# Mathematicians - please provide some context on this freshman math example **URL:** \ **Category:** Factual Questions\ **Created:** [September 7, 2015, 11:11pm UTC](https://boards.straightdope.com/t/mathematicians-please-provide-some-context-on-this-freshman-math-example/730308 "2015-09-07T23:11:16Z")\ **Posts on this page:** 5\ **Page:** 2
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 8, 2015, 6:36pm UTC](https://boards.straightdope.com/t/mathematicians-please-provide-some-context-on-this-freshman-math-example/730308/21 "2015-09-08T18:36:36Z")
> [@Thudlow\_Boink](#): > > (BTW, I trust you enough not to check that equation, but I did at least look at the last digits as a quick plausibility check. :)) For what it’s worth, this has a precise analogy in the OP’s situation, where we can look at the p = 0 case as a quick plausibility check. (One can also quickly check the equation at infinity and at -1 (the latter chosen to conveniently make the denominators 1), and then by degree considerations the equation is fully established. But the most important takeaway is that this sort of cleverness is unnecessary.) ---
**Author:** ![JWT\_Kottekoe](https://avatars.discourse-cdn.com/v4/letter/j/3ec8ea/32.png) [@JWT\_Kottekoe](https://boards.straightdope.com/u/JWT_Kottekoe)\ **Post date:** [September 9, 2015, 1:39am UTC](https://boards.straightdope.com/t/mathematicians-please-provide-some-context-on-this-freshman-math-example/730308/22 "2015-09-09T01:39:57Z")
After a full year of calculus in high school, another full year as a freshman in college, the first seriously difficult math class I took was called “Introduction to Real Analysis,” taught from “The Elements of Real Analysis,” by Bartle. I was put off by “Introduction” in the title, because I wanted a bigger challenge, but it was the hardest class I took as an undergraduate. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 9, 2015, 1:54am UTC](https://boards.straightdope.com/t/mathematicians-please-provide-some-context-on-this-freshman-math-example/730308/23 "2015-09-09T01:54:41Z")
OK, “all” was obviously hyperbole, but it’s still quite common, even in upper-level graduate courses. ---
**Author:** ![Melbourne](https://avatars.discourse-cdn.com/v4/letter/m/b5e925/32.png) [@Melbourne](https://boards.straightdope.com/u/Melbourne)\ **Post date:** [September 9, 2015, 2:39am UTC](https://boards.straightdope.com/t/mathematicians-please-provide-some-context-on-this-freshman-math-example/730308/24 "2015-09-09T02:39:28Z")
> [@D18](#): > > Here’s the general question 1): are there freshman university students who can look at the steps from equation 3 to 4 and see how the latter follows from the former at a glance? . Most ofl the freshman engineers at my university in 1977 would have seen that at -slow- glance at the start of the year. The larget question that it is a part of was not part of the syllabus: I think it would have been part of first year math for math students. But at the end of the second year, I would have expected most engineering students to be better at the specific question than most math students, because they were learning about things like “the set of all positive rationals” while were were learning polynomial equations. ---
**Author:** ![glowacks](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/glowacks/32/5548_2.png) [@glowacks](https://boards.straightdope.com/u/glowacks)\ **Post date:** [September 9, 2015, 11:22pm UTC](https://boards.straightdope.com/t/mathematicians-please-provide-some-context-on-this-freshman-math-example/730308/25 "2015-09-09T23:22:58Z")
I wouldn’t say that I could figure out at a glance, but as the rest of us have said, by the time you’re at that point of your mathematical career, you know exactly what steps the author used to get there, and there’s nothing hidden that’s going to trip you up. If the author of the book says that’s the answer, you’re probably not going to check because there’s no reason to. Often details of proofs will often be given as exercises for students, but the detail omitted doesn’t really correspond with anything interesting. Normally such exercises deal with applying axioms and definitions that you’re learning in order to make sure that you understand them, but the steps in between the two lines there are elementary algebra that anyone who is taking a class beyond calculus would have absolutely no problem with doing, and wouldn’t possibly learn anything. And yes, a whole lot of mathematics textbooks start with “An introduction to”, and quite often anything that doesn’t is written for professionals, not students. There are plenty of counter-examples, but that’s the general trend. Mathematics is a very deep subject and people have spent quite a lot of time and effort developing every branch as much as they can. They don’t need big budget laboratories to do it, and only certain disciplines even could theoretically make use of computers. So anything that’s established enough to be taught to students probably has been developed far more than students can handle immediately. [Previous page](https://boards.straightdope.com/t/mathematicians-please-provide-some-context-on-this-freshman-math-example/730308.md?page=1)