Post 1 of Wally's Math Books: The Syllabus + Problem 1

As I opened up my grandfather's math books - Advanced Algebra by Edgerton and Carpenter, published in 1925 and Plane Analytic Geometry by Barnett, published in 1927 - I saw a piece of paper folded up.  I carefully opened it and realized it was the course syllabus! How exciting to see how a syllabus from the fall of 1927 compares to the current syllabi I write for the math classes I teach.  Before you read my observations about this document, I encourage you to look at it yourself.  Zoom in.  What do you notice? What do you wonder?  Feel free to add a comment to this blog post.

What I Noticed 

The paragraph at the top of the paper contains many instructions found in a typical syllabus. 

1. Time Spent Outside of Class - It says that each assignment "merits two hours of study and review". My syllabus says "You are expected to spend at least 7 hours outside of class working on problems or studying for this class." 
2. Number of Classes Per Week - Although I don't see how long a class is on this syllabus, the class meets 4 times each week.  This would translate into 8 hours of work spent outside of class.  My class meets 3 times each week for 70 minutes each class period.  So, it is possible that the amount of in class time may be similar.
3. Ask Questions and Get Help - It is clearly stated that the instructor Professor Waltz wants the students to ask questions during class and outside of class.  There is no mention of specific office hours.  Maybe office hours were a construct that became standard after 1927. 
4. Saturday Help Sessions - There is time and a location for help.  Saturday at 9 AM would not go over well for most students. But then again, it is a time when all of them would be available.  We currently offer virtual help sessions 11 hours a week and every day of the week. except Saturday!

What I Wondered

1. What problems should be done? The list of problems was outlined, but what did 5n, 2n mean?  As I looked in Wally's math books, I noticed that he had checkmarks beside certain problems.  Every 3rd problem or every 5th problem. So, this notation was to show multiples of a given value.
2. Assessments Where there quizzes or exams?  It says "Final Tests" on class meeting #62.  Since it says "an average of A or B will exempt from final tests", there must be something that is being graded.  But what?
3. Where are the problems found? There are two books listed and it looks like Plane Analytic Geometry book is used starting on October 31.  However, it is not clear that Advanced Algebra is the first book.  And does October 10 - 97(5, 8, 10) mean page number 97 and problems 5, 8 and 10 was the assignment on October 10th?  Maybe...but neither book has a page 97 with those problem numbers.
4. What is up with the margins? What is the arithmetic that Wally did on the side?  It looks like these may be his grades in the class and he is averaging them.  Perhaps he is trying to be sure he is exempted from the "Final Tests".

What did you notice and wonder about the syllabus?

Problem 1: This is not a problem that was assigned, but whas listed as a theorem on page 70 of Advanced Algebra.  It states "The sum of the squares of any two unequal real numbers is greater than twice their product.  That is if a ≠ b, a² + b² > 2ab."  Feel free to create your own proof and upload it in the comments or on twitter.  Make it an algebraic proof or a proof without words.  I have already started to work on a way to visualize this with Desmos and will share my solution in the next post.