Some Assembly Required, The College Computer Guide: June 2006, Part 1b: Context

So last article I completely left out one of the most important parts of any advisory guide – the writer’s context.

Probably like most of you reading this today, I grew up in the time period where computers, and later, the internet, transformed into integral parts of everyday life. I was one of those kids that was deeply interested in all aspects of computer and technology, and I’ve kept track of new hardware and software as it’s come along through the years. I’ve built my fair share of computers, and I’ve always been a big proponent of the DIY, or “do-it-yourself” computer segment, favoring computers that you build yourself rather than pre-made computers bought from the store or online.

At the same time, for much of my life I’ve been technologically-deprived by contemporary standards, especially among those here in California. While I’ve always built my own computers, and therefore had access to a greater variety of more cost-effective parts, most all of my rigs were more in the bargain-basement range than anything high end. Like most public schools up until the early 2000’s, my experience with computers up through middle school was all Mac-based, and the schools I attended weren’t the kind that had much of an emphasis on computers or technology. The high school I attended was probably above-average as far as technology emphasis went, although it didn’t become that way until my last couple of years, and even then it lacked the kind of hardcore and cutting-edge computer or digital media classes. Most importantly, my mini-generation (4 years) of high school students was approximately the group that ushered in broadband internet connection as the mainstream, bringing in all of the p2p file-sharing, streaming video, Flash, and the rest of the Web 2.0 applications with it. Throughout this time, I was part of the remaining few (especially of those working or studying on the forefront of technology) that was still stuck back on 56k dial-up connections. Put all of this together, and you come up with someone who is in fact a fair bit behind the technological curve, with a mindset that is still thinking more in 2003 terms than 2007.

I’ve had a computer for as far back as I can remember, and I probably started using it heavily around 1997-1998 (4^th grade). I started using internet probably around middle school, at libraries and school and such, but I didn’t get real online access until about 2002 (9^th grade), when I finally got signed up for dial-up access at my house. I’ve had several-ish desktop computers (or two-ish computers that have been continually upgraded Mr. Potato-head style), which handled all manners of word processing/productivity apps just fine, and at various points in time were able to handle some games, although never the latest and greatest. I finally picked up my own laptop when I started college – like all of my desktops, about two generations behind the newest curve, but able to handle general processing just fine, although it struggles with games and intensive digital media work.

I’ve done lots with computers. I used to play games a lot, although most all were on the low-end in terms of performance needs (no FPS’s, and obviously, no MMO’s), although I rarely do any of that these days. I use Office productivity apps like anyone else, although probably Excel and Powerpoint more extensively than most people. Compared to most people, I’m probably more utilitarian online, using it for email and forums, and probably far less than the average person for more bandwidth-intensive stuff like p2p filesharing or streaming video. These days as a student and half EE, half CS major, my main computer tasks boil down to general internet communication use (email, IM, forums, and blogging, none of them hardware or bandwidth intensive), computer programming (typing text – not hardware intensive at all), and digital image processing (heavily memory and display (monitor) intensive).

If there’s anything to take into context while you’re reading this series, it’s that I come from a heavily utilitarian, Spartan even, mindset. I’ve worked a lot with computers, on the hardware side, on the software side, and on the networking side, but I’ve mostly done it with bare bones equipment, so my philosophy tends toward making what you can out of the fewest possible resources. I’m also… how should I say this… used to slowness, and perhaps I’m more patient and forgiving when it comes to performance expectations from hardware, although with my experience I’m probably far more efficient and less wasteful at eking out performance from the hardware. Thus, most of what I write here should be fairly accurate with what people really need, but as far as “luxury” performance goes, it’s an unfamiliar territory that I often write about but haven’t actually experienced much of. Madness you say? No, this is SPARTA! Figurative, computer Sparta. Where Macs are Persians, those god-damn Persians…

Here’s my plan for the rest of this series:

Windows, Mac, and Linux, oh my!
Laptop size/formfactor, and display
CPU
Memory
Hard drive
GPU (graphics processor)
Miscellany (optical drives, wifi cards)
Which computer manufacturers, and where to buy

Some Assembly Required, The College Computer Guide: June 2006, Part 1: Desktop or Laptop?

If there’s a single thing that becomes your life in college, it’s your computer. For some time now, access to computers and access to the internet has been an essential part of studying, working, and social networking. For most people, the move to college makes the computer an even more integral part of life, or for some, the definition of it. For many students, the move to college brings a huge part of social networking and communication online, and even if one were to avoid that, the bevy of schoolwork and even school administration tasks administered by computer ensures that it is a vital part of life.

With the computer being such an important device, and one that you’ll be using extensively for several years, choosing a right one will probably be one of the most important decisions you’ll make in college.

This article is a guide for choosing a new computer, including a debate, dissection, and explanation of computer components and which to buy.

Before beginning to choose a computer, there are two very important questions you need to answer, which will have the biggest role in shaping your eventual computer. The first is, “Do I want a Desktop or Laptop”, and the second is “Do I want a Windows-based PC, Mac OS-based Apple, or Linux-based PC?”

Desktop or Laptop?
There are two main types of computers, classified by their formfactor. One is the desktop, which is the large metal box that sits on desks or floors that most everyone is familiar with. The second is the laptop or notebook, which is a much smaller, portable computer about the size of a large textbook, that integrates all the display screen, computer, and input controls such as the keyboard into one package.

Desktops have always been superior to laptops in every single aspect besides portability. With a desktop you have much more choice and control over the parts you want, much better equipment at much cheaper prices, and far easier upgradeability and more modularity (on a desktop you can change any component at will). On the other hand, you can’t bring a desktop anywhere else but your desk.

The simple answer is that, for a college student, a laptop’s portability not only exceeds all the benefits a desktop offers, but is necessary for college. And while this wasn’t the case in 2005, or even early on in 2006, laptop technology in 2007 has reached a point that the median laptop can equal the median desktop in most regards, except at a higher cost. Certainly, even a modest laptop will be ‘good enough’ for the vast majority of applications for the vast majority of students, except in the field of cutting-edge computer gaming.

For taking down notes in classes, computer-related classes, and working on group projects, a laptop is essential, and no desktop computer could replace it. Various group projects I’ve worked on over the past year, for example, all involved everyone in the group getting together with laptops to jointly work on papers or reports or research – without a portable computer to bring, a group member really wouldn’t have been able to contribute or do any work at all.

An interesting alternative that I thought of before beginning college was a dual laptop and desktop solution. Specifically, getting whatever souped-up desktop you want to use as a ‘main’ computer at home and getting the cheapest laptop possible as a pure ‘notebook’ computer to use away from home. This solution offers the best of both worlds, with all the power and features you want at home, and the portability to have a computer on to go as well, where you wouldn’t care about having a powerful computer to play games, do graphics works, etc. Given the very modest prices for desktops, and the price of the cheapest laptop, such a setup would run for about as much as a high-end laptop (which still wouldn’t be as powerful as the desktop, nor as portable as a cheap laptop). After a year of experience in college (with just a single laptop) I’ve rethought this idea, for several reasons:

It’s difficult to coordinate files between two computers. Having two computers, both of which you use to do work, would lead towards a situation where you have multiple versions of the same file stored on different computers, with the tedious task of synchronizing all of them and making sure you have the latest one. It’s more of a nuisance, and there is software out there that will automate tasks like this, but for the most part (see below) this isn’t really worth the hassle.
Laptop prices have dropped a lot in the past year, making the dual laptop-desktop combo less financially appealing. Two years ago, a laptop that could truly “do-it-all” would run around $1500, while for $800-900 you could get yourself a fairly decent desktop and for $500-600 you would find a low-end laptop. In today’s market, the same fairly decent desktop may run $700-800, and the cheapest laptop may be $400-500, but for $1000 you can find a laptop that can handle most anything (high-end gaming aside), and many $800-900 laptops are up to the task as well.
Laptops today are far more capable than they were 1 or 2 years ago. Until recently, getting a laptop meant compromises in limited hard drive space, limited choice in graphics processors and CPUs, and small screens – or if you wanted the biggest baddest processor and huge 17” screen, this meant a pitifully low battery life and large size that removed any sense of portability. Today, laptops can come with hard drives that range into 200GB (comparable to a desktop hard drive, and definitely sufficient for most needs), as well as full-fledged graphics cards and CPUs. In addition, external attachments like more storage space through external hard drives and better and bigger screens through secondary monitors have become much more viable as costs have plunged. On top of all that, designed-for-portability low-wattage processors (as well as other components) mean that many of the powerful laptops still have respectable battery life and portable size.

