Navigating Math After High School: Where to Go Next?

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After completing college algebra with trigonometry, the most recommended next step is to begin studying calculus, specifically "Calculus 1," as it builds on the knowledge gained from pre-calculus. While geometry can be pursued later, starting calculus while the material is fresh is advised. Following the completion of Calculus 1, the logical progression typically leads to Calculus II or linear algebra, depending on individual goals. Establishing a structured curriculum is essential to avoid aimless study. Ultimately, the direction should align with personal academic or career objectives.
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OK, I'm teaching myself all the stuff I didn't learn in high school. I just finished up college algebra with trig, and now I don't know which way to go from here. I was thinking maybe I should get a good geometry textbook and go with that, or maybe some more trig or more advanced algebra. I don't know. What is the most natural route from one subject to the other?
 
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Calculus.

- Warren
 
Beginning Calculus or "Calculus 1" is the most popular next choice. You could choose Geometry if you did not learn it well earlier, but you just finished studying a "Pre-Calculus" book and this has prepared you for studying Beginning Calculus; best to start it now while you are still fresh. Besides, you can always choose Geometry later.
 
Thanks for the replies, folks! So calculus it is. I have a beginning textbook. So, after that, what is the next natural course? Do I just go on to calc II, or linear algebra, or what? I just want to put together a natural curriculum to follow, and not jump around blindly. What are the tried and true courses?
 
What's your ultimate goal?
 

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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