(Originally by Dr. Neal R. Amundson, Fall 1978. Modified by Dr. V. Balakotaiah, Fall, 1996)

• 1. In an advanced course in applied mathematics which has any substance there will be no text which contains all of the material presented.

• 2. Teachers who know their subject will always present material not in the prescribed text even when one is prescribed.

• 3. If there were a text which presented all of the material there would be no need for the lecturer.

• 4. In a course of any substance, it will not be possible for the student to understand or follow all of the arguments instantaneously all of the time.

• 5.Assuming that 4 is true it is essential that good notes be taken. Usually this is not possible. Normally the notes will be very sketchy and if they are to be of any use later, they must be expanded upon by the student as soon after the lecture as possible.

• 6. Because of 5 notes in real courses must be recopied, filled out, corrected for any teacher aberrations, misprints, errors, etc. so that the student ends up with his own text.

• 7. Notes which have not been so treated are normally almost useless for later reference.

• 8. In science & mathematics, one must learn (memorize) and put knowledge in the bank from which he (she) can withdraw later. If nothing is ever put in the bank then one is intellectually bankrupt. Most new ideas and concepts are generated by modifying existing concepts or finding connections between them. All knowledge is what one knows. If one cannot verbalize what he (she) knows then he (she) probably does not understand what he (she) thinks he(she) knows.

• 9. First year students, in general, must change their ways of studying from their undergraduate habits since in respectable graduate programs the emphasis is on understanding rather than getting through the course. This necessary shift is why many first year graduate students go into shock after about six weeks of graduate work.

• 10. If a student aims toward a PhD degree, he (she) is expected not only to understand but be able to improve by generalization or better by innovations. Good graduate programs require the latter.

• 11. 10 is what research is all about.

Offered 2022, 2023, and 2024 (not offered any longer in the future)