With all this in mind, for the average user (meaning anyone who doesn’t demand live and die on their games’ fps rates – if you don’t know what that means then thankfully this isn’t you!) a laptop makes the most sense. The desktop provides few benefits that a laptop wouldn’t be able to provide at a higher cost, the biggest among them hard drive space in excess of 300GB (although the current 200GB or even 100GB available should be very sufficient, and adding on external hard drives is always an option) and lack of the highest-end graphics processors (important solely for gaming, and even then, not a necessity). A laptop with similar specifications will cost more, but the extra cost in exchange for portability to use a computer in class or collaborative group work is more or less a necessary sacrifice in today’s world. The one exception is for pure gamers – those who would demand the highest performance possible (meaning well over $2000 for a desktop), who would be much better off getting a cheap laptop in addition to their desktop just so they will have something to use for outside-of-home schoolwork. This issue being settled, and the only recommendation for a desktop going to hardcore gaming benchmarkers (which is considerably non-education related), the rest of this series and the final recommendations will focus solely on a single laptop platform, although a desktop guide remains a possibility (and may happen, just for fun) if there is enough popular demand.

The College Decision

It seems as if everyone is figuring out where to go for college this time of year, and if my College Monster project would ever take off I had imagined the article at this time to be a compendium of personal experiences about how all of us last year's graduates decided on a college. Well, here's still hoping to get some other responses.

Unlike my other articles where I spent time trying to write in a comprehensive and objective way, I decided that it was pretty much impossible to write something like that in this case, so instead you all get my own personal story, specific to my case and therefore probably not helpful at all to any of you, but it's yours to read on the offchance that you might gleam some advice.

I started out my college admissions season applying for six schools, and eventually getting into four of them. I had started out applying to MIT, which had always been my dream school, and somewhere along the line from early childhood to 12th grade, CalTech got thrown in there as a top school as well. So with either of those I was set, although I wasn't confident at all at getting into any of them. I had three UC's as safety schools, figuring I'd get into at least one of them, although I really didn't know anything about any of them. At the last minute, I threw in Stanford as a token "Hey this will be fun if Sean also gets in".

My mistake during this time was not really paying attention to college at all. I had just figured out my hierarchy of colleges: MIT, CalTech, Berkeley, UCLA, UC San Diego, and I probably figured that if I somehow got into Stanford, then MIT/CalTech would've been there too. So in any event, I'd have my list of schools to run down and choose one, and if not any of them, I'd be headed to CCSF and be done with it. All would have been well and I'd have no article to write today.

As it turns out, I got deferred from CalTech and then deferred from MIT, from the early admission round to the regular round, so I'd be finding out about all my colleges in March. First UC Irvine rolled in telling me I had gotten accepted (although I never applied), then San Diego invited me to New Admits' Day although I wouldn't get the actual acceptance letter until several days later. Then I got my rejection letters from MIT and CalTech, at which point it was all UCSD, and then I got the UCLA and Berkeley letters, and I was all set and ready to go to Berkeley (per my pre-decided hierarchy). Then Stanford, fashionable entrance as always, mails there letter several days after everyone else, and now all of a sudden I've got a conundrum on my hands.

Now I should note that perhaps my biggest mistake was really not looking into any of the colleges. I mean sure, you look over at all the rankings and see (Oh! So and so is ranked best program. I've got to go there!), but how does a blanket #1 ranking at one school compare to a blanket #3 ranking at another school? Does that mean the #1 was magnitudes better than the #3? Or was there only a marginal, subjective difference? What kind of criteria did this ranking organization even use? What if enrollment diversity or financial aid was one of the major factors, but you really just want to know about quality of education? Or vice versa?

You could also take a look at the public information that universities offer about their programs. School pamphlets and brochures, but most especially school websites. These can be helpful if you look hard enough, but a lot of the time, and especially on the shallowest of passes, these kinds of resources all spout the same feely-but-non-specific information. For example, Berkeley's Department of Architecture has this to say about the program's focus: "Because of the great diversity of offerings in the College of Environmental Design and in the Department of Architecture in areas such as building environments, practice of design, design methods, structures, construction, history, social and cultural factors in design, and design itself, it is possible to obtain either a very broad and general foundation or to concentrate in one or several areas." I'm sure that just about any other architecture school says the same basic thing on their website.

You might be able to take a look at classes, and what their curriculi specify. The hardest part about this is knowing what classes you're going to be taking (which requires some digging through the website for your major), and even then it may be heard to find information, or even know what that information really means. For example, the description of Math 54 (linear algebra & differential equations) at Berkeley say this: Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product as spaces. Eigenvalues and eigenvectors; linear transformations. Homogeneous ordinary differential equations; first-order differential equations with constant coefficients. Fourier series and partial differential equations. Most high school students still being at the Trigonometry or Calculus level, it's impossible to have any idea what eigenstuff is, and most students, not really knowing what their majors will entail, can't have any idea about how or if any of this stuff applies to what they'll be doing or how important any of it really is, making most research into publicly available information useless.

What many students try to get away from either public information or discussions is a sense for the education philosophy of a particular school. As noted before, most schools are pretty vague and non-specific with their public information, so it's hard to tell. A sometimes dangerous trap is to catch onto something someone said and begin taking that as fact. For example, when I was debating between MIT and CalTech for my college choice hierarchy (this was before I would find out that I would get either), I had often heard that CalTech was much more theory-based, and found itself more on the cutting-edge, if more abstract, side of science, while MIT had a much greater focus on real-world practice. Now, this was a nice and clean-cut way to qualify the differences between both colleges, so it sounded nice and I was inclined to believe it. In retrospect, I'm not sure if this is true at all - I have no idea what source I had heard it from, and I surely have no idea what source that source derived this information from. It's also a very general statement and I'd very much doubt that it's a true blanket statement for all programs at either school, or that it really restricts your academic choice (it's ultimately within your power to decide if you want to study/research into a more theoretical or practical line of studies). In all likelihood, some guy probably decided to say "MIT's does more practical stuff, and CalTech does more theoretical stuff" and people started just taking that as fact. Another common example is that almost everyone will say, "Berkeley Engineering is really competitive. Almost anyway will stab you in the back for a grade." A lot of times, especially at the high-school-about-to-head-off-for-college level, where you're soaking up all sorts of information and speculation like a sponge, especially from people who really don't know or have a limited scope of knowledge about a particular college (a freshman student like me, for example!), generalizations like that just tend to sprout from off-the-cuff remarks, and snowball into de facto knowledge.

Even knowing anything about the curriculum being taught tells you very little about the actual quality of education - after a year of experience here at Berkeley I can definitely verify what many other college students have said: the quality of education is highly variable from teacher-to-teacher, and perhaps even moreso, teaching assistant/graduate student instructor to TA/GSI (at Berkeley anyway). With a crap teacher or crap GSI, you'll learn absolutely nothing (or you'll have to do all the learning on your own), and good ones will be able to greatly facilitate your education. Don't make the mistake of thinking of thinking, "Oh, so-and-so is a prestigious university, so at least I know I'm not going to have a completely horrible/incompetent professor there", or also thinking that little-known universities preclude good teachers. How do you know if a place has good teachers or not? All of this information is fairly subjective, although generally I've found that getting advice from older students (especially TA's and GSI's in my classes, on other professors in that department) is a ton of help - they seem to have a lot of experience with professors, especially within their major and can be extremely insightful. However, this tends to have the problem of a small sample size, and for high school students this doesn't really help at all. A bit amusingly, I've found that another great resource that solves both problems is http://www.ratemyprofessors.com/, which is exactly what it sounds like - a compendium of student-written ratings for various professors. Now, there's obvious potential for bias, so keep in mind you'll need to sift through for the more insightful comments rather than taking the actual rating numbers. You can use that site to look up specific professors and read comments, or find all the professors working in a particular department.

