High School Guidance - Answers to Math & College Q's

[drosser]

I have several questions hoping someone could help me.

I am nearing the end of my 10th grade year. I realized I should start thinking about college soon so I taughted myself calculus from Howard Anton's book called Calculus with Analytic Geometry last month hoping I could test out of calculus next year. I found out that I wasn't allowed to and that it wasn't a good idea anyway because calculus was the basis for all future math. I made sure I understood the concepts from the book by setting a goal for myself by explaining the concept to my friends and mom (who had no prior knowledge) on an index card. I was informed after calculus there is advanced calculus. Is there any recommended books for this topic?

My next question involves college. I have been slacking the last two years not taking any advanced classes except math. I plan on taking 7 AP classes the last two years of high school. I will be taking AP Chemistry, AP Biology, AP Physics, 2 years of AP Computer Science, AP Calculus AB, and AP Calculus BC. I want to go to a highly rated college like MIT or Caltech and the like because I really like math and physics. Does it matter if I take AP English? Are foreign languages important (should I take 2 or 3)?

For physics I plan on picking up the book called Problems in General Physics by I. E Irodov. Are there any other recommended books for physics?

 

[arunma]

Hello Drosser. It's good to see that you're thinking about your college career this early. Oh, if only I had thought that far ahead when I was your age!

I have several questions hoping someone could help me.

I am nearing the end of my 10th grade year. I realized I should start thinking about college soon so I taughted myself calculus from Howard Anton's book called Calculus with Analytic Geometry last month hoping I could test out of calculus next year. I found out that I wasn't allowed to and that it wasn't a good idea anyway because calculus was the basis for all future math. I made sure I understood the concepts from the book by setting a goal for myself by explaining the concept to my friends and mom (who had no prior knowledge) on an index card. I was informed after calculus there is advanced calculus. Is there any recommended books for this topic?

"Advanced Calculus" by Gerald B. Folland is a pretty good book. I used it when I took advanced calculus, and it had a good mixture of theory, examples, and pictures. Just be warned that advanced calculus is not much like the calculus you're used to. This topic focuses more heavily on proofs and mathematical theory than on practical applications (which is true of most forms of advanced math). I'm not saying it's more difficult; it's just different.

Also, I'd have to agree with the person who said that you shouldn't try to test out of calculus. When I was about one year older than you, I also taught myself calculus. I still found the actual course to be quite challenging. Taking the class gives you a certain intuition that self-study won't, and this intuition will be very useful in physics, where calculus is indispensible.

My next question involves college. I have been slacking the last two years not taking any advanced classes except math. I plan on taking 7 AP classes the last two years of high school. I will be taking AP Chemistry, AP Biology, AP Physics, 2 years of AP Computer Science, AP Calculus AB, and AP Calculus BC. I want to go to a highly rated college like MIT or Caltech and the like because I really like math and physics. Does it matter if I take AP English? Are foreign languages important (should I take 2 or 3)?

Well I can't say anything about MIT or Caltech. I went to the University of Minnesota. But English doesn't really matter. At my school we had to take freshman composition (which I got out of, since I took community college courses in high school). That was about it for the English requirement. You will want to make sure your writing skills are good though, since writing is pretty important in science.

As for foreign language, this might be an issue if you get a BA in physics, but probably not if you're getting a BS. At the U of M, a BA in physics required four semesters of foreign language, but a BS required none. You might want to check with MIT and Caltech (you can probably just spend 20 minutes on their websites and figure it out). But unless you want to get a liberal arts degree in physics for some reason, which I wouldn't recommend, you likely don't need to worry about foreign language beyond whatever is required for college admission.

However, I'm pretty sure that math PhD candidates are required to have proficiency in at least one foreign language. So if you want to get your PhD in math, it might not hurt to take some foreign language as an undergrad. They usually recommend French or German for math students.

For physics I plan on picking up the book called Problems in General Physics by I. E Irodov. Are there any other recommended books for physics?

"Physics for Scientists and Engineers" by Paul Tipler was the book I used for physics 1-3, and I found it extremely useful. It doesn't make a particularly good reference book. But it's great for someone who wants to learn the concepts.

 

[d_leet]

I have several questions hoping someone could help me.

I am nearing the end of my 10th grade year. I realized I should start thinking about college soon so I taughted myself calculus from Howard Anton's book called Calculus with Analytic Geometry last month hoping I could test out of calculus next year. I found out that I wasn't allowed to and that it wasn't a good idea anyway because calculus was the basis for all future math. I made sure I understood the concepts from the book by setting a goal for myself by explaining the concept to my friends and mom (who had no prior knowledge) on an index card. I was informed after calculus there is advanced calculus. Is there any recommended books for this topic?

To be rather technical calculus is not the basis for ALL future what you would probably consider future math. Off the top of my head, Abstract Algebra, and Topology both come to mind that do not require very much calculus for the fundamentals of both subjects. As for calculus if you want to study calculus in a greater depth, but not quite at the level of rigor as analysis or advanced calculus I can suggest Michael Spivak's book, or Richard Courant's book, both of which are highly recommended on these forums.

