You need to reassess how you learn. We covered it all in class, most of it several times. It is all in the text. So why didn't you learn it?
That is a real question for you to ponder and address. 

Here are my thoughts. Do they apply to you?

  • It takes many hours of thinking to become good at a language. Recent research shows that a lot of useful thinking occurs when you are "not doing anything." Those of you who are always doing something on your phone are reducing your learning by an amazing amount. Not only are you not learning when you are on your phone, but you are erasing your recent experiences that might have gone into long-term memory!
  • Suppose you are walking to your next class.You could be thinking or you could be on your phone. It is known that going over something in your mind right after learning it is the best way to remember it. Doing anything else actively (like paying attention to music, or texting someone) appears to erase the "learning" you might have had.
  • You have so many choices! Some are more fun and inviting that others. Who can resist electronic devices? However, if you choose to do something other than just think in your own head you will not reap the long-term benefits of hours and hours of thinking.
  • Almost all grad students have learned techniques to avoid distraction and give themselves time to think. They are more experienced than you and they have learned what doesn't work. Undergraduates need to learn sometime. When are you going to learn how you learn?

I believe what you are learning in this course will be very valuable your future math work and for your regular life, regardless of whether you go on in math. Logic and clear thought will make your decisions in daily life better. Understanding symbolic mathematics and methods of proof will make your future in math much easier. 

 

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