For example, if I wanted to check out the comments on professors in Berkeley Bioengineering, I might simply grab a listing of all Biology teachers and take a look:

http://www.ratemyprofessors.com/SelectTeacher.jsp?the_dept=All&sid=1072&orderby=TDept&letter=B

Even better, I'd go to the Bioengineering site and take a look at the recommended curriculum, which handily outlines the general coursepath for all four years of your college education.

http://bioeng.berkeley.edu/program/bioemajor.php

After that I might go to the college class search and find the classes I might be taking in the first semester, or even the future:

http://schedule.berkeley.edu/srchfall.html

And then look up the professors teaching those classes.

------------------------

Well, it seems as if my subjective personal narrative of my college-choosing experience has veered off into objective analytical commentary once again. Well, in short, I never really did any of the stuff I mentioned above. I was all set on resigning my fate to Berkeley (without any real research, just based on the assumption that "Well, it's more prestigious than UCLA/UCSD right?") when the Stanford admission letter rolled in, and now I was in a bit of a conundrum.

There were a lot of people with strong opinions, mostly towards Stanford for the obvious (but in retrospective, naive and foolhardy) basis of prestigiousness. Well it's Stanford. Everyone wants to go to Stanford. Stanford is famous. The Google Guys came out of Stanford. Who the heck comes out of Berkeley? And admittedly, my personal feelings leaned that way as well. At my school at least, everybody went to Berkeley. Each year we'd send a dozen or so kids to the school. But when was the last time we saw a kid go to one of the elite private schools? In my mind, I also tried to imagine myself as a prospective employer, and I could definitely imagine a sort of exclusive aura on the guy with Stanford on his resumé, while I thought of the guy from Berkeley as more of a common ore. In retrospect, all of that talk about prestigiousness was just extremely superficial junk that parents and maybe even teachers, who are all years removed from college (and in my case, immigrant parents and teachers who never actually experienced the college system here but simply heard of places the legendary placecs like Stanford and MIT.) believed heavily. Once you're actually in college and settle in, all of the auras of different schools that you regarded as a high school student sort of fade away - the belief that Stanford is a more "prestigious" school or that the other UC's are "less prestigious" doesn't really register anymore, and projecting myself again as a prospective employer, I found it very difficult now to see how a student's particular college is a really relevant factor.

With that "prestigiousness" myth dispelled (hopefully - unfortunately for many high school students it's both the worst and most common reason they decide on a college), I'll move on to the four major reasons I did decide on Berkeley over Stanford. They're not meant to be a comprehensive list of reasons you should consider, and they certainly weren't all good reasons (in fact, retrospectively none of them were), but they were my initial reasons, and thus the only ones I can authoritatively write about from personal experience.

Friends going to Berkeley, none going to Stanford
Support-structure philosophy
Cost
Failure insecurities

I hate to say this was the defining reason I came here, because it wasn't, but at the end of the day, I think the dealmaker for Berkeley and the dealbreaker for Stanford was that at Berkeley, I'd have a significant contingent of friends who would be going there with me - friends I very much wanted to keep and share the same college experience with. While a lot of people might view this as a cop-out from forging ahead and blazing my own trail with a brand-new network at Stanford, and clinging onto some security blanket of high-school friends at Berkeley, I saw it a lot differently. To me, Stanford, while it seemed much more fun and alluring, felt a lot like abandoning all the old friends I had for greener pastures, and both then and now I desperately wanted to hold my existing social web together, not really for fear of making new friends or having no friends, but because for me that web was darn-near the most treasured thing I had to own. With college it's inevitable that people had to split apart, and since one can't obviously go everywhere, I made do with what allowed me to keep close to as many people as possible - still close enough to home to keep with all the people going to community college, situated en-route to Davis, and most of all going to college with the small group of people who were going to Berkeley. I think my view was shaped in large part by my high school experience - I left for my high school with more or less one close friend, while nearly the entire rest of the class went over to other major high school in our district. For the most part, contact and friendships with all those people who went away died off with the distance and different schools, but at the same time my friendship with the one friend who had come to this high school with me is to this day one of the closest friendships I have, and one that I honestly couldn't imagine a life without. All the others who went to a different school? There's not so much a sting or pang anymore, as there are simply moments of melancholy and regret that I couldn't - or didn't - keep those relationships alive. In high school I went on to find friendships that developed into even closer or more integral parts of my life than my friendships in middleschool, and it was the last thing I wanted to let go.

How did that all turn out? Only a year removed from high school, I don't know if I can really give a definitive answer, but from my own subjective experience and attempted objective observation of others, it doesn't seem as if going off to college with all your friends really makes any sort of difference - knowing a dozen students while your daily interaction might bring you in contact with any of the 30,000 students here doesn't significantly help or inhibit your ability to socialize and form new networks in any way - many of the people I knew last year have truly blossomed into an entirely new network of friends and contacts, more or less that trailblazing, starting from scratch social experience that they said I'd find at Stanford. On the other hand, there are others who didn't plunge head-first into the social scene, at least not as quickly, and are a bit more isolated in their freshman year of college than they were in their senior year of high school, but not necessarily their freshman year of high school. From observation and retrospect, I think the various social lives that resulted came about from the personality and goals of the individual, rather than having anything to do with whether or not anyone else from high school came along to college. For me, personally, the kind of network I imagined - the close-knit high school group that might simply grow to include the new contacts and networks that were made - never really materialized. Some friends stick around, but at the same time there are many who are just as eager to shed the inhibitions of their high school bonds and start a brand new life from scratch, and I tend to think most everyone, at least to an extent, is inclined towards the latter. For almost everyone, college is about finding a path. In high school you're fed assembly-style through the same pre-packaged education, but it's in college that you find your independence and niche, and choose the path towards the career and even person you want to be. At least a little bit of that involves some experimentation and exploration, and while it doesn't necessarily demand a complete abandonment of the old life, at least a part of that life is shifted to a lower priority, at least in the present, in order to permit for the true independence that allows it to happen. So a year after I had envisioned a college life including the same high school cast, I find a lot of them, including some who were at one point the closest and most integral relationships, off pursuing their own lives. After a long while fighting it, I think I'm starting to come to the same conclusion that perhaps everyone else had already prepared themselves for before we had even gotten to last year's graduation - that with the move to college, and the makeup of individuals with different interests and classes and majors that find even more familiar and relatable niches in a broad and diverse student body, a distancing and breakdown of your former relationships is inevitable to some extent, and you can't really depend on the assumption that anyone is going to be able to stick around with you forever.

The second reason I went with my choice of Berkeley over Stanford was the support system structure. During my college decisions process, I had made an overnight stay at Stanford, and had made a somewhat less informative day-tour of Berkeley. The most drastic difference I had perceived between the two schools was the support structure. In my stay and the various informational activities at Stanford, one of the emphases was the vast support structure available at Stanford - there were academic centers and tutors and numerous other resources available to help students out, and in addition to that the entire community seemed.... well, like a community. In my brief stay at the dorms, everyone there seemed immensely close-knit, far more than any I've experienced or witnessed here at Berkeley. In short, Stanford was the one that seemed a lot like a natural progression from high school. Berkeley, on the other hand, was subject to the biased comments I had received offhand and the limited day-tour I got; Berkeley was the place where you were thrown to the wolves and had to find a way to fend, learn, and organize for yourself, because you sure weren't going to receive any help from your compatriots in the Engineering department. While that perception was indeed drastic and exaggerated, in my experience so far the 'fend for yourself' aspect has very much applied - while in high school, everything from homework assignments and lectures were spoon-fed to you, here at Berkeley much of your education and success is up to your own initiative - 500-person lectures will blast by if you're not able to keep up with what's going on, and it's really up to you to take the initiative to put in the extra mile in classes or during office hours, start or join your own student organizations, or even make new friends. It's very unlike the high school experience, where teachers can tailor classes to meet the needs of a 30-student classroom, and where teachers will spell out each homework assignments and take you to task individually if you haven't been keeping up. Most of all, it's very unlike the high school atmosphere where a small school and classes with the same people day-in-and-day-out, year-after-year, more or less force social relationships and professional partnerships to develop. Berkeley has been anything but that experience, but on the contrary I very much believed then and still somewhat believe now that Stanford would have been something much more akin to the high school experience. While not a bad thing, and while I very much wanted to hold onto my existing social web from high school, I ultimately thought that the Berkeley corporate culture if you will, forcing students to develop independence, fit the kind of life I wanted to start pursuing more, and better fit the kind of culture that I believe the professional workplace demands - self-driven individuals capable of working independently. And so this reason was my overriding 'official' and justified reason I ended up with Berkeley over Stanford. I'll tell you in another five years whether or not this works out.

