<p>
I’m not arguing that it’s useless. I’m arguing against the notion that knowing about the two-tailed t test is extremely practical, but knowing what a limit is is somehow completely wasted time. (I know you are not making this argument)</p>
<p>
</p>
<p>The post you are apparently replying to was in response to the discussion about “rushing to learn calculus instead of more practical things like balancing a checkbook”. To which the previous poster replied that, while the previous poster learned calculus but not balancing a checkbook in school, learning how to balance a checkbook took only five minutes.</p>
<p>In any case, I remember when checkbook registers and paper bank statements contained instructions on how to balance your checkbook.</p>
<p>Also, the post about rates of change was not about simple percentages.</p>
<p>
</p>
<p>As someone who studied some CS courses for majors and had many CS major friends/colleagues, we’d all disagree with that. If you don’t have, at an extreme bare minimum, a strong grounding in algebra and some geometry…you’d certainly be among the 50%+ who would be weeded out of the intro courses. If you fail to take post-calc seq courses such as Differential Equations, linear algebra, and algorithms…you’re unlikely to be anything more than a mediocre code monkey at best. </p>
<p>One friend who works for a major computer technology company once summed up CS as “mathematical theory with electricity.” No math required in CS…that will cause anyone who has studied CS at a decent program to be ROTFLOL.</p>
<p>
</p>
<p>Huh? A student two years ahead of normal sequence should complete AP Calculus BC in junior year, not senior year:</p>
<p>7th: Algebra I
8th: Geometry
9th: Algebra II
10th: Trigonometry / Precalculus
11th: AP Calculus BC
12th: Sophomore level math at a community college if desired</p>
<p>
</p>
<p>No idea where you got “no math required” in computer science from, because computer science does use considerable amounts of math in some areas, although it is usually not the continuous math of calculus and analysis. Discrete math, algorithm and complexity theory, language and automata theory, and number theory for cryptography all come into play in computer science.</p>
<p>Of course, less technical areas like IT or MIS are often taught through business divisions, and contain little math beyond “calculus for business majors”.</p>
<p>Well, ucb, since we don’t have a national math curriculum, different states and districts teach math differently. Here, if you are two years above grade level the sequence goes:
Seventh grade algebra I
Eighth grade geometry
Ninth grade algebra II
Tenth grade precalc
Eleventh grade calc a-b
Twelfth grade calc b-c </p>
<p>Statistics are another course, not in that sequence, taken usually in 11th or 12th grade. We do have kids who move above and beyond what I’ve listed, and the district provides teachers for the few kids who have advanced faster than that sequence. Those kids do end up taking classes at local colleges.</p>
<p>IMO, you don’t have to understand a whit about calculus or ever read Plato. But, to have a flexible mind and to be broadly educated, you need to sample from the buffet, some breadth, some depth. As well as the variety of learning skills and thought processing that different disciplines offer- different emphases, analytical and reasoning styles. I find that “mind-expanding.”</p>
<p>Remember, we started with a discussion of the values to liberal arts- not requirements to enter a profession or follow along with the very best specialists.</p>
<p>With a BS in Electrical engineering and English I have two horses in this race. My EE degree got me my first job, and helped me be a problem solver as a manager. My English degree was also very helpful to rise through the management ranks. It taught me to write, to present, to listen, to participate in a discussion/meeting. Most importantly it taught me to be comfortable with ambiguity, how to take a position and run with it when there is not necessarily a “right” answer. </p>
<p>I have encouraged my Ds to go to colleges with some sort of distribution requirements or core curriculum. I think it really helps to exercise both sides of the brain in college.</p>
<p>This thread has encouraged me to un-earth and revise a response that I gave to a very specific question about studying science at W&M.</p>
<p>As a liberal arts college alumnus with a degree in Computer Science (granted, not physical or biological science, but science nonetheless), I feel that a liberal arts college is an excellent place to study science. My reasons may be a little different than those of others.</p>
<p>Regardless of which “STEM” track you choose, you will receive the instruction necessary to understand technically what is needed. In my case, the ability to do binary math, understand algorithms, etc.</p>
<p>So why does a liberal arts education matter?</p>
