Need help learning to construct proofs

[quasar_4]

so, I am in my first upper level math course beyond required calculus and the introductory linear algebra class. I don't know if it's just a great jump or if I slept through something, but suddenly everything is all about doing proofs. I'm okay with that, and I think it's fabulous because proofs seem to yield deeper conceptual understanding, but I have no experience whatsoever with writing/constructing proofs. I can memorize axioms and whatnot, but then how do I get started? anyone have any good texts on proof writing or know of any resources that could help me? I'm clueless here!

I don't know if it makes a difference (with regards to what kind of proof I should study) but the class is Theory of Linear Algebra. I love the topic, just have no idea how to prove things for every case...

 

[neurocomp2003]

yes there is a good book called Problem Solving by "C" Larson. Not sure if the C is the write letter.

the main way that I learned how to do proofs was to cram allt he theorems on one page. granted that you actually have to understand these theorems.

The straight forward method is to just rearrange your problem by regurgitating each step via one the theorems that you have learned up till that point.

Larson's Book outlines steps you should take to rearranging a given problem in such as looking for a counterexample(contradiction), recursion(can't remember the proper term...oh induction), look for symmetry and parity.

At the beginning of it all though try to define your problem based on all the previous defintions that you have learned.

...onc eyou become more accustomed to knowing some theorems and techniques then you can skip the majority of steps.

 

[tacman]

First of all, congratulations on taking on the challenge of an upper level math course! It can definitely be overwhelming at first, especially when it comes to constructing proofs. But don't worry, with practice and the right resources, you will become more comfortable with proof writing.

One of the best ways to improve your proof writing skills is to practice, practice, practice. As you mentioned, memorizing axioms is a good start, but the key to constructing proofs is understanding the underlying concepts and being able to apply them in different situations. So, make sure you fully understand the definitions and theorems in your course material.

In terms of resources, there are many great books and online sources that can help you with proof writing. Some popular books on proof techniques include "How to Prove It" by Daniel Velleman and "Mathematical Proofs: A Transition to Advanced Mathematics" by Gary Chartrand. These books provide step-by-step guidance on how to construct proofs and include lots of examples and exercises for practice.

In addition, there are many online resources such as video tutorials and practice problems that can help you improve your proof writing skills. Some helpful websites include Khan Academy, Brilliant, and Math Stack Exchange. These websites offer a variety of resources for different levels and topics in math, including proof writing.

Lastly, don't be afraid to ask for help from your professor or classmates. They can provide valuable insights and feedback on your proofs. You can also form study groups with your classmates to work on proofs together and learn from each other.

Remember, constructing proofs takes time and practice, so don't get discouraged if you don't get it right away. Keep practicing and seeking out resources, and you will become more confident in your proof writing abilities. Good luck!