The next issue is one that every student, no matter their situation, will have to consider, and for my parents I think it was probably the biggest factor. While everyone else at my school was rooting for Stanford (being the most prestigious), my dad had made the valid point that the reason Stanford was being unanimously pushed without reservation was because none of them were actually paying the bill. In truth, cost aside I think my parents wanted me to go to Stanford as well, but cost, especially when you've also got two-college bound siblings in the coming years, tends to take precedent over your own personal feelings and inclinations. While I'm sure my parents wouldn't have objected if I had chosen Stanford based on cost alone, and while I'm sure that almost all parents would find a way to support their child with where ever they decided to go, from a responsibility standpoint I found it too difficult to ask my parents to foot the huge bill that a private college needed - the near-$50,000 per year that Stanford would have cost was enough to cover both myself and my sister to go to college, or even both my siblings if they were to end up at the lower-cost CSUs. The counterargument for this was that I would make up the extra tuition in no time - the higher income I'd make as a Stanford graduate would far outweigh the tuition premium I would be paying, and in addition at Stanford there was a greater potential to meet the kind of world-class geniuses, or get involved with the next up-and-coming projects or research or start-ups, and really hit it big, something that would be much harder at a place like Berkeley. (all the old adages about "it's not what you know, but who" and "seizing opportunities" applied here). When you get past the speculation and take a look at the actual numbers, however, the first argument doesn't really pan out - the difference in starting salaries is usually something less than 10% - let's say the difference between a Berkeley CS graduate and Stanford CS graduate was 70,000 vs 77,000, a 7,000 or 10% difference. A full six years at Berkeley (four years bachelor and two year's master) would end up costing around $150,000, assuming no major tuition changes, while a full six years at Stanford would have cost around $300,000. At even a $10,000 difference in salary, it'd take 15 years to make up that difference - a long ways off and even more to the point, not fast enough to help my parents repay the cost of my education, or help my siblings pay their way through theirs. The second argument I'll talk about in the next paragraph, but the chances of that are small, despite the few highly publicized cases; the actual average college graduate tends to make, well, somewhere around the median, which as I've just shown doesn't make a lot of financial sense, at least in my situation.

I'd like to caution everyone else on purely making this a financial decision, even though this is what I somewhat did. Regarding the cost, I turned my analysis into a purely cost-benefit rationale, and at the end Berkeley came out ahead in this regard (as almost any California public school will). But there are innumerable other factors that can't be quantified - the kind of social life you want, the kind of independence you want to gain, the geographical location you want to spend the next for years of your life, or even how much you value the actual education you get, rather than simply its ability to find you a job in the workforce. For myself, my own personality issues and sense of responsibility prevented me from ever being able to consider those aspects - college to me is first and foremost an educational institution, and while you make what auxiliary education and personal development and experience as you can, I don't think I could have ever asked my parents to spend more to allow me to indulge in those strictly 'luxury' aspects of college if the level of education itself couldn't justify it, and in any case I don't think it could have ever been fair if I were allowed to indulge myself with 50k a year at Stanford while my siblings were left to make do with whatever their more conservative UC or CSU educations could afford them.

Last of all, the reason for not-Stanford stemmed from a thought I knew was in the back of my mind the whole time, yet one which I never readily admitted to myself until after the decision had been all set and done. Throughout my consideration of Stanford, and a sort of accumulation of all the other pros and cons that came along, was my perception of raised expectations if I were to go to Stanford, and as a result a morbid fear that I would fail there. This is perhaps my most irrational of reasons, but one that I haven't ever been able to shake off, even now. Things were all fine and dandy when it was simply a personal decision. In a world of complete isolation, I didn't owe anything to anybody. I would be taking out a college loan myself, that I'd have to pay back. In the meantime I could stay and study as long as I wanted, and decide to study whatever I wanted, and not have to be responsible for anything except forcing myself to endure the various drawbacks of a life with a low-paying job. Unfortunately, I don't live in an isolated world, and as soon as the decisions process started I could start feeling expectations mount. I might be the first person from my school to go to a place like Stanford in a long time, and if you go to Stanford, that meant you were good. Real good. And if you're that good, you don't fail - people don't go to Stanford to flunk out. Or even to become mediocre. The people that go to
Stanford are brilliant and make changes to the world. Those were the expectations, anyway, or at least the expectations I perceived. At Berkeley I might go there and no one would expect any more out of me than the dozen other students that also went there, or the dozens more that would go there each successive years. But if I were going to Stanford, that meant I was something special - a cut above the group that went to Berkeley every year, and in that case I damn well better be brilliant. After all, why send the guy out to a hallowed institution like Stanford if he's just going to perform like everyone else who went to Berkeley, or LA, or San Diego, or Davis? The same rationale flowed into all my other considerations, although these were perhaps more well-grounded. What was the point of spending more than twice the tuition to send a student to a private school, if he was going to end up performing just like everyone else at a public school? What was the point of abandoning your friends to pursue glory at a place like Stanford, if you never achieved it? Even worse, what if I were to just completely flame out? Not only perform mediocrely, but to simply be a complete bust? It would have made me the greatest waste of hype, money, and abandoner of friends ever. For failure, it's one thing for it to happen when you're doing the same thing as everyone else - not everyone will turn out to be successful 100% of the time. But by going for Stanford, I would've made myself out to be in pursuit of some greater level of success, and in a situation like Stanford I would have been given every advantage to really become something great, and would have every expectation to do so.

Now, this line of thinking was completely irrational, and I knew it from the beginning. In my personal case, I think I have too many self-consciousness issues and too grand and pessimistic an imagination of the consequences of things. So I don't write about this particular reason out of possibly giving anyone insight, but for the sake of completeness and also to dissuade anyone who might on the offchance be thinking these same thoughts.

So at the end of April, these were the reasons that summed up my decision - my four dealmakers or dealbreakers. In truth, many or all of them turned out to be horrible reasons, and if I were to do it again, and do it right, I'd be doing a ton more research and have taken every opportunity I could to actually observe and experience classes and student life at the college - the two nights I spent at Stanford and the one day I spent at Berkeley provided more insight than any other information I had found, and if it were possible I think the best possible way to get a feel for a university is to spend an extended period of time there both in-class and with student social events. For those of you high school students, just about the best thing you can do is to sign up for those overnight host programs, or if you're close enough, look up classes and visit them youreelves.

Being far more personal and subjective than most of my other College Monster pieces, I'm sorry that I couldn't craft something more explanatory and insightful, but hopefully you'll all be able to gleam some useful tidbit of information through my experience.

College Monster Shadow Program

I'm in the midst of starting up a college shadow program for current senior students. For more information, you can email me at nathanyan@berkeley.edu

Preliminary information so far:
Email:

Hi all,

It's midway through March, and for a lot of this year's high school seniors, the college acceptance letters are just rolling in. As I'm sure most all of you remember from last year (or previous years), actually picking a college after that can be a harrowing feeling, especially when most students really don't know much about colleges outside of program descriptions, national rankings, and a surface tour of the campus.

