How Fast Should I Teach Myself Algebra?

  • #1
I'm teaching myself some algebra using Paul's Online Math Notes. I've been doing very well, (I understand the concepts, and I do well on Practice/Assignment Problems) but I would like to know how long it will be until I get to Calculus I? What are the hardest concepts to grasp when learning this topic? Also, should I use the Feynman Technique when learning each lesson? I'm sorry if I sound like an idiot, as I am an edgy 13 year old. I'm supposed to take Algebra this year, but I just can't wait to learn Calculus, (and ultimately a lot of physics) and I thought that these notes would be a good foundation. Thanks to anyone who read this far!:D
 

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  • #2
symbolipoint
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Typical community college courses of Algebra 1 and Algebra 2 are about 18 weeks each. That might be too fast for a 13 year-old person. A typical course at high school goes for 9 months. You should study from a good textbook/s, even if you try to study on your own to learn.

but I would like to know how long it will be until I get to Calculus I? What are the hardest concepts to grasp when learning this topic?
Calculus will require ALL OF Introductory and Intermediate Algebra, and about a full course-worth of Trigonometry. The typical courses route to reach first semester Calculus would be:
  1. Algebra 1
  2. Geometry
  3. Algebra 2
  4. Trigonometry OR Pre-Calculus.
Pre-calculus is usually a combination course of College Algebra AND Trigonometry, and the course name might be listed as "Elementary Functions".

The "Geometry" course might not be necessary but still a good idea. It might be required at your high school and some of the knowledge taught therein is essential, but the necessary Trigonometry will be directly used more.

The most difficult part of learning Algebra 1 and 2 is, for most or many students, Inequalities and Absolute Value.
 
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  • #3
Thank you for this information! What textbooks do you recommend?
 
  • #4
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I would also look into these resources when you have the time:

Khans Academy

Mathispower4u.com With a large collection of short math videos one per topic. Useful if there’s some topic you don’t quite understand you can find it here easily.

And lastly Openstax.org for a free Algebra, Geometry, Calculus 1,2,3... textbooks in pdf format. Again a good resource for when you don’t understand something or want to dig deeper.
 
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  • #6
symbolipoint
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The suggestions from jedishrfu are fine, but if you want a REAL textbook, an inexpensive source would be from a public or college library used-book sale. Look for algebra textbooks from such authors as Drooyan, Dolciani, Aufmann & Barker, Larson & Hostetler, Lial Miller, Wright & New. Other authors could also be good, not just those I listed. If the books found there are 30, or 40, or 50 years old, that's fine; not any problem. Introductory and Intermediate Algebra have been the same courses as they have been for many, many decades. The best ways of book-published instruction have been just as good ten years ago as well as 50 or 60 years ago. Meaning, between very good and excellent.
 
  • #8
symbolipoint
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You forgot Stewart Calculus.
You're right. I was focusing on the Algebras needed in order to reach Calculus.
 
  • #9
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You're right. I was focusing on the Algebras needed in order to reach Calculus.
No my bad, I didn’t realize you were mentioning Algebra books. Sometimes I read every other word and interpolate the rest that way I read twice as fast with half the comprehension. :-)
 
  • #10
Stephen Tashi
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but I would like to know how long it will be until I get to Calculus I?
The typical journey for a person who self-teaches (and many that get their learning in school courses) is that they tackle Calculus before they "master" algebra and trigonometry and experience many awkward moments in Calculus because of things they don't know about algebra nd trigonometry.

If you encounter such awkward moments in a course then it has consequences for your grade. However, if you are self-teaching, such awkward moments are private psychological phenomena and its up to you whether you want to endure them.

Some people have a personality that prefers to go step-by-step and be absolutely confident about what its doing. Other people are ... shall we say "adventurous". They begin studies or projects without a firm grasp of what they are doing. There is no general rule about which personality type is preferable. Since your original post hints at some impatience, my guess is that your are the adventurous type, but you are trying to tame your natural inclinations by using step-by-step materials.

My suggestion is to go ahead and look at some Calculus lessons. See if you know enough algebra to understand them. If you don't then that's more motivation to study algebra.