As for advanced calculus, which is often also called real analysis the only book that I have/am used/using is Walter Rudin's Principles of Mathematical Analysis which, although, it is a very difficult book I don't find it too terribly bad as a self study book. For a high school student, however, it might be a bit much if you haven't had experience with proofs and other upper level mathematics, but maybe I'm being a bit hypocritical here as I am still in high school. I have not looked at many other books on the subject though so hopefully someone else may have one to suggest for you.

My next question involves college. I have been slacking the last two years not taking any advanced classes except math. I plan on taking 7 AP classes the last two years of high school. I will be taking AP Chemistry, AP Biology, AP Physics, 2 years of AP Computer Science, AP Calculus AB, and AP Calculus BC. I want to go to a highly rated college like MIT or Caltech and the like because I really like math and physics. Does it matter if I take AP English? Are foreign languages important (should I take 2 or 3)?

It doesn't matter too much if you do not take AP English, however, it will certainly look good to colleges, and being able to read and write well is a very important skill that you will need all of your life in whatever career you choose to pursue.

In regards to foreign languages, to be honest I think most colleges like to see them, but if you have a good reason as to why you aren't or can't take them then I am sure they would understand. Most people usually only take one foreign language in high school, and I recall something that colleges seem to like to see three years, but again what I said before applies if you have other more important priorities.

Do you think you want to go to college to study math or physics or both? If math, may I suggest a look at the school I will be attending next year the University of Chicago, which has an amazing math department from my impression of the school, that is what attracted me to apply.

I wish you good luck with your college search, and the rest of high school. I hope that I may have been of some help.

 

[d_leet]

"Advanced Calculus" by Gerald B. Folland is a pretty good book. I used it when I took advanced calculus, and it had a good mixture of theory, examples, and pictures. Just be warned that advanced calculus is not much like the calculus you're used to. This topic focuses more heavily on proofs and mathematical theory than on practical applications (which is true of most forms of advanced math). I'm not saying it's more difficult; it's just different.

Isn't Folland's book intended to be a graduate level text? I took a look at this book the other day and it seems more difficult to me than Rudin's text.


Hmmm.. after a search on amazon I think I must be mistaken, and I am thinking of a different one of his books.

 

[arunma]

Isn't Folland's book intended to be a graduate level text? I took a look at this book the other day and it seems more difficult to me than Rudin's text.


Hmmm.. after a search on amazon I think I must be mistaken, and I am thinking of a different one of his books.

No, I'm fairly certain that Folland's book isn't intended as a graduate level text. In all honesty, advanced calculus itself is a pretty easy subject that likely wouldn't be covered in graduate school. Advanced calculus and real analysis aren't quite the same thing. Real analysis is basically a much more rigorous version of advanced calculus (I never took my math major very seriously, since I wanted to go to grad school in physics, so I just took math courses that would end up being easy A's). A graduate level text on real analysis would include a lot of material that Folland doesn't cover. Folland's treatment of integration, for example, deals almost entirely with Riemann integration. Graduate level texts on real analysis usually cover integrals with funny names that I can't spell.

Now, I will admit that the book covers stuff that a high school student would find rather challenging. But you guys are smarter than you're given credit for. Heck, when I took differential geometry my sophomore year, there was a high school student in my class! Of all the subjects out there, math seems to be something that bright high school students can excel at. So I think Folland is at the level where you'll be challenged without being swamped.

 

[d_leet]

No, I'm fairly certain that Folland's book isn't intended as a graduate level text. In all honesty, advanced calculus itself is a pretty easy subject that likely wouldn't be covered in graduate school. Advanced calculus and real analysis aren't quite the same thing. Real analysis is basically a much more rigorous version of advanced calculus (I never took my math major very seriously, since I wanted to go to grad school in physics, so I just took math courses that would end up being easy A's). A graduate level text on real analysis would include a lot of material that Folland doesn't cover. Folland's treatment of integration, for example, deals almost entirely with Riemann integration. Graduate level texts on real analysis usually cover integrals with funny names that I can't spell.

Yes I think I was thinking of a different book of his.

Now, I will admit that the book covers stuff that a high school student would find rather challenging. But you guys are smarter than you're given credit for. Heck, when I took differential geometry my sophomore year, there was a high school student in my class! Of all the subjects out there, math seems to be something that bright high school students can excel at. So I think Folland is at the level where you'll be challenged without being swamped.

Since I am one of these high school students, I understand exactly what you are talking about, and maybe I should take a look at Folland's text myself.

 

[drosser]

I'm thankful for the help people have given me.
The books that have been recommended are pretty expensive. My mom says she can pay for them because their for my education. But, a friend offered to lend me a book titled Advanced Calculus A Course in Mathematical Analysis by Patrick Fitzpatrick, that way I could save money for more books later. Is this a good book or should I consider buying Rudin's or Folland's book instead because I'd be guarateed a good source?

 

[Manchot]

Why are you taking both the AB and BC calculus exams? AB is just a subset of BC, and you'll gain nothing by taking both.

 

[drosser]

Thanks for pointing that out to me. I guess I'll choose a different counselor today because that recommendation proved even more to me that my previous counselor is incompetent. Thanks again, I could have wasted a whole year of math.

 

[turdferguson]

I guess your counselor didnt tell you there are 3 AP Physics exams, either. AP Physics B is a broader, more general exam without calculus. AP Physics C requires calc and is split into 2 full length, specialized exams: Mechanics and E&M