I'm thinking of starting a college shadowing program, similar to what high schools sometimes offer, and a bit like some college overnight stay programs - essentially the high school student gets to follow around someone already in college, go to classes and experience studies and social life and living over there. Westmoor's spring break is April 9-13, and for most colleges I've looked at so far, most of us are still in/back in school during that time. For students who don't have their spring breaks planned out yet, it might be a good time to visit campuses, and we can have college hosts take students around to the classes, dormitories, dining commons, etc. to show them how college life is like at that particular school.

If you're interested in doing this, you can email me back, or visit:
http://collegemonster.wikispaces.com/Shadow+Program
http://berkeley.facebook.com/group.php?gid=2255893676

And yes, I'm looking for people from community colleges too - the vast majority of students from Westmoor actually go here rather than a UC or CSU, and it'd be good for a lot of students who ponder going all 4 years or doing a 2-year transfer.

I also sent this out to some teachers and a few senior students, mainly to see what ideas you had - any feedback or suggestion at all would be great.

-Nathan Yan
nathanyan@berkeley.edu

Wikispace site:

We're currently in the process of planning out a shadowing program for current high school seniors. As college admissions letters are rolling in throughout March, high school students will have the next month or so to decide where they want to go, and as I'm sure many of you remember from last year, it's not always an easy or clear-cut decision.

For myself at least, one of the hardest things about choosing a college last year was not having any real feel at all for how it was actually like to live and study there. Going into the choosing process, most students can easily find out all about the strength of programs and national rankings, and take a tour around to look at all the buildings on campus, but there's really very little in the way of providing prospective students with an actual glimpse into the real college experience. That's the broad, overall goal of this program, to provide students with a firsthand experience at prospective colleges, to help them decide which college they really want to go to.

In pursuit of that goal, this project aims to set up former Westmoor students as "college hosts" that students can shadow. College students who were interested could put themselves on a list, and high school students who wanted to check out a particular college could look up who was available at that college and contact them to make arrangements for shadowing. The college host could then show the high school student, or student(s) around, take them to classes, out to dining commons, social events, and possibly even stay overnight* (see below). Being former Westmoor students, there's the added bonus of having the same perspective in hindsight - we've gone through similar classes and education, and can more accurately advise on how well such-and-such class prepared for college courses.

Westmoor High School has its Spring Break over April 9 - 13. After a quick sampling of a few neighborhood colleges, it seems that many of us, if not most, will be in school during that week, which means that it would be the perfect opportunity for seniors who have nothing to do to visit at colleges.

The whole idea/project/plan is still in the works, but right now the plan is to get a list of the college students interested, and possibly get high school students to organize via a Westmoor liaison. We can work out some kind of activity outline if you'd all like that, but as the different college campuses, and even us individual students, are extremely diverse, I think it's best for everyone to decide on their own what exactly they want to do - the idea is to just give the student(s) a comprehensive experience of what they can expect at that college. My original idea was actually for an overnight stay program, which would really give students a comprehensive idea of how dorm or apartment life was like, but after talking with a few people, I think I agree that it's too complicated and messy of an idea to tackle, at least this year. However, it's still on the table, if anyone is interested in, or wants to talk about, the idea, but for now it looks like college hosts will be sort of a day-long tour guide session for prospective students.

If you have any questions or ideas, you can contact me at nathanyan@berkeley.edu.

Reflections on my high school education in the field of Mathematics

Note: this article makes references to two distinct types of students, known as “techies” and “fuzzies”. It’s an important distinction, because the two realms of students experience quite different courses and course requirements and in general have quite different priorities with regards to education. In a quick definition, a “techie” is a student who is pursuing or plans to pursue an education in engineering or math or ‘hard sciences’ like physics, chemistry, or biology. A “fuzzy”, in contrast, is a student who is pursuing an education in the arts or ‘social sciences’, and are so named because of the “fuzzy” and ambiguous nature of their studies, in contrast to the distinct definitions and black and whiteness often encountered in “techie” fields of study.

In part 2 of this series, we’re discussing high school mathematics. Unlike my previous piece on foreign language, here’s a subject that’s near and dear to my mind – I was heavily invested into math throughout high school and even middle school, and the subject is a major part of engineering majors in general.

I’ve decided I’m going to begin each of these articles with perhaps the most illuminating question of all: why is this subject important? Yes, this is a college blog, and I’ll still be primarily writing a retrospective on my experience in high school with the hindsight of my experience so far in college, and give advice on what students should do. But in explaining that retrospective, the context of my thoughts are very specific and exclusive – despite my attempts to be as objective and comprehensive as possible, my commentary ultimately describes my situation, and stems from observations and evidence that I’ve experienced only. The best way to find your own answer, and find meaning in what I write for yourself, isn’t in all the specifics that I provide, but in viewing them through the lens of this question: what is the significance of this subject for me?

So, why is math important? For engineers and students pursuing hard sciences (or math itself), this question is easy – it’s at the core and arguably the root of their very profession. Math on its own is the most basic level of logic, and the purest – math is black and white, and everything it states and does is fact, and quantifiable. For this reason, it is the building block towards understanding the physical world around us – it is only through math that sciences could ever grow out of a mere set of observations and become serious, quantifiable, and meaningful ways to understand the universe we live in. Understanding mathematics is essential not only to understanding current science, but it’s also essential to broadening of realm of future science as well.

For that alone, there are numerous importances to understanding science, and therefore math, but we’ll cover that later in the science piece. Outside of science, however, math is simply logic. It’s not through philosophy or the rhetoric of argument that we learn logic – logic in its most pure form, before it’s tainted by perspective and language, is represented in math. It’s through mathematics that we learn the concepts of equality, inequality, representation (variables), quantification (number values themselves), and relationship (matrices & systems of equations). At higher levels we learn reciprocal actions (inverses), and the link between sums and rates (calculus), among many other things. Math is the fundamental logic, and at the end of the day, all the philosophical and rhetorical logic (not to mention scientific logic) taught in the universities, and the logic we employ in everyday life are simply abstractions and distortions of the fundamental logic represented by math.

Pragmatically, what does that mean? Understanding math at a fundamental level certainly helped me excel in understanding almost every other aspect I ever studied. But what I’m talking about here is understanding math – simply learning it, memorizing sine and cosine values or mastering formulaic methods for computing integrals doesn’t really do anything. I would argue, for example, that learning how to calculate derivatives using the old, archaic limit h->0 [(f(x+h) – f(x)) / h] method is far more important than ever learning the power rule shortcut for derivatives – though you’ll learn and use the limit method for all of a week and then never look back, and the power rule is the applicable one that scientists and engineers and mathematicians will use in all applicable instances, it is the former that actually outlines the basis behind and definition of derivation, while the latter is simply a tool used to compute and solve. It’s a moot point for ‘techies’ like me, as both lessons – the fundamental concept and the pragmatic tool – are equally important in our line of study and work. But for every ‘fuzzy’ student out there who is wondering what exactly is the point behind all this math, here is the answer: mathematics is a representation of logic at its most basic level, and an understanding of logic through math (even subconsciously, perhaps) goes a long way in making sense out of anything in any field. As noted in the example above, sure, not all math is relevant if you’re in a field that doesn’t use it. Some math is for the sake of math, or for the sake of science only (where it gets abstracted from logic, like all other subjects), but there are important logic concepts within mathematics that everyone should learn, and I’ll point these out here.

A little context, as always, about my educational background:

I’ve attended public schools in P-12 all my life, except for P, and so in part fortunately and in part unfortunately, I never learned mathematics through the new and alternative educational methods that are sometimes used in private schools and seemed to be ushered in some time after I finished my elementary school education (I remember sometime in the elementary school, when my younger sister asked me for help on homework, and I couldn’t understand a bit of the multiplication they were teaching because it was some completely bizarre and non-traditional alternative arithmetic lesson). In any case, I never went through that, and somehow (perhaps just from this one incident) I came away forever thinking that the next several years behind me had always learned the fundamentals of arithmetic some different way. Well if it is, I’m sorry to say I can’t comment at all on how my early education could have been affected or how you readers are affected by some alternative educational scheme. If it isn’t, then ignore this entire paragraph.