If I've misjudged your personality and you need confidence at each step in order to motivate yourself, then you will naturally find a pace of studying algebra that suits you.

Whatever approach you take, you will find that Calculus is a culture shock if you have only studied its nominal prerequisites. For people who don't like feeling insecure, the prerequisites for Calculus should actually include an introduction to Logic, including an introduction to quantifiers ("for each", "there exists"). It should also include an introduction to formal mathematics ( e.g. The culture that definitions mean what they say, not how we Platonically imagine them.) Many students get their introduction to Logic and formal mathematics in their first Calculus course and often it is not a gentle introduction.
 
  • #11
symbolipoint
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The typical journey for a person who self-teaches (and many that get their learning in school courses) is that they tackle Calculus before they "master" algebra and trigonometry and experience many awkward moments in Calculus because of things they don't know about algebra nd trigonometry.

If you encounter such awkward moments in a course then it has consequences for your grade. However, if you are self-teaching, such awkward moments are private psychological phenomena and its up to you whether you want to endure them.

...

Whatever approach you take, you will find that Calculus is a culture shock if you have only studied its nominal prerequisites. For people who don't like feeling insecure, the prerequisites for Calculus should actually include an introduction to Logic, including an introduction to quantifiers ("for each", "there exists"). It should also include an introduction to formal mathematics ( e.g. The culture that definitions mean what they say, not how we Platonically imagine them.) Many students get their introduction to Logic and formal mathematics in their first Calculus course and often it is not a gentle introduction.
The first part of that is why the Pre-Calculus course is put in place at community colleges and universities.
 
  • #12
The typical journey for a person who self-teaches (and many that get their learning in school courses) is that they tackle Calculus before they "master" algebra and trigonometry and experience many awkward moments in Calculus because of things they don't know about algebra nd trigonometry.

If you encounter such awkward moments in a course then it has consequences for your grade. However, if you are self-teaching, such awkward moments are private psychological phenomena and its up to you whether you want to endure them.

Some people have a personality that prefers to go step-by-step and be absolutely confident about what its doing. Other people are ... shall we say "adventurous". They begin studies or projects without a firm grasp of what they are doing. There is no general rule about which personality type is preferable. Since your original post hints at some impatience, my guess is that your are the adventurous type, but you are trying to tame your natural inclinations by using step-by-step materials.

My suggestion is to go ahead and look at some Calculus lessons. See if you know enough algebra to understand them. If you don't then that's more motivation to study algebra.

If I've misjudged your personality and you need confidence at each step in order to motivate yourself, then you will naturally find a pace of studying algebra that suits you.

Whatever approach you take, you will find that Calculus is a culture shock if you have only studied its nominal prerequisites. For people who don't like feeling insecure, the prerequisites for Calculus should actually include an introduction to Logic, including an introduction to quantifiers ("for each", "there exists"). It should also include an introduction to formal mathematics ( e.g. The culture that definitions mean what they say, not how we Platonically imagine them.) Many students get their introduction to Logic and formal mathematics in their first Calculus course and often it is not a gentle introduction.
Thanks for all of the information! I tried to learn Calculus once, but it was too difficult for me to understand, and I felt like I wasn't learning everything I needed to progress to the next step. I felt like I was just doing random lessons.
 
  • #13
symbolipoint
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Thanks for all of the information! I tried to learn Calculus once, but it was too difficult for me to understand, and I felt like I wasn't learning everything I needed to progress to the next step. I felt like I was just doing random lessons.
Some parts of Calculus 1 are necessary for making the course sufficiently complete, but if you are interested in learning Calculus 1 and 2 as a tool for the physical sciences, you need to understand and be able to perform differentiations and integrations. You need a good intuitive knowledge of Limits of functions. One does not need to master the epsilon-delta limit proofs, but needs to study that enough to try to be familiar. Do not let that epsilon-delta stuff stop you from moving on into differentiation and integration. When you deal with Calculus for lower division requirements in Chemistry and Physics, you need to understand and know how to take derivatives and setup and performs integrals/integrations. You will not be dealing with the e-d limit proofs there nor need to be worried about struggling about continuity.
 

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