a question I should be asking myself, but I just wanted to hear other people's opinions on the topic. I plan on getting a PhD in physics so I realize I'll probably take these eventually but due to timing, I can only take the second physics course which allows me to fill my semester with math courses not explicitly required by my major.

It's really difficult to say whether or not to do this. Some people are naturally good at proofs (although a rigorous high school will help), other people really struggle through it. I don't think the semester will be too difficult, but you might prepare for some work (especially in the first few weeks when you're doing proofs in LA while not being very used to it).

You might want to go through a proof book right now to understand the basics. Velleman is a good book but perhaps a bit too long and detailed for your purposes. All you really need is to be comfortable with proofs by contradiction, induction and a bit of set theory.

 

[verty]

@synthrox:
Below is a candidate book to give you some confidence. I think your concern is not that you don't know proofs but that you may not be good at proofs? If so, this looks like the perfect antidote.

You will want to work through the first 3 chapters, the later chapters won't be relevant. Use the "look inside" feature if you want to read some of the first chapter.

Caveat 1: It has direct proofs and proofs by contradiction but not proofs by induction. But this is not an impediment, you would pick this up very easily from the "Preliminaries" chapter of most undergrad math books or online.

Caveat 2: I think it won't provide specific proof recipes. For example, how to prove an if-and-only-if statement. You would know enough to know why the statement is true but not necessarily how it should be written up. But this is pretty common for linear algebra students, you are not expected to be a master. I'm sure classmates or TA's would be more than willing to give advice.

https://www.amazon.com/dp/0486477673/?tag=pfamazon01-20