<p>English - The most important part of a STEM education. You must be able to understand a problem in human terms (not technical terms) first. Conversely, once you feel that you have a solution if you cannot clearly define what it is that you are trying to accomplish in everyday English you will struggle. In short, take all the writing and literature classes that you can. Also, you must be able to listen to and understand when other people communicate to you why your idea really is great or is not as great as you originally thought.</p>
<p>Additional Languages (Spanish, French, Arabic, etc.) - In today’s economy, you will work with non-English speaking people potentially in non-English speaking countries. </p>
<p>Economics / Business - You do not need to be a financial wizard, but you had better be able to understand basic concepts like ROI, cost variances, EBIT, and Marginal Utility if you want to be able to pitch your “technical” project in order to get funding. Even if it is the greatest thing in the world, if you cannot communicate why your project will actually benefit the business, it will not receive attention.</p>
<p>Accounting / Finance As a STEM person, you may be appalled that there are whole disciplines that function on Generally Accepted Accounting Principles and that the world is not always controlled by theorems, corollaries, and proofs. Get used to it. Even things as seemingly math-ey as Accounting have grey areas.</p>
<p>Politics / Government / Geography / History - At a macro level, you need to be able to understand regulations and explain why your project is necessary to keep the CEO out of prison, even if it has no ROI. On a personal level, it helps to be able to relate to the experiences of your new co-worker from Georgia (the state or the country). Learn from History and not repeat some of the same mistakes that other individuals and groups have made.</p>
<p>Math - Yes, you will need to understand at least basic algebra and geometry in the real world. More importantly, understand that the most important part of math has nothing to do with numbers. It teaches you how to logically solve problems, follow directions, and back up your solutions… always show your work :)</p>
<p>Religion - This is related to Languages above. You will need to be able to relate to people with varied religious backgrounds. Try to get at least a basic understanding of as many religions as possible. Understand that not everyone has the same religious point of view as you and that does not make them heretics.</p>
<p>Ethics / Philosophy Be able to see both sides of both sides. Guess what? Your well thought out conclusion based on raw, unfiltered data may be completely different from someone elses conclusion based on the same data. There is a chance that neither or both of you are right. Also, please learn that just because something can be done does not mean that it should be done. Learn to think about the implications of your work before you do it. At a minimum, it is your duty to raise any questions about that which is being asked of you.</p>
<p>Psychology / Sociology / Anthropology - You need to have an understanding of what motivates and demotivates people and, yes, sometimes influence their behavior. At the micro level, try to at least pay attention to cultural differences to avoid that embarrassing faux pas. At a more macro level, there are whole worlds outside of your neighborhood. Get exposed to them. You may be living in one of them someday.</p>
<p>Physical Education / Kinesiology As cliché as it sounds, you really cannot be at your mentally fittest if you are not reasonably physically fit also. Eventually, you will not be able to survive on a coffee or beer IV drip. Also, sometimes you need to be able to turn off your brain or use it in a completely different way. It is amazing the level of clarity that comes from being completely physically exhausted.</p>
<p>In short, for science to be successful, you need to be able to communicate with and relate to a wide range of people. The ability to create an isomorphism between technology and the “real” world is imperative. By way of examples, here are some personal experiences where a liberal arts “science” education has helped me.
- Science / Technical - I admit that I have converted license plates from hex to decimal while sitting in traffic.
- Developed a presentation that justified the need for a System Development Life Cycle and Programming Standards entirely based on Monty Python and the Holy Grail. This mortified my boss (an engineer), but I got a full “pardon” from the CIO and the funding to move ahead with the project.
- Work daily with plant floor workers and have to explain in human terms why a particular technology helps them (safer, more efficient, etc.). The guys will also appreciate it when you explain how to use technology to improve their Kim Kardashian wallpaper, but I digress.
- I worked in Brazil for a while. Although Brazilian’s speak Portuguese, I was able to apply the Spanish that I learned in college to be able to relate it to Portuguese and at least figure out enough Portuguese to survive and read basic email, instructions, etc.
