Spring 2017 - Introduction to Abstract Mathematics

“I have had my results for a long time, but I do not yet know how to arrive at them.” --Carl Friedrich Gauss

“Mathematics is the science of skillful operations with concepts and rules invented just for this purpose.” --Eugene Wigner

“Proof in mathematics is a creative process.  What can one resonably expect to create in 5 minutes?” --Anonymous

Announcements:

• Due to the cancellation of the first midterm originally scheduled for 2/15, I will be handing out an alternate take-home exam in class this Wednesday, 2/22.  It will cover the same material as the original exam, and will likely be closed book/notes and timed.  I'll specify the due date when I hand out the exams on Wednesdays.  If you have any concerns or questions, please don't hesitate to let me know.
• The first exam is quickly approaching!  For more information, including what it will cover and where it will take place, consult the exam information page.
• Since it seemed to give everyone so much trouble, I posted an alternate solution to exercise 4.3.3 on the homework page, called Handout 1.  In it I provide a direct proof of a stronger result which immediately implies 4.3.3 as a consequence.  I tried to write it as generally as possible, so you may find it easier to follow if you assume all the numbers involved are real!

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