tag:blogger.com,1999:blog-9469908.post111721680179909833..comments2023-09-21T02:09:59.105-04:00Comments on the (Frustrated) Over-Analyst: Looking Back (EDITED)janushttp://www.blogger.com/profile/07480388456822784209noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-9469908.post-1117926531777670312005-06-04T19:08:00.000-04:002005-06-04T19:08:00.000-04:00but good to think ahead, Jasun--maybe someday you ...but good to think ahead, Jasun--maybe someday you will be an undergraduate chair for a math department.<BR/><BR/>i had wu for complex analysis as an undergrad. now it makes sense that ideas like those in the paper were brewing in his head at the time (I guess then he was also teaching his experimental courses. I'm not sure mine was an experimental course because it was numbered as the standard requirement, but it wasn't honors or anything, maybe that was the grad school track.) he had a tendency to lecture on broader things, and wanted us all to buy this book, "what is mathematics." i bought it, but confess i don't think i ever got around to reading it. he also had a reputation for grading hard and gave me the worst grade for all my undergraduate time.<BR/><BR/>it may be obvious to some that as an undergrad i didn't know that i would go to grad school in math. but i wouldn't have liked to exclude any possibilities. if two versions of a course were offered i would have probably sat in on both and went with my gut on which one to pick. i guess i would have been likely to pick the one aimed at grad school wannabes since that's where i found myself eventually, but then again, intent is one thing, result another when it comes to teaching, so my choice would still heavily depend on that intangible gut feel i get from a class during the first week.fragments of angry candyhttps://www.blogger.com/profile/11109917825562066871noreply@blogger.comtag:blogger.com,1999:blog-9469908.post-1117333863002046082005-05-28T22:31:00.000-04:002005-05-28T22:31:00.000-04:00I'm going to interpret your statement as: people w...I'm going to interpret your statement as: <I>people who won't go to graduate school <B>in mathematics</B> have no need to study math</I>. If this is not the spirit of your comment then I apologize, but I cannot vouch for fields other than my own.<BR/><BR/>Next, I don't think I'm qualified to say how much the <B>average college student</B> should study math. It varies by discipline and by choice of career (though that isn't easily determined in advance), but I would like to think that the average student should acquire some appreciation and flavor of <I>what mathematics is</I> other than an introductory sequence in single-variable calculus.<BR/><BR/>That leaves the mathematics majors who know they will not proceed to graduate school. By their very choice they have to study some mathematics, and I believe the question is: <B>what type of mathematics</B> and <B>how much</B>?<BR/><BR/>This is a hard question to answer, but it isn't too hard in some cases. For those who wish to become actuaries or educators in K-12 schools, then it might be best to have a more specific curriculum to suit their needs.<BR/><BR/>Thinking more about it, it would be nice if mathematics departments offer information (possibly workshops) on what sort of careers are available for college graduates with a background in mathematics. It is important to know what your goal is and plan accordingly for it.<BR/><BR/>The general mathematics major should study a variety of topics, and this does depend on pure or applied maths. My essential idea is that they should be aware of what the field is, have a general understanding about sub-fields of study (basic facts and theorems) and the techniques developed for such study.<BR/><BR/>For pure majors, I would suggest an introduction of equal treatment to some core areas, such as geometry, analysis, algebra, and topology. They should also have some knowledge of more specific areas such as number theory, ODE, and combinatorics. <BR/><BR/>From there, if certain areas catch their interest then they should be free to pursue them. Perhaps a requirement of a fixed number of upper-level courses will do, but there is no need to demand variety: that is what the introduction is for.<BR/><BR/>I should not say anything about applied mathematics because I don't know how that field works. However, let me reiterate a previous point: I believe it is important that applied mathematics majors have a sense of what careers in industry are like -- possibly an internship program or co-op (as the engineers do). <BR/><BR/>In this way they can determine how their coursework should be fitted to their future, and this is not isolated to mathematics: perhaps they'll find that computer programming or some background in materials science will also be helpful, and they should be allowed this flexibility.<BR/><BR/>I could be wrong about many of these ideas; I'm just a graduate student, not an undergraduate chair for a mathematics department. If any of what I've said is unreasonable, then please say so.janushttps://www.blogger.com/profile/07480388456822784209noreply@blogger.comtag:blogger.com,1999:blog-9469908.post-1117330318340664472005-05-28T21:31:00.000-04:002005-05-28T21:31:00.000-04:00Would you agree with the following statement: "peo...Would you agree with the following statement: "people who won't go to grad school have no need to study math"?Anonymousnoreply@blogger.com