- Yes, I did have a co-worker from Georgia (the country) with whom I was able to discuss what I learned in my Poli. Sci. classes to reality. We became good friends.
- I work daily with Christians, Hindus, and Muslims. I have applied knowledge from comparative religion classes to have a basic understanding if for no other reason than to know when to stop a discussion before it gets out of control.
- I have performed countless technical interviews for hiring.
- I have written countless performance evaluations that not only conveyed praise as warranted, but also motivated many purely technical people to advancement within the company.
- I use basic math to be able to determine how much of a given product can fit on a truck based on dimensions and weight. Yes, I even have to calculate the volume of a cylinder and determine grams per square meter regularly.
- I have worked on a project that used computers to harvest and combine personal and financial data about individuals and their families. It was my duty to explain to the company why their handling of the results was potentially negligent both morally and legally.
- I have worked on technical solutions that would miss the point without an understanding of female reproductive rights in the affected countries.
- To fulfill a requirement, I began martial arts training in college. 25+ years and 4 black belts later, I still train, but really enjoy working with kids and seeing the difference that it can make in them.
- Used Bach’s Crab Canon to explain to two people why what they thought were opposing views were really saying the same thing.</p>
<p>CS Majors: While you are learning the latest programming language (C++, C#, PHP, Python, JAVA, JavaScript, etc.), be sure to learn English first.</p>
<p>At the UG level, colleges job is not to make you the next Albert Einstein. It is to teach you how to become the next Albert Einstein. In case you are unfamiliar with him, Albert Einstein was a German, pacifist, violinist who dabbled in STEM related subjects too.</p>
<p>Now, in the spirit of this post, please proceed to rip it apart.</p>
<p>
</p>
<p>I got my undergrad degree in EE overseas. It was then a 5 year program after 11th grade. Being that it was from '70 to '75 I honestly don’t remember exactly what all it covered. In the first couple of years I believe we did general Calculus primarily to support physics, and Linear Algebra. We started taking EE courses from year 3 and math was specific to it - I know we did a fair amount of math involving complex numbers, transforms, and lot of applied math in areas such as Navier Stokes equations as applied to fluid motion and heat transfer, which were a big factor in integrated circuits. While we didn’t have a comp sci dept then, some of the material was covered in EE and discrete math was another area that was covered. </p>
<p>The one big plus I found in the US environment is opportunity for someone who seeks it. My son, who I had influenced a lot in Math, Comp Sci and EE from early schooling was able to connect with like-minded kids in practice sessions and tournaments such as ARML where these high schoolers were well versed in material that my classmates only first encountered in college. Areas like discrete math which were weed-out courses in his college weren’t that difficult for him because of his earlier exposure. On the flip side I doubt if either of my daughters will even remotely reach the level of math I was exposed to by HS even after they finish college, but given their interests, I don’t see why they need to.</p>
<p>To be clear, I certain admire intelligence in all of its manifestations and agree that anyone interested and able should pursue as much math and science as they are able to handle. I am not proud of my relative ignorance of math, but simply questioning the need for higher levels for those not specializing in fields requiring it. I agree that Renaissance persons who have an excellent understanding and facility with nearly all fields represent the supremely educated ideal. </p>
<p>However, that is a goal that very few people truly meet and I am not sure that leaves the rest of us uneducated, or incapable of valuable insight or logical argument. Certainly, there are persons with little formal education but significant worldly experience and formable intellects who would qualify, in my estimation, as educated persons with valuable points of view despite rudimentary education in some specialized fields. My uncle, despite not finishing college, runs a machine shop and has designed and built sophisticated equipment for larger companies needing his expertise gained through experience - and he intends to retire to pursue his passion of painting. He is a renaissance man without great formal education.</p>
<p>Being canny enough to ask the right questions about what one does not know strikes me as one potential mark of an educated person. I am not going design bridges, spacecraft, software, hardware, human clones, etc. The math and science I once knew has atrophied over time, but I am curious enough to read descriptions of scientific discoveries for lay persons.</p>
