I was looking at college programs with my son, and he wants o major in Mathematics. However, looking at the different programs, I noticed that there are "applied mathematics" vs. "mathematics" vs. computer mathematics" and so on. What are the different math majors offered and what are differences between these different Mathematics majors? Any input would be appreciated.
Oh, I'll take a crack at this. Applied math would be for some technology or business programs. Math math could vary quite a bit and be for a mathematics program or a science program or a teaching program or to avoid life. Computer math would cover the specialized math of the digital world. The math of the engineering and hard science world is like real hard stuff. Not to be glib but this varies so much that you'll probably have to point to some actual programs to get a much meaningful reply.
The follosing is my take on the topic. Pure math is the top over all group, of which applied and computer math are subsets. If mathematics is a separate department it will generally cover broad math topics such as calculus, analytical geometry, topology, etc. Pure math departments and studies often do not look for application of math, but study the theory behind math. Applied math is the application of math to problems often through developing the algorithms that can be used to apply math. It will often cover statistics, simulation, linear programming, and similar. Key area are computational fluid dynamics, pattern theory, and similar. Statistics is a major subset also. Computer math can be a more focused segment of applied math, but it can also go into how computers handle the applied math.
At most schools there will be a lot of overlap. Likewise, at most schools any of the variations will be suitable for a graduate math program (with the exception of math/teaching options, which might be ok for an advanced degree in math teaching). At Berkeley, for example, there's very little difference between applied math and pure math. The first two years are virtually identical. After that, there might be some differences in electives. Applied math majors might take courses that focus a bit more on applications (engineering courses, probability-statistics, numerical analysis etc.), while pure math majors might continue with analysis, abstract algebra etc. Don't be fooled, an applied math option will require lots of math and lots of theory. I don't think there's much difference in difficulty. Some people find applied courses easier; some find them harder. As other have said, it may depend on the school. At least at Berkeley, depending on the electives taken, one could do a pure math degree that looks like applied math, and an applied math degree that looks like pure math. Here are the required courses at Berkeley for pure math: Mathematics 1A Calculus Mathematics 1B Calculus Mathematics 53 Multivariable Calculus Mathematics 54 Linear Algebra & Differential Equations UPPER-DIVISION REQUIRED COURSES Mathematics 104 Introduction to Analysis Mathematics 110 Linear Algebra Mathematics 113 Introduction to Abstract Algebra Mathematics 185 Introduction to Complex Analysis And applied math: Mathematics 1A Calculus Mathematics 1B Calculus Mathematics 53 Multivariable Calculus Mathematics 54 Linear Algebra & Differential Equations UPPER-DIVISION REQUIRED COURSES Mathematics 104 Introduction to Analysis Mathematics 110 Linear Algebra Mathematics 113 Introduction to Abstract Algebra Mathematics 128A Numerical Analysis Mathematics 185 Introduction to Complex Analysis Any difference comes down to electives.
Re: Re: Mathematics Anyone? Ok...here are some of the programs/schools that we are considering (he wants to stay local, BTW): http://www.cims.nyu.edu/ http://qcpages.qc.edu/DMNS/ http://academics.adelphi.edu/artsci/math/ http://student.cuny.edu/cgi-bin/RegisteredPrograms/Programs.pl?KEYWORD=Mathematics&COLLEGE=Baruch+College&LEVEL=All http://www.hofstra.edu http://www.stjohns.edu http://www.oldwestbury.edu/mathematics.cfm http://naples.cc.sunysb.edu/CAS/ubdepts0305.nsf/pages/ams http://www.cwpost.liunet.edu/cwis/cwp/clas/math/math.htm http://www.molloy.edu/academic/math_csc/courses.htm I hope this gives this some more direction. Some of the schools chosen (adelphi &LIU) are due to possible Alumni Scholarship potential (both are my alma mater's)
I'm glad to see that your son is looking to continue on in the world of math. It looks like you have gotten a few good responses already. As one who has a pure math undergrad degree, I can definitely understand the difficulty of choosing which path to take at this point. I personally didn't start out to get a degree in math, but things happen and I changed my major from architecture to math (of course the Air Force picking up the tuition bill definitely made the decision much easier). I took the pure math route mainly because I had a better interaction with my instructors and I seemed to grasp the theoretical concepts a bit better. Of course now, being in the non-academic setting I almost wished I would have taken the applied route which may have helped me a bit more in current job (testing ICBMs over the Western Test Range and yes it is as easy as rocket science) where a deeper understanding of differential equations and engineering applicaitons. So the best advice I could give would be to guess on what the post-undergrad plans are and to take the initial courses towards that goal. Encourage your son to get in touch with the different faculty members to help guide him down the best path for his developing interests and also his particular abilities. One warning though, the junior and senior level courses are nothing like the introductory courses or high school courses. The majority of work is completing proofs of various functions, abstract group theory, etc. There is very little in the way of performing computations where you plug numbers into a formula and this also is about the time when the majority of math majors switch to another major. Jon
Re: Re: Re: Mathematics Anyone? You are fortunate to be in an area with many schools and not so fortunate in that they tend to be expensive schools. And schools like NYU can be picky on admissions. As melrog's post might indicate, I think he needs some good advice from the schools as to which math courses he should take to pursue whatever is his goal. That's especially important, IMO, if he wishes to go on to graduate school. Maybe you'll get something more specific from they who've been there.
I also majored in math. This is good advice, especially the part about the upper level courses being very abstract. If I had a nickel for the number of times people gave me the career advice "if you like math, you should be an accountant." Strangely, a lot of math has very little to do with actual numbers, and almost nothing to do with adding columns of numbers.
Thanks for the helpful advice. The other night, I was discussing this information with my son, and he revealed to me that he is interested in taking up the following in school: Mathematics and Computer Science (as a dual major) with a concentration in Computer Graphic Art. Any thoughts?
One thought is that you might want to include the local community college and SUNY-Farmingdale (haven't checked their catalog for applicability) to your search. Should he change his major to Pre-Columbian Ceramics, you'll appreciate the money saved.
Like Melrog, I have a BA in Pure Math. I took mine at York University in Toronto where most of the math faculty had come from NYU. My algebra prof had a PhD from Adelphi. I agree with Melrog that unless your son is intending to become an academic, he will definitely need some applied type courses to be “useful” to the working (real?) world. My usefulness comes from some courses in financial math and operations research taken after my BA. In the NY area, NYU is definitely the best choice for math with the world-renowned Courant Institute. SUNY at Stony Brook has a very good science program and is associated with the Brookhaven Laboratories and the Hatcheries in Cold Spring Harbor (I think) so math is probably important there. (I think last time I was on the Island I read about a teenage girl genius who took the math degree at SUNY SB at a young age) If your son wants to become an academic then he should identify the professors that he wants to study with and apply to those schools. My nephew on LI is going to George Washington for computer graphics. I don’t know if GW has a reputation in computing subjects. Best wishes----Jim