I was always a pretty good mathematics student, and I say this in the context of my above commentary on fundamentalism and pragmatism – I learned how to use all the tools and which ones to apply to which problems very well, as did most people, but beyond achieving the right output I always picked up the actual concept fairly quickly, something that, from observation over my P-12 years, not all students do even if they achieve the right grades and otherwise “do” the work right. I had algebra in the 7^th grade, and re-did algebra in the 8^th (as there wasn’t anything left), so while I entered into high school at the same level as everyone else taking geometry, I probably had a bit more refinement and experience dealing with that kind of math. Overall, my pre-college math education looked like this:

7^th grade: Algebra (independent study)
8^th grade: Algebra (same material as 7^th)
9^th grade: Geometry
10th grade: Algebra II/Pre-Trigonometry
11^th grade: Trigonometry/Pre-Calculus
12^th grade: AP Calculus AB, AP Statistics, AP Calculus BC (independent study)

I ended up scoring very highly on AP and SAT mathematics tests, and ended up at UC Berkeley under an engineering major. So far in college I’ve completed one semester of Multi-variable Calculus (3^rd semester calculus, after AB and BC) and am currently in the middle of Linear Algebra & Differential Equations.

You should thus take my context from the standpoint of a “techie”-centric student (although I have a lot of fuzzy roots, which I’ll explain when I get to the ‘social’ sciences), who went through high school on the more advanced math track, and never really struggled too much with the subject. I’ll admit that I lack any experience in the realm of students who started high school doing Algebra and took Geometry their second year, and also those who went with a 3-years-and-out approach towards math classes, although I’ll attempt to take the perspective of “what if” my education ended with Trigonometry or even Algebra II.

Perhaps it’s best to discuss mathematics with a walkthrough, starting with middle school education. The unique thing about mathematics is that it’s a strict sequence – each course is a prerequisite for the subsequent one, and once you’re on a certain track, mobility into the advanced courses is nearly impossible (which isn’t the case for English, science, or social science) – if you started out your freshman year doing Algebra, there’s not much chance to be able to take Calculus in your senior year. For that reason, your mathematics education gets decided all the way back in middle school, when you decide (or perhaps get tossed into) either pre-Algebra or Algebra as an 8^th grader.

The advice I want to give is this: every student should take Algebra as an 8^th grader, and skip straight ahead to Geometry in the 9^th grade (without any “I’m doubting myself maybe I should retake Algebra in high school?” questions), because being an entire year behind in math is a very big step back that is very hard to “make up” if you decide you want or need to be a more advanced student later, and moreover because I have very strong opinions on students taking Calculus by their senior year. However, it’s advice that I’m very reluctant to push, knowing that not every student can handle that pace (which is why this track is the “advanced” one and the standard math track starts with 8^th grade Pre-Algebra and 9^th grade Algebra) – perhaps I want to push it very badly because math to me is so relevant and all-important, and from my observations of an admittedly very-biased sample of friends, all the students I knew were completely capable of learning on this advanced track, including those that started out with 9^th grade Algebra after having taken Algebra in the 8^th grade.

The almost surefire advice is that those students who have already taken Algebra in the 8^th grade shouldn’t doubt themselves by retaking it in the 9^th. Algebra was always the big and momentous subject in middle school (maybe my perspective is exaggerated because it seemed even bigger in 7^th grade), but in the context of high school math, algebra is actually a fairly shallow subject – just variables, equations, arithmetic properties, and maybe an intro to coordinate systems, right? It’s not a core part of Geometry, and the month at the beginning of Algebra II spent reviewing over basic Algebra more or less covers and refreshes everything you learn in Algebra. I validate this speculation with my own experience (perhaps not very convincing) and observations from nearly ever 9^th grade Algebra student that the year spent in review was a waste of time (much more convincing, although I should caution against the bias of my observation samples).

As for students who have only pre-Algebra, or those 7^th graders who aren’t sure if they can handle Algebra in the 8^th grade, the answer is a lot muddier. Again, the advice I want to give is to just go for it, but in reality not every student is prepared enough to take on algebra and grasp the concept of variables at 8^th grade (although many who don’t can be, if they tried), and there’s no way for students who enter high school having only pre-Algebra to magically jump a level into Geometry. Students in this situation are essentially stuck with 9^th grade algebra, but they’ll have a choice to either stay along the basic mathematics track or work hard enough to move up a level.

Move up a level? Yes, you can; admittedly, the mathematics education track isn’t as locked in as I made it seem before. If you’re on the standard math track but want to move up a level so you can take Calculus by senior year for example, the concurrent enrollment programs offered by many community colleges is an alternative. Concurrent enrollment is a program offered by community colleges (In the Daly City area, City College of San Francisco (CCSF), Skyline College, and College of San Mateo (CSM) are probably the largest) that allow high school students to enroll into college classes and earn not only college credits but high school credits as well. Usually, high school students sign up to take a class at the community college over the summer break, and more rarely during the actual school year (with night or weekend classes). The classes are free for all high school students, but you’ll need to speak to your high school counselor and get permission to enroll into classes (you should also ask your counselor how the class would apply to high school credits).

So for students who want to move up a level, concurrent enrollment programs allow you to take Geometry during the summer after freshmen year, for example, and move straight into Algebra II for your sophomore year, assuming that you’ve already talked to your counselor and/or teacher and they’ve approved that taking the college course can fulfill your requirements for high school.

There are drawbacks, however. The first is that you’ll have to put in a lot more work – your whole summer spent going to school again, for example. It shouldn’t be a deterrent; it just means you’ll have to actually dedicate your time and effort to doing well, just as if it was any other class. The second is that, being a college class, concurrent enrollment is generally more rigorous than a typical high school class. By no means is it beyond the grasp of high school students, but it requires need more effort than a typical high school class would. Third, and perhaps the most important, is the time constraints – you would normally take a mathematics course spaced out over the entire school year – 10 months from August to June. For concurrent enrollment courses, all of that material is crammed into a 2-3 month semester – you’ll end up doing the same amount of work (1/3 of the time, but classes may go on for 3 hours instead of 1, for example), but it’ll be at a highly accelerated pace. A summer course in math is like an extended cram session – you may memorize everything and get the grade on the test at the end, but how well everything actually sticks is another matter. Depending on the kind of student you are, you may or may not learn as well as you can with a full-year course, repeatedly working on the material day-in-and-day-out; generally everyone can grasp the fundamental concepts equally and those stick, but students who just tend to memorize things well can hold onto the pragmatic tools they learn from short summer courses better. Ultimately, however, in my opinion (not in my validated commentary), a student who takes a summer of concurrent enrollment along with four years of high school math comes out better prepared and knowing more than a student who only takes four years of high school math and ends up a year behind. It should also be said that if you’re dedicated and willing enough to go to school during the summer to advance a level, you’re probably a student who would be capable of starting 8^th grade out in Algebra and starting 9^th grade out in Geometry.

With that aside, the only question for concurrent enrollment is whether or not a particular student is willing to put in the effort, and if he or she actually needs it. Thus begins a walkthrough of my perspective through my high school and early college mathematics experience, to hopefully reveal enough foresight for each of you to make your own decision.

Geometry

I started out my high school education with 9^th grade Geometry. It was a nice small, 20-student class, which I believe is a standardized maximum for freshmen math in California public schools. Although the majority of this is probably obvious, having 20 students means the individual questions of students can be addressed much more comprehensively, and on the flipside, although many won’t like me saying this, the low student capacity allows for classes to be much more tuned to the level of student ability – classes with more advanced students spend a lot less time bogged down by a handful of students who can’t keep up with the rest of the class, and classes with slower students aren’t hopelessly drowned out by the pace of more advanced students.

At the time, and for a long while afterwards, I detested Geometry. As I’m sure it was for many, Algebra and variables and solving for them was an absolute delight. Going into geometry, with all of its coordinates and shapes and 360 degrees (what kind of unit system is base-360??) (context: possibly I’m not a ‘visual learner’), and the doldrums of memorizing theorems and postulates and proving this and that when things were, “Just look at the thing! It’s quite obvious without a theorem, wouldn’t you agree?”, was quite an exercise in tedium and an absolute bore.

