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--- math121a-f23:september_6_wednesday [2023/09/07 01:02]
pzhou
+++ math121a-f23:september_6_wednesday [2023/09/07 01:10] (current)
pzhou [post lecture note]
@@ Line 40: / Line 40: @@
 can you define multiplication on it?  $( 1+ x + x^2) (2 + x) = ?$
-Does every nonzero element has a (multiplicative) inverse? For example,  $x$  has inverse, $1/x = x^2$.  $x+1$  has inverse, we have
+Does every nonzero element has a (multiplicative) inverse? For example,  $x$  has inverse,
+$$ 1/x = x^2.
+ $x+1$  has inverse, we have
  $\frac{1}{1+x} = \frac{1-x+x^2}{(1+x)(1-x+x^2)} = \frac{1-x+x^2}{1+x^3} = \frac{1-x+x^2}{2}.$
+Does  $x-1$  has inverse?
 -------
 you may ask:  why we care about other 'field'? I am happy with  $\C$  and  $\R$ . I don't have a good answer for that, maybe you will find some application some day.
+==== Exercise ====
+(part of homework)
+Read Boas Ch2, section 1 - 9,  find 5 interesting problems there and do it. (copy down the problem, so the grader / reader know which one you are doing).

Lecture Notes