- Prerequisite techniques needed: from Math 32B, 33B, 115A (recommended)
- See website of other classes: 131AH, Tao, Winter 2003, two, three, four
- One important aspect of this class is about writing proofs. You should practice as much as possible by writing, re-writing.
- There will be questions asking you to state some theorems. To memorize the statements of theorems:
+ When doing homework, write clearly, explicitly how you apply theorems.
+ Know counter-examples if some assumptions are omitted.
- Try all questions in the textbook.
- In the era of internet, one can easily google for solutions and copy to homework. That's the main reason that homework scores contribute little to the total grade.
- Work with friends.
- One main purpose of this class is to learn how to write a mathematical proof. So when grading, we are very strict. If you make an unclear argument, or jumping argument, you will get at least one point off.
- Tips for writing:
+ Read this http://www.math.ucla.edu/~heilman/teach/matharg.pdf
+ State the statement or the claim you want to prove.
+ If you use the triangle inequality, write it.
+ If you use the continuity of f at a certain point x_0, write it.
+ If you want to use a claim that is 4-5 lines backward, label that claim by (*), or (**), or (1), or (2), then state that "by (*), ...." or "from (*), ...."
+ To prove two numbers x and y are equal:
*First, we will show that x ≤ y.
(blah blah, proof goes here)
*Then, we will show that y ≤ x.
(blah blah, proof goes here)
+ To prove two sets A and B are equal:
*First, we will show that A ⊆ B.
(blah blah, proof goes here)
*Then, we will show that B ⊆ A.
(blah blah, proof goes here)
+ If you are curious how a mathematician writes, see https://terrytao.wordpress.com/advice-on-writing-papers/ and references therein.
-Instruction in midterm 1:
Read problems very carefully. If you have any questions raise your hand.
You are allowed to use only the items necessary for writing. Notes, books, sheets, phones are {\bf NOT} allowed, please put them away. You can write on the back pages.
Justify your answer. You may cite theorems, problems, exercises proved, learned in class. When you are not sure if it was taught in the class, write it as ``Claim'' or ``Lemma'' and prove it later when you have time.