That said, in reflection geometry introduced a number of fundamental pragmatic tools – beside the basic ones like SohCahToa and various useful theorems for angles and shapes, geometry was the first in-depth application of algebra in tangible terms. You wouldn’t solve for some abstract variable, but for an angle, an edge of a shape, a perimeter. Applications in geometry is still very much a pragmatic tool – it doesn’t quite reach the level of abstraction you’ll find with vectors and n-space (fully explored in college-level linear algebra), but it’s the first stepping stone that allows you to grasp the same basic concepts in more familiar shapes and 2-dimensional-space.

The real beauty of geometry, however, and the most valuable lesson I took away, was the raw usage of logic to handle and solve problems. While, like any other field of mathematics, applying the tools to problems was part of the class, the largest part of Geometry was rather substantiating the validity of those tools. For every algebra-application “X and Y are similar shapes; find X’s dimensions given …” problem, there were two “X and Y have given properties; prove their similarity” problems. Rather than computation or tool application, Geometry was an exercise in logical analysis and conclusion.

What does Geometry mean now, as a second-semester engineering freshman? Pretty much as soon as I finished Geometry, I dropped just about every pragmatic tool save SohCahToa – throughout a science education filled with Physics, Chemistry, and Computer Science and a math education with Algebra II, Trigonometry, Calculus, and Linear Algebra, I rarely ever needed to calculate the angles of the vertices of a regular polygon, and only rarely did I ever have to do things like show congruency between sides. There were a few things, like the introduction of the Sine, Cosine, and Tangent trigonometric functions, as well as the properties of parallel and perpendicular lines, that stuck and proved to be repeatedly useful, but the entire pragmatic side of Geometry consisted simply of math-for-the-sake-of-math or math-for-the-sake-of-science tools. The extensive (and mandatory) use of logic, however, was what stuck most and prevailed as a foundation for future learning – everything that was validly useful was derived from a fundamental logical base, and understanding that logical base proved instrumental in not only knowing where any tool could be validly applied, but whether it was valid at all. As most of my later teachers would tell you, I refuted everything I was taught until I could substantiate it through my own train of logic, a refusal of the common ‘memorize, plug, and chug’ learning that lets many students pass classes but leaves them grasping for any understanding whatsoever. Although I probably hadn’t realized this point at the end of 9^th grade, the necessity for a foundation of logic for everything was went on to define my approach to education. Arguably, it was the biggest reason I ended up learning and understanding as much as I did in all my subsequent education.

Algebra II, Trigonometry

The next two years of math education are a bit of a blur, although perhaps it’s because it feels so long ago (a scant three years!). For the most part, Algebra II and Trigonometry/Pre-calculus taught a smattering of useful (and some not-so-useful) mathematical tools. The most important concept here was the coordinate system – Algebra II first explores this and uses it to represent equations in a graphical form. Trigonometry delves into this deeper, with more non-linear equations, and towards the end of the year (in my class at least), the presentation of alternative coordinate systems, such as polar and parametric coordinates. Understanding coordinate systems is the stepping stone to the more general topic of vectors, and within the domain of high school has applications such as dealing with vectors quantities in Physics. While it’s not necessary, understanding coordinate systems is an extremely beneficial supplement when learning vector quantities (such as any kind of Force) in Physics, a topic that surprisingly many struggle with (even at the college level, in my first semester Physics class) - as a tie-in with science, I started both Algebra II and Physics in my sophomore year and found the former to be extremely useful in understanding the latter.

For the most part, students who don’t live and die by mathematics usually don’t find the somewhat random smattering of Algebra II or Trigonometry very interesting or relevant, and it’s around this stage that many of the 3-years-and-out students elect not to go for their 4^th year of mathematics. The very next level of math, however, is what (in my experience) puts it all together in a single, shockingly relevant and simplistic system of mathematics.

Calculus

Out of any math I’ve ever taken, Calculus (taken in my senior year) proved to be the most revolutionary and eye-opening concept since Algebra. Up to this point, the majority of mathematics had simply been for the sake of math and science – learning math in order to do more higher-level math, or applying it to solve science (mostly Physics) problems. While I personally loved it and excelled, for any non-techie student, there admittedly wasn’t much appeal or immediate relevance in any of it. Calculus changes all this, with the introduction of the derivative, and later on the integral, two concepts that, for myself at least, offered a shockingly new way to think about nearly everything, from making sense of statistical data (distribution curves in particular), to understanding economic and business concepts (trend indicators, for example), to gaining an even deeper introspect into the workings of everyday physical phenomena – in short, for pretty much anything with quantifiable values, Calculus redefined it in an entirely new and elegant way. To give an example, before Calculus and the introduction of rates (derivatives) and sums (integrals), one might very well understand any individual quantity such as velocity, displacement, or time, and even understand their relations to each other (D=RT). One might also take the quantities of height, gravitational acceleration, and time and understand their relation in a state of free-fall (t = √(2h/g) ). Calculus offers a mathematical system that combines the awkward old system that used to define a new set of quantities and formulas for each different state or situation. Through Calculus, students come to learn that constant velocity and the free-fall situations mentioned above are actually just specialized forms of one single, universal equation that defines all the possible relationships between distance, velocity, acceleration, jerks, and so on, which in itself is a specialized form of the single equation which defines a general sum and any of its rates.

I’m not sure if I could quite convey this without explaining derivatives and integrals themselves, and I’m not sure anyone reading this could actually understand without understanding derivatives and integrals themselves. Suffice to say, Calculus unlocks a truly unique way to look at almost anything, specifically to look at relationships as not awkwardly defined in their own unique terms, but to boil down the definition of anything and everything into a single elegant system of simple rates and sums of other quantities. And understanding and viewing the world through the scope of this system both simplifies almost everything you already know, and makes many of the toughest new concepts easily graspable in familiar terms that you already know, by allowing you to define everything in terms of something else.

So now that all of you soon-to-be seniors know that Calculus is the most important and most applicable math ever (so don’t even consider chickening out and not taking math your senior year!), the biggest question many students face is to take AB or BC? In my senior year of high school, I did both, although not exactly in the conventional classroom setting. At my school we only offered Calculus AB as a class, although our very dedicated Calculus teacher held a weekly afterschool BC session for a few of us who essentially independent-studied the Calculus BC material. Thus, not having ever taken BC in a classroom setting over a full year (or semester), I’m not sure if my commentary is truly reflective of what most students will face, although in independent study we still covered all of the BC material and I was able to manage a 5 (out of 5) score on the BC test, for what it’s worth.

First of all, what is the difference between Calculus AB and BC? College calculus starts with two semesters, and high-school AB courses roughly cover the first semester of material while the BC courses cover both the first and second semester of material. For the most part, AB covers the basic concept of the derivative and integral, along with the various methods to compute the most common ones. In my BC experience (keeping in mind that I never took a BC course in the classroom setting), the BC material simply consisted of more advanced ways to solve trickier derivatives and integrals – methods like ‘integration by parts’ that, while needed to solve otherwise impossible integrals, contributed little if anything to the fundamental concepts of the derivate and integral, or any other relevant concept for that matter. Pragmatically, however, the BC material was a slightly different matter. Many of the integration methods would prove to be useful (and necessary) later on in Math. In the first math class I took in college, Multivariable Calculus (3^rd semester Calculus), complicated integrals that required knowledge of BC methods were ubiquitous (although unnecessary with regard to the actual fundamental concepts), and so the pragmatic skills learned in BC would be useful. In all subsequent math (that I’ve experienced so far – Linear Algebra & Differential Equations in my second-semester of Math), and certainly all science and any “real life” application, BC material is essentially worthless. While as a math major, abstract integrals like the integral of xcos^2(x) may be worth knowing how to calculate, the fact is that for any other field, integrals like those virtually never show up in real-world problems; outside of mathematics (and outside of 2^nd and 3^rd semester Calculus, even), I haven’t ever encountered a situation where I needed anything beyond the skills I learned in Calculus AB. Even in the rarest of rare situations where such an integral might arise, the far more efficient and common sense method is to simply use a calculator (what AB students do) or at worst look up the integral in a table (something even my post-Calculus graduate student instructors (GSIs) admit is the sensible thing to do). Methods are good to learn when they’re relevant to understanding fundamental concepts, or when situations that require them are bound to appear frequently enough to make them practical. Outside of perhaps a math major, the methods learned in BC don’t apply to any situation that anyone would encounter, either as a student or in any working profession.

