Undergraduate Mathematics Major

College Majors
1

<p>I would like to start a discussion on the undergraduate Mathematics curriculum in the US, in reference to the following sources:</p>

<p><a href="http://maa.mc.edu/proceedings/spring2000/leavelle-etal.pdf%5B/url%5D"&gt;http://maa.mc.edu/proceedings/spring2000/leavelle-etal.pdf&lt;/a>
Moving</a> Beyond Myths: Revitalizing Undergraduate Mathematics
[ go to "read the book online" and peruse relevant / interesting sections ]</p>

<p>In the opinion of the readers, is there a problem with mathematics education? Should the use of computers in mathematics be emphasized or downplayed?
Should the dichotomy of pure/applied math persist?</p>

<p>I'd like to hear some thoughts on this.</p>

2

<p>Whats the point in using technology, when its not needed? Especially in a math curriculum where the focus is on learning logic. Anybody can read a tutorial on mathematical software. This can be done after they graduate. College is about learning critical thinking skills and logic(we can all agree that this is really what makes a person succeed, if you don't believe me, just read The Bell Curve(i don't agree with everything in this book, but it has some good pts backed by extensive research). And math does a pretty good job at this. Technology is just a waste of time because 1) it can be learned quickly 2) it does not require much skill and does not develop much skill.(note: I am not dissing CS majors because its just math in a different form of logic done on a screen)</p>

3

<p>Do you think, though, that mathematics students could benefit from classes in computer science topics, as many computer science students have benefited from classes in purer math?</p>

4

<p>Yes, it would give them a new perspective in problem solving. But I do oppose the usage of computer science in a math class. </p>

<p>I've discussed this in the stereotype thread.</p>

<p>
[quote]
Really, its already happening in the US where more and more applications are used in introductory college math courses such as calculus. The issue is double faceted. Almost always this leads away from mathematical rigor and focuses on computation and regurgitation with a mix of applications. This lowers the level of critical thinking among college science/engineering students and mathematics students. Of course you can make the argument that critical reasoning is not reduced because the applications need not be regurgitation. While that may be true, its also clear that the problems become limited in difficulty due to the time constrants. A math professor may not have enough time to throughly cover the principals of engineering or physics or any other field requiring mathematical applications. Thus, the problems are often very simple and lack creativity.</p>

<p>This leads to the next problem: redundancy. Most applications in math revolves around physics problems and occasionally other problems within natural and social sciences. This applications are likely to be discussed ad nauseum in their respective classes and need not be discussed again in math. For example, when doing a torque problem, one has to use integral calculus to find the moment of inertia. This is also covered in calculus but is dumbed down to simplify things. If you want to learn how to calculate moments, you should just take a physics class. Not a math class. Unfortunately, many engineering students are having their education robbed from them after the revelation that they had not learned a single thing in math because it was all covered in physics. Most likely they would have not only learned more in theory oriented calculus, they would have also become stronger critical thinkers and problem solvers.</p>

<p>Moreover, even without application, math majors are still very useful in the sense that they develops strong thinking skills. And its precisely these critical thinking skills that makes one successful in his/her jobs. Also, these skills are useful in standardized testing which, believe it or not, is still the gate to many high end careers(med, law etc).</p>

<p>A poster from the columbia spectator mentioned: </p>

<p>'In 5 minutes of searching, I found this...If you rank the average GRE scores by department, physics/astronomy rank 1st in quantitative, verbal, and writing. LSAT scores ? Physics/math takes it again. GMAT? Physics is first again. If you look at the combined scores for the three tests, and add in the average salary for graduating seniors, the top three are physics, math and economics. Surprise?'
Down-grading | Columbia Spectator
Why Economics?

[/quote]
</p>

5

<p>I do not oppose the use of technology in math classes in general. For example, I could imagine some fun projects with Mathematica in Calculus classes. Centering pure math classes around technology might not be the best idea, but a computer project every now and then could help students gain a deeper understanding. I also know a math professor who does research in combinatorics that relies heavily on the use of technology - so yes, computers can be very helpful even in pure math. </p>

<p>I am more critical with the suggestion that math majors should (have to) take classes in fields that rely heavily on math. I should mention at this point that I am coming from a pure math perspective and I like the field in particular because of the logic and paper-and-pencil problem-solving involved. I do have some background in physics and computer science and I have decided for myself that applied math is not something I am interested in. If I had to take more classes on applied topics, I might be a philosophy major instead. </p>

<p>In some parts of the worlds math majors are required to minor in another subject like physics, computer science, economics or education, but I am glad that this is not generally the case in the US. Maybe some students would greatly benefit from more exposure to applications, but for other students (and many researchers in mathematics) math simply is an end in itself.</p>

6

<p>Here's a brief summary of the Chinese maths curriculum.</p>

<p>(1) Starting on grade 11, high school students must choose from one of the two broad concentrations: (a) science and technology, (b) arts, literature, economics, and management. I will only discuss the science/tech concentration.</p>

<p>Those who take the science/tech concentration pursue an uniform curriculum, which covers the equivalent of (a) calculus 1 and 2, some of calculus 3, (b) calculus-based physics 1 and 2, (c) one semester of stats, (d) half a semester of discrete maths. Emphasis is placed on proving theorems and solving multi-step, difficult problems.</p>

<p>Maths majors in college take few general education classes - usually (a) 1-2 semesters of Chinese, (b) 4-6 semesters of English, (c) 1-2 semesters of philosophy+sociology+communist propaganda, (d) 3-4 classes from biology, chemistry, geology, etc; (e) 1-2 classes from arts/economics, etc.</p>

<p>Most non-major classes meet only 1-2 times a week (such as Chinese). Some meet only 1-2 times a month (such as philosophy+sociology+communist propaganda).</p>

<p>Some major classes meet infrequently, too. Classes in very specialised topics of maths might meet only a few times in the semester.</p>

<p>Other classes meet frequently, however. There could be 5 lectures a week on important subjects like advanced calculus and differential equations, then 5 discussion sessions.</p>

<p>So it is possible for a student to take 10 or even 15 classes in a semester.</p>

<p>The first class for maths majors is not basic calculus since it was covered in high school. some schools have a "review" class that develops on high school calculus, others go straight into linear algebra and differential equations.</p>

<p>Because of the availability of pirated Mathematica and Maple, many students use these programs on their own for solving problems beyond calculus. Not many schools use these programs in class. Of the schools that do, they use them sparingly because the emphasis is still on proving theorems and solving multi-step, complex problems.</p>

7

<p>As a math major, I can honestly say that you don't even need a calculator. This is generally a Good Thing. I guess I should explain.</p>

<p>Much of the UG math curriculum revolves around--or should revolve around--proving theorems and solving problems. </p>

<p>"Calculus" and the other nonsense in high school isn't really emphasized in the math major, there's a field called analysis.</p>

8

<p>Just out of curiosity, did anybody look at the article[s]?</p>