Is "College Algebra" really just high school "Algebra II"?

In summary: I know that at my high school, Algebra II was only one semester. But regardless, it seems that College Algebra covers similar topics to Algebra II but goes into more depth and is more fast-paced. It may also depend on the university and the professor teaching the course. Overall, it seems that College Algebra is not just a repeat of Algebra II, but rather a more advanced and rigorous course.
  • #36
gmax137 said:
Yes but my question was, does it make any sense for a closed set to have "infinity" as an upper bound?
No of course not, it's just notation, like x "approaching infinity" in the case of some limits.
 
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  • #37
Muu9 said:
No of course not, it's just notation, like x "approaching infinity" in the case of some limits.
If infinity is one of the limits for an interval, this is not a clearly understood precise number or value, so that end of the interval remains "open"; so this is why the parenth is used to show that side of the interval (the inner curve of the parenth facing the infinity symbol).
 
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  • #38
sbrothy said:
I'm again on thin ice here but from what I've heard from college mathematics introductions some start courses simply assume that pupils didn't understand or pay sufficient attention during high school and thus start from scratch quickly going through the basics just in case.

That happened in my degree in Australia. To get admitted you must have done Math B and C roughly equivalent to UK A Level Math which is Calculus BC plus a bit more. Yet we had Calculus A, which was just a boring rehash of HS calculus. The real shock came with Calculus B which was real analysis. I loved it, but most detested it. The latest I heard is they don't do that any more, starting with Probability and Stochastic Modelling, Abstract Mathematical Reasoning, Linear Algebra, and a Second Major Elective (all math majors where I went do a second Major, which can be an area of math like Stats, Operations Research or Data Science) first semester. Real Analysis was a 3 credit course when I did it. They replaced it with Abstract Reasoning (4 credits) which includes Real Analysis plus a bit more. They got rid of Analysis entirely for a while, which I found a bit depressing.

As far as HS goes likely math or associated majors such as Actuarial Science, Mathematical Physics etc is accelerated a bit and do (at many schools) the equivalent of Pre Algebra, Algebra 1 and 2, and Geometry starting in year 7 in 3 years instead of 4. Then Math B and C years 10 and 11 and 4 year one university math subjects senior year. Taking two Subjects over the summer means you can complete the degree in 2 years instead of 3.

Then I found something interesting. In the US 7000 students take the Calculus BC exam in year 8 or less, with over 50% passing. I thought what? I suspect we can accelerate calculus even further for better students.

To answer the original question in the Australian context if you have not done Math B and C at HS you do Math B as one 4 credit subject then Math C as another 4 credit subject except they call it by different names like foundational math etc. Many degrees just require Math B, some none at all. The thing I find depressing is that 45 years ago (god I am getting old) everyone, and I mean 100%, did the same subjects in years 11 and 12. English, Math B and C, Physics, Chemistry and either Technical Drawing or Biology. Tech Drawing was for those interested in engineering. Biology for those interested in being a doctor, nurse etc. Mathematics guys like me were advised to take whatever appealed - I did Technical Drawing.

Now, and it is a big worry, less than 8% take even Math B and even fewer take Math C. Sad, very sad.

Thanks
Bill
 
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  • #39
The Queensland (i.e. not all of Australia) A/B/C curriculum was replaced with General Mathematics, Mathematical Methods, and Specialist Mathematics, respectively, in 2019. Students in New South Wales can take Mathematics Extension 2, which is more advanced than Queensland's Specialist Mathematics (formerly C).
 
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  • #40
gmax137 said:
Yes but my question was, does it make any sense for a closed set to have "infinity" as an upper bound?
Your remark is correct. I guess, no matter the context or the notation, including infinity limit requires special attention. Thanks for bringing it up.
 
  • #41
gmax137 said:
Yes but my question was, does it make any sense for a closed set to have "infinity" as an upper bound?
I learned infinity is always written as an open-ended set. Thus [2, ∞] makes no sense. Is the same true with the American notation?
 
