At the start of the new semester I started studying Lang’s Basic Mathematics in preparation for a higher calculus textbook such as Spivak’s Calculus or Apostol’s Calculus. But I’m struggling with managing it with my classes ( I’m taking 4 APs this year including APUSH). Does anyone who has attempted or is attempting something similar have any advice? I don’t have anyone offline to go to for help or to use as a role model, so this is kind of a solitary affair unfortunately. My goal for this year is to finish Basic Mathematics and then hopefully pick up Spivak during December or late November so I can spend the rest of the school year on it. Is this realistic? I plan on using supplementary texts such as Book of Proof, and An introduction to Inequalities to help transition into more proof-based math. I also have Mathematical Proofs: An introduction to Advanced Mathematics but I would plan on using that more for reference since it seems to discuss topics beyond Calculus in some chapters.
Please explain why you are doing all of this self study in math.
Why aren’t you taking a math class ?
You are on a dangerous path. Math builds. You need to understand to move on.
You’re not.
Take with a teacher. Not on your own. You are not helping yourself.
Just for context, I was a math major in university and have used math in my job on multiple occasions.
To me reading math yourself is something that you do for fun, if you find it to be fun. Whether I personally find it to be fun might depend upon which day you talk to me and what sort of advanced math is involved.
Math is a subject where what you are learning now depends a great deal on what you were learning last year, and what you are going to be learning next year will depend a great deal on what you are learning now and what you learned last year. This means that it is very important to have a solid foundation. You want to learn every step very well.
Just to give you one example, I recall a couple of very difficult math problems that I needed to solve on the job. One required quite a bit of multi-variate calculus and stochastic processes (the latter is something that you take after first studying probability and statistics). However solving this tough math problem also required a lot of high school algebra and in one case trigonometry. I needed to be very solid in high school algebra in order to be able to solve any of the toughest math problems that I have ever needed to deal with. What this means is that when you are studying high school algebra you are learning things and developing skills that anyone who is good in math is likely to need to use a lot for many classes in the future and potentially on the job in the future.
And I think that you will learn math much more thoroughly in a class, with a teacher, and with exams that you can use to judge how well you really understand something.
What math have you completed in school?
This.
And thus my original question…why self study this?
There isn’t any dramatic reason. I’m just interested in the subject.
I’m not sure I understand the reactions on this post however. Isn’t Calculus offered in most high schools? And Basic Mathematics is just algebra with a slight focus on proofs and the like. Is any of this really as overboard as you are making it sound?
When you apply to college, the colleges will want to see how you did in actual classes in math. As long as you fulfill the recommended math courses for your college applications, then this is fine.
If you are doing self study to fulfill some higher level math, the colleges might not recognize this…unless they do placement tests for math placement…and some do.
IMO you need to re-prioritize.
- Focus on the actual classes you are taking. Do not lag behind in your HS classes to follow your own personal agenda.
- Take the highest level of math you qualify for at your HS (if you have completed the sequence offered at your HS consider a class at a local CC or with an accredited online school).
- Get involved in ECs that are meaningful to you.
- After all of the above, read the math books if you have time and are interested.
If you find yourself with extra time and interest for extracurricular math, I would suggest looking into something like AoPS where you would have a curriculum, classmates and a teacher. AoPS can complement rather than replace the material you study in HS. It’s also a lower level of a commitment than taking a community college class… you can always drop it if you get too busy.
This is likely an EC that OP finds worthwhile, or at least meaningful.
OP, Lang’s Basic Math was not written to be a first text in the subject of high school math. If you’re seeing things for the first time in Lang, you’re making things needlessly difficult for yourself. That being said, proof based math takes time, and if you are making progress and learning, that’s a good thing. If you want to tone it down a notch, what you should switch to depends on what you know so far.
OP’s school is unlikely to offer courses in rigorous proof based mathematics (other than geometry, which is quite watered down relative to the level of the rigor of the book OP is going through)
Check out Past Problems | USA Mathematical Talent Search
You can also look at past problem sets to selective summer math camps like Ross, CanadaUSA Mathcamp, PROMYS e.g.
https://oss.linstitute.net/wechatimg/2019/02/2019promys.pdf
Consider applying to them as well, many selective summer math camps offer financial aid
Please take your high school courses seriously. Meet the HS diploma requirements for HS graduation.
Are you planning on applying to colleges, at some point? Colleges and universities aren’t going to consider your “hobby” of studying math. They’re going to look at your grades.
It’s all about grades in a classroom.
My husband loves math. He finds it “fun” to do proofs in his head. (His Caltech-father tutored him and his twin, in math, in Middle School).
While in high school, my husband took math courses at the local university (SDSU) and was required to take a math entrance exam.
(They ran out of courses, at his HS, at his level. He had already surpassed the community college level math courses.)
He did not struggle to learn the material and kept up with his AP courses and ECs. But because he had professors, he could gauge his progress and ability. Math has always been an “easy” skill for my husband. (Our kids are the same in their ability to calculate in their head. -Dad tutored them in math.)
If you’re at that level, then I say: “Yes, go ahead. Do it on your own and study”.
It’s not an EC, and it would only be for your benefit.
But if you’re struggling, that tells me that self studying is not beneficial for you or your time.