Courses, homework, exams, etc.

The typical program for a mathematics major (whether prospective teacher or not) is outlined in the catalog, as well as in the Guide to Typical Programs, so it won’t be repeated here.  Instead, we’ve elected to present some “factoids” about the program that may help you make sense of it all. Student reviewers gave thumbs up  to an idea they thought was particularly important.

• Courses become more rigorous as course numbers increase  – more reasoning and less routine manipulation of symbols.
• Symbol manipulation has its place at all levels.  Think about these first two ideas.
• Proof is what determines if a mathematical conjecture is true, not lots of examples.
• Examples have their place at all levels.  Think about these two ideas.
• Homework – do it whether it is collected or not.
• Math is not a spectator sport; you have to do it to learn it.
• Some problems are meant “not so much to be solved as to be tackled.  The value of (such) a problem is not so much in coming up with the answer as in the ideas and attempted ideas it forces on the would-be solver” -- I. N. Herstein
• Ask questions in class; ask other students questions.  
• Come in and see your professor in the office & ask questions.
• Each day, work on learning that day’s definitions, and theorems, as well as reviewing earlier definitions and theorems.  Don’t wait and try to cram them all in the night before an exam.  
• Expect to use ideas, theorems, and definitions in the daily homework.  The author went to great pains to find problems that would give you some practice in using those ideas, so don’t short-change yourself by trying to do the homework by trying to find an example you can just mimic
• Prepare for an exam by doing lots of practice, culminating in a “dress rehearsal”— giving yourself practice in a realistic way.  Solve practice problems and write out solutions just as you would be expected to on the test.  Time yourself.
• Keep your math course notes.  Bring them with you to campus each year.  You will need to look up ideas for use in later courses and your earlier course notes are good reference sources since you know where things are in them.
• Keep your math textbooks; don’t sell them.  Bring them with you to campus each year.  You will need to look up ideas for use in later courses and your earlier texts are ideal reference books since you know where things are in them.
• If you plan to teach, you may wonder why you have to learn all the “advanced stuff”.  Here are a couple of reasons.  Our goal is that you become a practitioner of the discipline – you need to be a good mathematician – before you attempt to teach it.  That means knowing a lot more than just the minimum you need on most days in a class.  Secondly, you may be called on to teach an advanced course, now or in several years.  For example, without a good grasp of real analysis (MA 431) you’ll be in over your head in trying to teach calculus.  In such a case, you may well use some of the “advanced stuff” in your class!