Linear Algebra Spring 2017
Comments on the first exam

Scores for the first exam have been posted on blackboard.  Exams will be returned in class on Tuesday, 2/21/16.  It is important that you come to class to pick up your exam because you are assigned to work with a group to write up a set of solutions that will be due Tuesday, 2/28.  Exam solutions are a required component for the course portfolio.  Specific directions are posted here.  

When you get your exam, please double check that I have added up the points correctly and also that the score on your paper is the same as the one posted on blackboard.  I try hard not to make errors totaling or recording scores.  But if an error has been made, I will want to correct it as soon as possible.

The exam scores are shown in the histogram below.

exam 1 histogram

The histogram shows that the class as a whole did pretty well.  Nearly 1/2 of the scores are at 90 or above, and all but one of the scores are at 80 or above.  At this point nearly everyone is earning a satisfactory grade, and most are on track for a final grade of B or better.   To interpret your exam score, you should understand my grading system.  I work with a numerical scale from 50 to 100.  When I grade the answer to a problem, I first make a judgement as if I were assigning a letter grade to that particular item.  An A answer should receive between 90% and 100%  of the points;  a B between 80% and 90%, and so on.  So if you receive half the points on an item, that means I consider the response to that item as a fail.  Anything less than 70% on an item indicates your response was judged to be unsatisfactory.

Additional Comments About Common Errors
For several problems, I had a hard time understanding what students meant by their answers, and often this reflects misuse of terminology, such as mixing up the terminology that concerns matrices, systems of equations, and sets of vectors.  Here are some common examples of misuse of terminology:
If you use any of these, you are mixing up meanings and using language imprecisely.  You may know what you mean, but you are not communicating that knowledge accurately, because I can only guess about what you mean.   And if you are not careful about the fine distinctions in the use of terminology, that can hinder your understanding of lectures and reading assignments.  When you hear a term used in lecture or see it in the reading, you will not fully understand whatever point is being made unless you attach the same meaning to the term that is assumed by the speaker or author.   Say for example that you have an incomplete or incorrect understanding of what is meant by a parametric vector form for the solution set to a system of equations.  If I say in lecture that for a homogeneous equation the parametric vector form for the solution demonstrates something or other, you will not be in a position to see how or why my statement is true, or even when the statement applies.

The statements of theorems and definitions in the book are carefully formulated to say precisely the correct thing, and to say it in a concise way.  If you really understand what those statements mean, and why they are true, then you have gone a long way toward mastering this subject.

Proper Use of Math Language is Important.  Some students find this insistence on correct use of language annoying.  Some think that I am just way too picky a grader.  I understand that point of view, but there is a method in my madness.  The fact is, extremely careful use of language is a significant contributor to the amazing record of mathematics in avoiding error and identifying truth.  In just about any other field you can name, theories come and go, and what was accepted lore one day becomes discredited or at least reinterpretted the next.  Not so in mathematics.  Once we know what is true (once we have proved theorems), those results persist pretty much forever.  But obsessive care with the precise use of language is one of the prices we pay for that.  As a math teacher, I want my students to at least understand in overview what the mathematical method is and how it works.  You should know not only what tools linear algebra gives you, but how we know that these tools are valid, and when they are applicable.  Part of this requires careful use of language and terminology.  I know that this kind of attention to detail is not appealing to everyone.  But if you want to really understand math, that is what is required.