I am a student in community college and I plan to transfer to uc in my third year but our college don't teach us proof so I want to know what proofs are necessary to handle when in my first and second years. looking forward to your help!!
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Most universities offer a course in 'mathematical reasoning' or a similar name where an introduction to proofs is offered. If that or another proof-based course is a prerequisite for the courses you are interested in, then some background in proofs will be assumed. Otherwise, I doubt instructors will assume you are familiar with proofs. If in doubt, you can always ask. – Jair Taylor May 29 '17 at 21:46
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That the geometric series converges and its value, that the binomial coefficients are integers, the factorization (with proof) of a quadratic polynomial, the decimal expansion of $\pi$ using $\lfloor \pi 10^k \rfloor$, how to draw $3 x^2+9x-10$ in 30 seconds, solving using substitution a set of 2 or 3 linear inequations, those kind of things. – reuns May 29 '17 at 21:53
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That $\sqrt{2}$ is irrational. Also being comfy with set theory things, e.g. a set $X$ is infinite $\iff$ there exists a proper subset $T \subset X$ such that $|T| = |X|$; and that $\mathbb{N}$ and $\mathbb{R}$ have different cardinalities. Working with injective/surjective/bijective functions. – Kaj Hansen May 29 '17 at 22:01
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Hello. Usually you begin with basic algebra and analysis courses. There are no specific facts you need to know, but you need to have developed some ability to reason rigorously in math. There are books that can help you make this transition if you've only had courses in non-rigorous calculus. I strongly recommend Journey into Mathematics by Rotman. It also has a solution manual. – user49640 May 29 '17 at 23:15