In what math level do you learn about bases?

Question

I never heard of unwritten bases on numbers (that are not logs) that give out different results?
Is this in a higher level math? I am in Calc 2 now

Answer 1

I learned about them in computer science and in number theory. I actually learned about binary in highschool though, but that is just an introduction to bases. Sometimes ed majors learn about different bases in their math for ed major classes. Also some math for liberal arts classes talk about bases.

If you are interested in the subject you can read about bases in Number Theory by George E Andrews. It is a Dover book so it is under $10. This would be a good book to read if you are considering higher level mathematics.

Here are some web pages you may find interesting:
http://mathforum.org/dr.math/faq/faq.bases.html
http://www.math.com/students/converters/source/base.htm

Answer 2

Mathematics is not built like a column where everything is in a linear relationship to everything else. Let's say that calculus 1 is the lowest level, then everything starts branching out from there (or even before). After calculus 1, one could then study statistics, probability, discrete mathematics, linear algebra (a beautiful course), real analysis, abstract algebra, graph theory, or more calculus.

I don't recall learning about bases (other than what is encountered in the typical logarithm chapter from college algebra) until I was studying a freshmen-level electrical engineering course. The professor thought it would be a cool idea to introduce base n along with the usual bases 2, 8 and 16. Using various bases is quite intuitive and interesting in its own right. The level of sophistication required to study various bases is somewhere about high school algebra 1 or 2. It is definitely not a calculus-level topic. On a side note, our mathematics could have developed just as well if we humans only had 8 digits instead of 10.

Update: Abelian groups in 4th grade? I suppose we could all say that we studied group and field theory in elementary school since we did...in a way. However, we didn't realize these facts until we were knee deep in abstract algebra at some college or university. I can just see an elementary school teacher trying to answer Johnny's question, "Miss, what is a group? Or, "Miss, how do we know a group is Abelian?"

Answer 3

There is not much to learn. All you need to remember is that you can use any number system defined by:

...+ b^3 + b^2 + b + 1 + b^(-1) + b^(-2) + b^(-3) +....

where b is your 'base'. Furthermore, you can represent any number in this base by using
numbers 0 through b-1. Thus if you decided to use base 3, your digits are 0,1,2. If you decided to use base 16, your digits are 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15. Rather than use double digits for 10 thru 15, you could use: A,B,C,D,E,F where A=10, B=11, C=12, D=13, E=14 and F=15. So for example the number 1E in base 16 is really the same as 30 in base 10. You get the idea?

Answer 4

In Ontario, (Canada) in grade 4, in 1966 we learned about number bases. I remember doing questions in base 4 and base 7. Later in engineering in 1976 we got into base 2, base 8 and base 16. Obviously a computer engineering class! In grad school in 1984 learned about algebra, abelian groups again but with a twist -looked at it with a base 2 system -was the basis for some computer communication theory involving checksums, public key cryptography and so on.

Looking back on it, I remember taking Abelilan groups in the grade 4 class. Now that seems a little astonishing, but it is true.

Answer 5

Whenever you want. The idea is very simple: the base is the group size necessary to pop over one place value. So in base ten, "1" is one, "10" is ten ones, "100" is ten tens, and so on.

In base three, "1" is still one, but now "10" is three ones, "100" is three threes, and so on.

Multiplication, division, addition, subtraction, etc. all work in whatever base you are using, because math exists no matter how many fingers you're born with. For more, find a copy of Courant's "What is Mathematics?" (Oxford University Press).

Answer 6

I learned about base 2 through 10 in 5th grade. Learned about octal and hexidecimal together in college electronics.

Answer 7

You won't usually study bases in a math class. If you're interested in them look into an introductory computer science class.

Answer 8

I learned about bases in 7th grade.

Answer 9

Bases?

What level?

Algebra.

You're in calc II?

What did you do in Algebra.......doodle?