MAT 271

Proof writing is hard.  While grading the latest homework, I am struck by the lack of questions.  I know when you are stuck it is easy to put your pencil down.  But if you are stuck, the proper action is to think of a question(s) to ask.  If you don't know how to prove 3 is a limit point of (3,4), then what can you ask me or a classmate that can help you (besides something like "What's the answer?")?  

Being stuck is part of being a mathematician.  Being stuck isn't bad.  It's just part of the process.  You may have been told in the past (implicitly or explicitly) that doing math quickly is what counts.  You may have been told in the past that being stuck is bad.  But that's all wrong!  Problem solving takes time, and getting good at problem solving requires problem solving skills, which you are developing now.

Developing the ability to do proofs reminds me of something from science.  When ice turns into water, there is a transition period where the temperature stays constant.  The energy is going into the transformation of states, so the temperature stays the same during the transformation.   Your efforts may not appear to be making a change, since you are often stuck on a problem.  The message here is that the energy you are exerting is going into your own, personal transformation.  You may not see the differences in the usual ways, and the results may take a while.  Giving up in the middle of the process is perhaps the biggest disservice you can do to yourself.  Keep pushing the rock...

Dr. Y

How big is a Trillion?

A trillion is a milllion million.  The world economy has lost trillions of dollars recently due to the global financial crisis.  One trillion dollars is enough to buy one million $1 million homes.  So pretty much everyone in LA city could live in a mansion for that amount of money.  Or you fund the CSU system for about the next 200 years.  It's a lot of money.

MAT 521: Next week is spring break.  We will meet next on April 6.  Your project outline and bibliography are due along with 41-45 from Clark's book.

MAT 308: The last set of problems was more challenging.  Don't be discouraged.  Rather think of this as an opportunity to review some math that you may not have used in a geometry context before.  Algebra and Geometry are not separate fields. They are closely linked and as you have seen.  

MAT 271: Proof writing is hard.  Period.  Your role as 271 students is to spend a lot of time thinking about the concepts and breaking things down as best you can.  Doing nothing (i.e. quitting) is not an effective strategy.  Never give up.  Try simple cases. Then try to generalize.  Believe in yourself.

Dr. Y

PS  This whole flap about AIG is way out of proportion.  Our economy is losing trillions.  The bonuses to AIG is less than 0.01% of the problem.   Reminds me of Dr. Evil... Link

Special Cases

When you're stuck on new material, try to break things down into simpler cases or special cases.  By working out the special cases you can think about the ideas you are stuck on in a more concrete form.  Even though the special cases may not solve the original problem by themselves, the insights gained are often necessary in the development of the final solution.  

A funny comic from the Far Side. 

School and Work

We see this all the time at CSUDH.  Many CSUDH students take on too much.  They work 30+ hours and try to take a full load of classes.  When midterms hit, they are sunk.  Bad grades, stress, too much homework, etc.  It's no fun and not good for you.  If you work more than 20 hours per week, I strongly advise you to be a part time student and take two courses per term. Enjoy the process of learning and get good grades.

There are options out there to get loans and scholarships.  Go to the financial aid office and see what is out there.  If you can work less, then you can take more classes and graduate sooner (while maintaining good grades).  

Homework for next week has been posted.  Click through the links at www.stanyoshinobu.com

Dr. Y

Emailing Attachments

Hi all,

Just a friendly reminder that if you email documents please try to use a universal format such as .pdf or .txt.  MS Word is notoriously incompatible with itself across different versions and platforms.  

gmail has a nice feature that allows you to fetch email from a pop server.  If your DH email account has the pop server enabled, then you can use gmail to fetch your DH email, and then forward it (if necessary) to your preferred email account.

Spring Forward

FYI -- Daylight savings begins on Sunday.  So come to class next week with more sunshine... and more proofs! :)

More on being stuck -- I've noticed in grading some of the problems that some of you are still leaving blanks.  I know what it's like to be stuck.  What I suggest you try is to at least look at some specific examples.  Then you are emphasizing on your homework what you CAN do.  Learning will be much more enlightening when you see a solution presented by a classmate.   This advice is especially important for MAT 271 students.  You are on your way towards upper-level math classes.   When stuck, break it down, take your time, and think about what it making you stuck.

One more thing -- if you have not read "Fermat's Enigma" by Simon Singh, it is highly recommended.  It reads like a mystery novel, and gets into the history and proof of Fermat's Last Theorem. 

Square Root Day

Hi all,

Today is square root day.  The date is 3/3/09.    What are the other square root days are there for each century?

Week 6

Hi all,

It's another stormy Monday.  Well maybe not stormy...  This is a friendly reminder to tell you to check your CSUDH email regularly. Blackboard uses your CSUDH email.

MAT 521 -- I enjoyed the discussion on blackboard.  Many good questions are being asked, and I like that.   This week we'll be doing more Euclidean Geometry as well as discuss Schoenfeld's article.  For next week, you need to come up with your topic and abstract for your project as well as a working title.  (You can of course change your title later).

MAT 308 -- We're going to be doing some measurement and then the Pythagorean Theorem.  Good times!

MAT 271 -- As we head into Topology, I want to emphasize that getting stuck is part of being a math or science major.  Enjoy it.  Yes, enjoy it!  It's when you learn.  Getting stuck and then unstuck is where you learn, and what we will work on this term is to help you develop tools for dealing with being stuck.  (I know this sounds like MAT 143 -- 271 is like the big brother of 143).   

Dr. Y