Math Books for First-Year Undergrads: Proof-Based Learning

[peanutbutterb]

I am a first-year undergrad and I've recently discovered that I am fascinated by math proofs and therefore would like to do some self-study because the courses that I am able to pick cannot satisfy my need. Could you recommend some books suitable for someone who's just starting?

 

[mrwall-e]

I am a first-year undergrad and I've recently discovered that I am fascinated by math proofs and therefore would like to do some self-study because the courses that I am able to pick cannot satisfy my need. Could you recommend some books suitable for someone who's just starting?

If you are new to proofs in general, I highly recommend "How to Prove It" by Velleman. If you're looking for proofy math, I did find that Pinter's abstract algebra book gave good instruction on proofs that did not require much background.

 

[jk]

Creative Mathematics by H.S. Wall. It is a calculus book where you supply the proofs. It is intended for someone like you who is beginning the study of advanced mathematics and who has a strong interest in learning how to write proofs. It is not easy and is not the kind of book you just read...you have to work through every page which is really the only way to learn mathematics...by doing mathematics. Once you have worked your way through it, you will have a high level of mathematical maturity

 

[peanutbutterb]

Thank you very much for your replies. I think I may want to build a more solid background in theorems rather than learning how to write proofs in a structured manner at this stage. Additionally, I am taking linear algebra this semester; although I've found the concepts really interesting, I have failed to find the course very challening. So I guess recommendations for linear algebra books would also be greatly appreciated?

 

[VulcanWong]

If you are looking for some proof-based linear algebra text.i think "linear algebra:An introduction to abstract mathematics" may be an option to you.It explains everything you found in "ordinary" Linear Algebra text.
What "ordinary"means?It means those just taught you computation techique,but this book explain the underlying theory in linear algebra and even some abstract mathematics.It may be a good option to you

 

[DivisionByZro]

Thank you very much for your replies. I think I may want to build a more solid background in theorems rather than learning how to write proofs in a structured manner at this stage. Additionally, I am taking linear algebra this semester; although I've found the concepts really interesting, I have failed to find the course very challening. So I guess recommendations for linear algebra books would also be greatly appreciated?

What does "a solid background in theorems" even mean? If you want to learn math, you'll have to know how to write some proofs. Theorems are statements that are shown to be true using proofs... I'm not sure what you mean at all. Your best bet is to get a proofs book and practice writing them. Practice a lot.