<p>I'm a high school junior and next year I'll be taking all dual enrollment courses (finished high school requirements) either at a top 50 university or a mediocre state university in the same city (depends what I get into).
I want to take some math classes, probably stuff like Calc III, discrete math, elementary number theory, or linear algebra. Maybe calculus-based physics.
(I'm taking the AP Calc BC test which will place me out of Calc I and II.)
Basically, what do you think is the maximum number of math-intensive classes I should take per semester to avoid failing/going insane?
Is there any way to determine how difficult a class will be before I sign up?</p>
<p>College students who really like math (majoring in math) may take two to four within a normal full time course load, or even more if overloading (four or maybe five courses is a typical normal full time course load).</p>
<p>But as a high school student taking dual enrollment courses along with a presumably full high school course schedule, it may be difficult to schedule more than one at a time, unless you are taking fewer high school courses.</p>
<p>Typical college sophomore math courses are multivariable calculus, linear algebra, and differential equations, as these are typically required for any math intensive major (e.g. math, statistics, engineering, physics, PhD-bound economics). In semester system schools, the latter two are often combined in one semester-long course, or split into two mini-courses (half as many credits each, so you could take both together instead of one regular size course). Multivariable calculus is typically a semester-long course.</p>
<p>Other college sophomore math courses could include discrete math (may be required or recommended for math or computer science majors) and a proof techniques course (to prepare for proof-oriented college junior math courses that math majors take; proof techniques may be included with discrete math or honors freshman/sophomore math courses instead of being a separate course).</p>
<p>I’m finishing all my high school graduation requirements this year, so I’m probably going to stay with relatives in the college town and take all college classes.
Do you think four total classes per semester is reasonable?
(I think I want to be a math major, and it’d be nice to get a full year of college for free. And if I end up not wanting to be a math major, at least I won’t have to pay to find that out.)</p>
<p>Four or five normal size courses (3 or 4 credit-hour-units per course) per semester (15 to 16 credit-hour-units total) is a typical full time college student course load. But note that many colleges of courses of varying credit-hour-units, supposedly proportional to workload.</p>
<p>Nominally, each credit-hour-unit corresponds to 3 total hours of work per week, including both class time and out-of-class time. So 15 or 16 credit-hour-units nominally means 45 to 48 hours of work per week spent on school work. In practice, the average college student these days spends less time on school work than that. But note that courses with labs (usually sciences other than math) tend to be higher workload even though they may have the same number of credit-hour-units. So can courses with computer programming assignments or any kind of term projects.</p>
<p>Thank you.
How do college math classes work? Is it mostly just lectures and problem sets/assignments from the textbook? Do you have to write papers?
Does having all the prerequisites guarantee that a course is within my abilities? Are there any notoriously difficult weed-out courses I should probably avoid if I don’t want any horrible grades? (Unfortunately, these affect my high school GPA. A bad grade in a college math class will be considered exactly the same as a bad grade in Algebra I.)</p>
<p>Mainly lecture, discussion, assigned problems (may be from the book or instructor’s own problems) and tests. However, more advanced courses and honors courses tend to have more proofs among the problems.</p>
<p>For many students, the college junior level courses in real analysis and abstract algebra are major hurdles due to being proof-oriented, in comparison to computation-oriented courses taken previously. However, some students prefer the proof-oriented courses (including honors versions of the college sophomore level courses).</p>
<p>Most of the classes designated as freshman/sophomore level classes have problem sets similar to high school assignments: exercises where you learn to apply the methods being taught in that section. There may be an occasional proof thrown in, but they’re mostly straightforward (this could possibly be false if you have a particularly demanding teacher or it’s an honors version of a class or something). These courses are things like calc 1-3, differential equations, most intro linear algebra classes, and maybe discrete math.
Starting with the third year classes (abstract algebra, analysis, etc.), the focus will be more on proving things, which does not come naturally to all people who are good at applied math.
There are also a few upper level courses like complex analysis and PDEs that are taught closer to the first way.</p>