University Math A LOT Harder Than High School Math?

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I'm in 2nd year Mathematical Physics and ya, CRAZY math courses. I don't understand how anyone going into math in university would know that they can handle it with just high school math experience. Like how do they know that they will be good at university math? My conclusion: just because you do excellent in high school math does not mean that you will even do decent in university math. Same goes with physics. Another conclusion (no offense to anyone who sucks at high school math or physics): In high school math and physics you memorize algorithms to solve problems. In university math and physics you need to know the concepts very well and USE YOUR BRAIN to think of how to solve the problem.

i applaud you for trying university. certainly is hard, but you learn many skills the more classes you take.

Completely correct.

If you are taking high school math, the types of questions you'll see are: Can you differentiate a function? Can you solve an equation? Can you take the sine of an angle? In other words, stuff for which there is a definite process you can fall back on if you don't want to "think it through".

On the other hand, you might see questions like these in college (pre)calculus (or so I would hope): Can you use the limit definition of the derivative to find a derivative? Can you use inequalities to find the upper bound and lower bound of a function? Can you prove a trigonometric identity? These are things for which there is no algorithm. There may be a few heuristics, but in the end it's a function on whether you can think through the definitions and write proofs of theorems. Unfortunately, the original poster is right: Almost nobody teaches the pure reasoning skills you need to prove theorems. I'm working through a proof-based linear algebra class - my THIRD proof-based math course - and I still don't understand proof writing to its entirety.

I think it's largely a failure in the educational system.

We let people get out of high school with little more than a barely functional understanding of math, and university (for minimal required classes) expect you to master higher applications of math, but the gap between the fundamentals and college math is fairly large.

It was so bad in my home state (Florida) that the community college allowed students 3 classes to get up to the entry level math they needed to start earning credits toward the degree requirement.

3 classes just to get to entry-level college math?

In hindsight, the college math wasn't all that hard, but if you weren't math inclined and/or didn't have a very good teacher, it was impossible to learn.

That's actually why I excelled in university level math and physics, since it wasn't just memorization, it was understanding the reason why thing were and using general logic to solve for things.

Tell me about College Math, right now I am doing transfer credits and I literally failed the 1st attempt of the 2nd easiest Math class and dropped the 2nd attempt, due to the fact that I started working so hard, but i found out that I started to work hard really late in the class. Seriously, Math is a real pain in the f********king butt. You have to memorize certain rules, figure out when and how to implement certain rules and figure out when, how and which ways you are going to set up your rules and so on. It is literally really hard stuff. No joke. I am going to do my easier classes first and plan to handle my math later, seriously. Math is not mentally confusing, but drains you emotionally. No joke.

This is very true.

It's also why I lost all interest in math and physics in high school (stupid "do it my way" rules) and didn't regain it until I tried the two years of math and physics that start an engineering degree.

How I learn math is backwards to how they teach it in high school. My process is something like:

1. Get some idea of a topic and related problems that can be solved.

2. Throw away textbook.

3. Stare at the ceiling for a while.

4. Write down solutions.

5. Recall that "by staring at the ceiling" is not a commonly-accepted answer to "how did you get that?" Nor is, "but it just is that way." Set about creating either a proof or a process that can be explained to someone else.

I got an introduction to abstract math in a NSF program while still in high school. I'm glad I didn't need most of it for a physics degree.

Math theory is horrible. I took Elementary Analysis, and I had to work my ass off just to get a C-. I was seriously afraid that I was going to fail it.
Keep in mind that I got A's in math until AP Calculus (which I got C's in, but I aced the AP test)... I'd probably get it after taking a couple more classes. But since I'm not going to be a mathematician, there's no point in me taking it.

As for the main theme of the thread: yes, college math is harder. Besides the theory classes though, it's really only harder because you're taking higher levels of math.

The best approach is to begin with trying to understand the definitions, then rote learn them. Do the same for the theorems and examples. Then practise. Rote learning really helps solidify your knowledge.

But please do try and develop some relational understanding.

I agree, I was good at highschool level math but when I got to college they taught it very differently. I am really good up to algebra II, ok at pre-Calc. When I got into Calc, it got so hard I barely passed Calc 1 and I failed at my first attempt of Calc 2, passed decently on my second attempt. I especially suck when Im expected to learn math from a theoretical standpoint. Im good at number manipulation and memorizing problem strategies.

Yeah, it's really tough but I never did good at Math in high school. I got put in an Honours class in high school. I got a B the first semester and then had to work really hard to get grades of C- after that. My high school only required 3 years so I didn't take a fourth year.... which I kind of regret now.

I decided to take Social Work in college because I find it interesting and I though it would be an interesting career because I wouldn't really need math much. The only problem is that my university expects me to pass Statistics to get my degree. I've flunked it the first time and I got an unauthorized withdraw grade the second time (because I stopped showing up when my grade in the book was -2 on a scale of what was supposed to be 0-100). This requirement is especially stupid since I don't want to do research... but my friends who want to teach only have to take a class called "Math Ideas" which is really easy.

For me, the University maths was not harder than high school. If anything, it was easier - precisely for what you've mentioned: in high school it is all about learning by heart, and in university they actually teach you to understand what you're doing. Once you understand the concept, everything becomes much easier. If you know the definitions of mathematical paradigms and why they are this way - you can do maths with your eyes closed.

In the UK, I'm doing A-levels (UK pre-university qualification - usually people do 3 or 4) in Maths and Further Maths (both to A2). Normal Maths isn't that challenging, but Further Maths goes into topics that will be most likely met in first year university level mathematics. However most UK universities don't require Further Maths since the first few weeks' work assumes that not everyone has done it.

I'm doing the OCR-MEI course, you can see the past papers here to see how it bridges unviersity level mathematics (I don't do ALL of the modules):

HERE ARE THE PAPERS!

I will have done C1 to C4, M1 to M3, D1, S1, NM, FP1 and FP2. FP3 is the hardest of the lot but it matches a few topics from first year university level mathematics.

C1 doesn't look too hard. I'm in 2nd year university BTW.

Yeah C1 is easy - it's the first ever A-level maths module every student does. It's mostly content from GCSE as well.