College Mathematics Overview (107664)

This Open Educational Resource  site contains an overview of the essential mathematics for a STEM-education, including:

• College Algebra 
• Precalculus
• Differential Calculus
• Integral Calculus
• Multivariable Calculus
• Linear Algebra
• Differential Equations

Additional topics will be added as time and sanity permits.

The publicly available portion of this site has static information:  video lectures on topics and text links.  

If you register for a (free) MyOpenMath account, you can add this course and get access to additional material, including graded review problems that you can use to test your understanding. 

To gain access to these additional features, you will need a (free) MyOpenMath account.  Go to MyOpenMath and follow the instructions for creating a new account.

After you've created an account, you can add this course using the CourseID:  107664.

You will also be asked for an enrollment key.  The enrollment key is a combination of the term (spring or fall) and the four-digit year.  For example, if you're joining this course in the spring of 1984, the enrollment key would be spring1984.  (This is used to determine when an account was created and, eventually, to clear out old accounts)

With a free account, you'll gain access to math questions with answers.  Most of these will be graded by the MyOpenMath system as soon as you submit an answer, giving you immediate feedback of whether you're on the right track.  (Some of the questions require manual grading; these will not be graded, but will give you some idea of some of the more rigorous questions you might encounter later in your mathematical studies)

Please note that we are continuously updating the questions, which means that from time to time, your scores will be reset.  

Successfully learning mathematics on your own requires the right combination of instructor and student.

First, you'll need to get a (free) MyOpenMath account to access the assessments.  This is important, because it's easy to think you've gotten the right answer in math.  But if you don't have a way to check it, you'll never know.  

Once you have a free account, go to the appropriate section.  Each section begins with a lecture, which consists of a sequence of short video lectures followed by some problems.  Watch the lectures and answer the questions that are below it.  If you don't get the answer correct, you may want to review (literally) the lecture to pick up what you've missed.

The questions in the "lectures" are the simple question that evaluate your understanding.  However, to really understand the material, you have to engage with more complicated problems, so each section also has an assignment, which are questions based on the lectures but are typically more involved.  You should do these next.

After you've done the assignment, try the quiz for the section.  Some of the problems are easy; some are difficult. Some require you to go through many steps before getting an answer, because they're trying to develop an idea that you'll need for later.  You can retry any problem as many times as you want.  

And you should.  Success in mathematics relies on being quick and accurate.  That's because the problems you do here are "step one" of many.  If it takes you five minutes to add two numbers, you will never be able to finish a problem in a timely manner.  And if you can add two numbers in a a second, but get the wrong answer, then you will be able to finish a problem...with the wrong answer.

So you want to fail a math class?  Here's how, in three easy steps!

Students say the exams are nothing like the homework; the instructors say they're over the same material.  How's that possible?

The courses are color coded following the rainbow scheme (red-orange-yellow-green-blue-violet), with red the most fundamental and violet the most advanced.  If you are upset by this scheme because you think it has a different meaning, you are overly sensitive and paranoid and should probably seek counseling.

Roughly speaking, courses within a color group require the same mathematical background (though of course, calculus 3 will require you understand calculus 2 and calculus 1).

A study recently published by the National Academy of Sciences emphasizes the importance of repetition.  

Reduced to its essentials:  It doesn't matter how much time you spend on something.  What matters is how many times you do something.

The research suggests a magic number of seven:  Do something seven times, and you've probably gotten it down.