  • #42
sbrothy said:
I learned infinity is always written as an open-ended set. Thus [2, ∞] makes no sense. Is the same true with the American notation?
Yes, in American notation it would be written [2, infinity)
 
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  • #43
gmax137 said:
Sorry for the tangent, but ...
What does the ,∞[ part mean? I understand if you write [2,b[ you mean everything from 2 up to but not including b. But when you put the upper limit as ∞, it is unbounded, right?

So I am asking, what's the difference between [2,∞[ and [2,∞] ?

Or [2,∞) and [2,∞]
In theory, there's this Compactification of the Reals; one-point or 2-point compactification that includes one of ##\pm \infty ##.
https://en.m.wikipedia.org/wiki/Compactification_(mathematics)
 
  • #44
Correct me if I'm wrong but, as I understand it, it's pretty much convention. Like they decided that infinity can never be inclusive. Much like you can never divide by zero. It's just the choice that makes the most sense.
 
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<h2>1. Is "College Algebra" the same as high school "Algebra II"?</h2><p>No, "College Algebra" is not the same as high school "Algebra II." While both courses cover algebraic concepts such as equations, functions, and graphs, "College Algebra" is typically more advanced and covers additional topics such as matrices, logarithms, and complex numbers.</p><h2>2. Do I need to take "College Algebra" if I already took "Algebra II" in high school?</h2><p>It depends on your academic goals and the requirements of your college or university. Some schools may allow you to place out of "College Algebra" if you received a high enough grade in "Algebra II" or if you pass a placement test. However, if you plan on pursuing a degree in a math-related field, it may be beneficial to take "College Algebra" to build a strong foundation.</p><h2>3. How is the difficulty level of "College Algebra" compared to "Algebra II"?</h2><p>Again, this can vary depending on the specific curriculum and instructor. However, in general, "College Algebra" is considered to be more challenging than "Algebra II" due to its more comprehensive coverage of advanced algebraic concepts.</p><h2>4. Will "College Algebra" prepare me for higher level math courses?</h2><p>Yes, "College Algebra" is an important prerequisite for many higher level math courses such as calculus, statistics, and linear algebra. It provides the necessary foundation and skills for success in these courses.</p><h2>5. Can I skip "College Algebra" and go straight to Calculus?</h2><p>It is not recommended to skip "College Algebra" and go straight to Calculus. "College Algebra" covers fundamental algebraic concepts that are essential for success in calculus. Skipping this course may put you at a disadvantage and make it more difficult to understand and apply calculus concepts.</p>

Related to Is "College Algebra" really just high school "Algebra II"?

1. Is "College Algebra" the same as high school "Algebra II"?

No, "College Algebra" is not the same as high school "Algebra II." While both courses cover algebraic concepts such as equations, functions, and graphs, "College Algebra" is typically more advanced and covers additional topics such as matrices, logarithms, and complex numbers.

2. Do I need to take "College Algebra" if I already took "Algebra II" in high school?

It depends on your academic goals and the requirements of your college or university. Some schools may allow you to place out of "College Algebra" if you received a high enough grade in "Algebra II" or if you pass a placement test. However, if you plan on pursuing a degree in a math-related field, it may be beneficial to take "College Algebra" to build a strong foundation.

3. How is the difficulty level of "College Algebra" compared to "Algebra II"?

Again, this can vary depending on the specific curriculum and instructor. However, in general, "College Algebra" is considered to be more challenging than "Algebra II" due to its more comprehensive coverage of advanced algebraic concepts.

4. Will "College Algebra" prepare me for higher level math courses?

Yes, "College Algebra" is an important prerequisite for many higher level math courses such as calculus, statistics, and linear algebra. It provides the necessary foundation and skills for success in these courses.

5. Can I skip "College Algebra" and go straight to Calculus?

It is not recommended to skip "College Algebra" and go straight to Calculus. "College Algebra" covers fundamental algebraic concepts that are essential for success in calculus. Skipping this course may put you at a disadvantage and make it more difficult to understand and apply calculus concepts.

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