<p>I do take exception to the assertion that we are where we are today due to math, science, and technology and nothing else. I won’t pretend to argue that math, science, and technology have not been hugely important. However, so have been political science, history, philosophy, and economics that were the basis of the Constitution which formed a government that allowed math, science, and technology to flourish. Math and science were not the basis of the civil rights movements with expanded freedom in this country; religion, philosophy, and art (particularly music) played prominent roles in the proudest moments of this country and are critical for establishing a more perfect union in this incredibly diverse society. The progress is not always upward and there have been terrible failures caused by pernicious religions, philosophies, literature and art, but poorly utilized technology has failed us many times as well. Improvements in creature comforts, longevity, health, etc. we owe to STEM, values, humor, entertainment (content anyway) we owe to humanities. Long lives without art in its many manifestations would be far less civilized and enjoyable.</p>
<p>Sometimes there is palpable disdain between qualitative and quantitative thinkers - less so between those who are very accomplished at both. There should be a symbiotic relationship between the humanities and STEM, an appreciation of what both bring to society and an understanding of their respective downsides, but not a rivalry.</p>
<p>“There should be a symbiotic relationship between the humanities and STEM”</p>
<p>As offensive as it seems to appear to some, that might very well be what a liberal arts education offers at a number of colleges.</p>
<p>
</p>
<p>For those who advocate such a thing, probably far too few colleges require such an education, since very few colleges do not allow students (of any major) to take the easy way out with breadth or general education requirements.</p>
<p>
</p>
<p>That doesn’t mean colleges don’t enable students to pursue such if they choose to. In fact, more stringent requirements could force students out of this by forcing them to take classes easier than they’d prefer to take. For instance, where I go in my major there are graduate and undergraduate classes in the same subject, but the graduate being deeper. The graduate versions cannot replace the undergraduate, so even if you take the graduate version of the course, they will make you take the undergraduate version.</p>
<p>Not exactly analogous to general education requirements, but I could come up with scenarios.</p>
<p>
</p>
<p>Most writing courses in high school and college center around the analysis of fictional literature. Most students of other subjects are left to attempt to apply such writing training to other subjects, whether such things as history, politics, science, etc… And most people in the real world will be writing about things other than fictional literature.</p>
<p>So should writing courses in college (or high school) be focused primarily or exclusively on the analysis of fictional literature (as they currently are), or should they be offered or required using various subjects as a basis content to write about?</p>
<p>"“I got my undergrad degree in EE overseas. It was then a 5 year program after 11th grade. Being that it was from '70 to '75 I honestly don’t remember exactly what all it covered…”"</p>
<p>Don’t know about the 1970’s. 
In addition to, 2 semesters of MVC, LA, and DE, plus 2 semesters of CV and PDE,</p>
<ol>
<li>Phasors and Laplace Transform in an introductory EE course,</li>
<li>More transforms in Signal Processing,</li>
<li>More PDE in E&M, Microwave, and Device,</li>
<li>Method of Moments in E&M, Microwave, and Device Simulations,</li>
<li>Stochastic Process in Communication Systems.</li>
</ol>
<p>More or less depending on concentration.</p>
<p>
</p>
<p>Ah, one of those schools that forces the best students in math to slow-pace calculus, even though the students who are two years ahead should be able to handle calculus at full college pace (i.e. calculus BC in one year). Meanwhile, students who are not advanced in math take calculus at full college pace as college freshmen.</p>
<p>
</p>
<p>This is strange as IME in both high school and college, no one I knew…including myself had problems applying the writing skills learned from analyzing literature and other subjects in those English lit/writing classes. In the case of those who attended my high school…that included a mandatory 20 page senior English thesis. </p>
<p>If anything, no one else in my high school would admit otherwise as it would be taken by most…especially those in the top quarter(The ones who ended up in the Ivies or peer elite institutions) that one was exceedingly dim in being unable to figure out how to adapt to writing about other subjects/fields.</p>
<p>A symbiotic relationship between STEM and liberal arts does not imply that each person should know both. It means that STEM heavy individuals should realize, and appreciate, what liberal arts do for them and society and vice versa.</p>
<p>Of course, which is the rhino and which is the egret can be debated!</p>