Custom Math Course: Refresh Arithmetic & Learn Algebra/Calculus

[Tri]

Hello all, I've decided to set a "math course" for myself, coming into Highschool I want to know as much as possible. I thought maybe review the basic arithmetic as a refresher then Abstract algebra (https://www.amazon.com/dp/0471433349/?tag=pfamazon01-20) followed by geom/trig, hopefully someone can recommend a website/book where I can learn this fairly quickly. After that is out of the way start on calculus( I have several books in mind). Do you find this track efficient, if not please recommend something better. :)

 

[micromass]

Hello all, I've decided to set a "math course" for myself, coming into Highschool I want to know as much as possible. I thought maybe review the basic arithmetic as a refresher then Abstract algebra (https://www.amazon.com/dp/0471433349/?tag=pfamazon01-20) followed by geom/trig, hopefully someone can recommend a website/book where I can learn this fairly quickly. After that is out of the way start on calculus( I have several books in mind). Do you find this track efficient, if not please recommend something better. :)

Abstract algebra?? You do know that abstract algebra is a college-level course, right?? And that Dummit & Foote is a university textbook, right?? I hope you're not confusing this with high school algebra, because it's very different!

If you do want to do abstract algebra, then you can. But be aware that the course is very proof intensive. You'll need to be quite acquainted with proofs and logic. There are some nice introductions to abstract algebra which should be quite accessible to (good) high school students. For example Pinter and Fraleigh are decent books.

 

[Tri]

Abstract algebra?? You do know that abstract algebra is a college-level course, right?? And that Dummit & Foote is a university textbook, right?? I hope you're not confusing this with high school algebra, because it's very different!

If you do want to do abstract algebra, then you can. But be aware that the course is very proof intensive. You'll need to be quite acquainted with proofs and logic. There are some nice introductions to abstract algebra which should be quite accessible to (good) high school students. For example Pinter and Fraleigh are decent books.

I'm sorry I didn't give detail on previous Knowledge, I know most of the subjects I've listed just with a bit of a superficial understanding, and I would like to get deeper into the pure maths. I realize it's a college level textbook(which I have read before, University Physics with modern physics). I wasn't sure though, the difference between Algebra and Abstract Algebra, but according to the reviews it's a good basis for higher topics so I thought it would be a decent choice :/, is there a chance i can still keep up with the book, where can I get set with proofs?

 

[Vorde]

Whoa hold your horses there, you need to realize what you're saying.

For starters, Abstract Algebra isn't the basic algebra you think it is. Abstract Algebra is a mathematics-major college course that definitely isn't taken until you've have Single Variable and Probably Multivariable Calculus, and taken Linear Algebra and maybe even Real Analysis.

The first thing you should do is get a nice introductory algebra ("basic algebra") book, that'll give you the basics. Then get a geometry book and learn a decent amount of geometry. After that you can progress onto basic analytic geometry and trigonometry. Only at that point can you even start to think about learning calculus.

That being said, I don't recommend this in any way.
First of all, it's going to take a while. What I just outlined is easily 3 years of math classes if not 4 or 5.
Second of all, self teaching is never the best idea. I'm not afraid to say that I am really good at math, and when I self-taught myself Differential Calculus I know that if I didn't have the mathematical skills I have I would have fallen far behind and suffered greatly by trying to leap ahead.

My advice is to take it a bit slower, wait to skip classes until you've gotten a bit farther along the math track.
That being said, I'd do whatever you want to do!
Best of luck :)

 

[Matrix0]

I understand the importance of a strong foundation in mathematics. It is commendable that you have taken the initiative to set a customized math course for yourself. I believe that reviewing basic arithmetic is a great way to refresh your skills and build a strong understanding of mathematical concepts.

I am not familiar with the specific book you have mentioned for abstract algebra, but I would recommend doing some research to ensure that it is a reliable and comprehensive resource. Additionally, there are many online resources and textbooks available for learning abstract algebra, so it may be helpful to explore different options and choose the one that best suits your learning style.

In terms of geometry and trigonometry, I suggest finding a reputable website or textbook that covers both topics in depth. These subjects are closely related and it would be beneficial to have a strong understanding of both before moving on to calculus.

As for calculus, it is a complex and challenging subject, so it is important to choose a resource that is well-written and engaging. I would also recommend seeking out additional resources, such as online tutorials or practice problems, to supplement your learning.

Overall, I believe that your proposed track is a good starting point. However, it is important to continuously assess and adjust your approach as needed. Good luck on your math journey!