That doesn’t answer the whole question, however. Useless as I think second-semester Calculus BC is, the fact is that it’s still required curriculum for many students. So the question, “should I take Calculus AB or BC in college” must be weighed against this. Fuzzy students obviously have even less use for BC material than techies, and my suggestion is that they check the requirements for the major at the college(s) they are planning to apply to – if second-semester Calculus isn’t a requirement (or part of some larger breadth requirement), don’t take it. If second-semester Calculus is required, however, I might suggest taking it in high school, depending on how confident you are about being able to pass the test. Since it’s a subject that really is irrelevant to your later fields of study, it’s much easier to pass the high school Calculus BC than it is to endure/waste an entire semester in college on Calculus, and it won’t really matter if you didn’t learn as much as you could have through an actual college course.

For techie students, my advice remains the same for similar reasons. Second-semester Calculus is almost an assured requirement, so there’s no way around it. As mentioned before, the tradeoff between a high-school BC course and a college course is that by passing the BC test you get to skip past what is otherwise a useless second-semester Calculus course in college, but will likely end up learning and retaining less (of somewhat useless material) than you would have in the college course. Although your mileage may vary, another consideration is the strict requirements that some colleges require for Calculus BC credit. At the UC Berkeley College of Engineering (which covers all engineering majors), for example, a perfect 5 out of 5 score is required to earn credit and skip second-semester Calculus – while many students from our small independent study group achieved this (note this is a biased sampling), a 5 is by no means automatic or easy, and students who struggle with Calculus may very well end up not receiving any credit for BC anyway and have a rushed/compromised AB education. Check with your college and intended major about the kind of requirements needed to receive credit for the BC test, and compare this against your proficiency as a student (if the requirement is a perfect 5, I might ask, “have I consistently been an A-student in math?”).

How will your BC-proficiency play out in post-second-semester-Calculus math? I’ve currently completed a single semester of third-semester Calculus (multivariable) and am halfway through another semester of Linear Algebra and Differential Equations, so my experience is fairly limited, but so far my BC education has either been monumental or trivial, depending on your priorities (I tend to view it as trivial). Having taken Calculus BC as a weekly independent study-like class, my retention of the material wasn’t nearly what it could have been with a full-on AP class, much less a dedicated semester-long college course, and this partially resulted in myself having pragmatic issues finishing out problems when I arrived at third semester Calculus (Multivariable). I had no hindrances in learning and comprehending all the fundamental concepts of multi-dimensional integrals and vector derivatives, however, as I had learned all that I needed from Calculus AB, and simply applied that to n-dimensional space. The result was satisfaction in having learned and understood all the fundamental concepts, coupled with a somewhat less-than-satisfactory grade because I wasn’t able to compute out all the problems, partially because of a lack of second-semester Calculus (BC) skills. Keep in mind that my situation is perhaps much more exaggerated than the typical high school student – I learned Calculus through a one hour-a-week afterschool class, while students who take actual BC courses get to have a full 5-days-a-week class, and thus will probably be far more prepared and retain far more material than I ever did.

Statistics

Usually the alternative senior-year math course for those who elect not to take Calculus, statistics is unique not only because it’s usually the only math course that doesn’t follow in the prerequisite chain of Algebra-Geometry-Algebra II-Trigonometry-Calculus (meaning you can jump into it anytime instead of following a strict order), but also because it’s a very self-contained subject – unlike other math, where you learn abstract math techniques and wait for a chance to apply them elsewhere in say science, statistics teaches you both the techniques and the myriad of statistical applications. I took the Statistics AP course concurrently with Calculus in my senior year, so my educational experience with statistics is likely more comprehensive than the non-AP Statistics classes that many schools offer or also offer.

Most students will get a taste of statistics in their Trigonometry class – when I took this in junior year we covered some basic concepts like probability, permutations, expected values, and normal distributions. Having taken Trigonometry my junior year, I think I was much more familiar with many of the initial concepts in Statistics, and this helped a lot to dive right in to the core subject matter – since I was already familiar with and understood the basic idea, I didn’t need to spend as much time figuring out what certain things meant (like the idea behind an expected value or how to interpret distributions), and could dive right in to learning how to use and apply them, which is what statistics is all about. Especially since statistics doesn’t really make use of any other mathematical concepts beyond basic algebra (exponents and logarithms are very important however), anyone who’s taken or is taking Algebra II should be able to handle statistics just fine (I think concurrent Algebra II might be a requirement as well – I’m not too familiar with this anymore).

I thoroughly enjoyed Statistics, and I might even venture to say that Statistics is one of the most appealing Maths for students who don’t like Math. The reason is that, unlike other subjects that are heavily weighted in abstractness that start with techniques and create problems for them, leaving a lot of students disinterested and wondering “When am I ever going to use this?”, statistics begins with the problems themselves and then finds techniques that allow students to solve them. While in any other math class a student might learn the Pythagorean Theorem and now have Sally mark a point and walk x meters down the river and measure an angle θ so she can find how wide the river is, this kind of example lacks immediate relevancy – people don’t encountering measuring the width of rivers in everyday life, and even if they do, they’d just take a measure straight across the river using a tape measure or some other device, not some cockamamie Pythagorean Theorem method! In statistics, we begin with very real-life problems – error probabilities and allowances with manufacturing facilities, or distributions for characteristics like a population’s height, and only then do we break out and learn about the tools like standard deviation and binomial distributions to solve them. I think I’m starting to talk too much from an educator’s perspective instead of a student’s, so in a nutshell, Statistics is very interesting, relevant, and great fun, even if you’re someone who’s been scared off by all other kinds of math in the past.

How is statistics important? Well, unlike the other mathematics courses, statistics isn’t really on the prerequisite list for anything, which is a shame because it’s probably the mathematical subject with the broadest and most immediate appeal and applicability to students studying in any field. Take a moment to think about the activities and tasks you’ll perform in your intended field of study, both academically and professionally. If you’re doing any kind of engineering or hard science, it goes without saying that all of data you collect from tests and experiments need statistical analysis to interpret them into any kind of useful information, and any product one might design or build would need to fit within certain specification and error parameters. If you’re studying business or economics, everything from market indicators to company finances and economic trends compose a major if not integral part of running any business, and the accuracy and significance of any of that information relies heavily not only on good statistical analysis, but good statistical practice in obtaining that data in the first place. The same goes for any of the ‘social sciences’ – anthropology or sociology or psychology deal very much with individuals and more “fuzzy” observations and notes, but at the end of the day, valid and meaningful information and conclusions can only be derived from collecting large amounts of such fuzzy data and interpreting them statistically. Even for the everyday person, regardless of college education or profession, statistics are encountered on a day-to-day basis, with information received from media outlets (television, newspapers, government or research reports) or when using statistical information to make decisions and policies. Thought it may not be readily apparent at first glance, statistics very much run the world, and while someone else may end up as the bean counter, it’s very important to know whether that person is counting the beans correctly and what all those beans mean in the first place.

I would recommend statistics almost universally to any student. In my experience at least, the curriculum isn’t nearly as rigorous as most of the other math courses, and it’s surprisingly approachable even by those who don’t have particularly strong math backgrounds. And at the end of the day, it’s a subject that almost anyone will find useful, both from fundamental and pragmatic standpoints.

In Summary

So I’ve just hit the 12^th page as I’m typing this out in Word, and I figure I better write a nice conclusion to sum this all up, particularly for all of you who haven’t the time to sift through the entire preceding portion of this article.

Math, from the simplest of arithmetic, to algebra and calculus and branching off into statistics, is the first, most fundamental step to understanding the world. Admittedly, a lot of high school mathematics gets muddled along with burdensome pragmatic methods which aren’t always useful and relevant, something necessitated by the generalized and mixed situation of high school education – high school mathematics is very much geared towards techies that will enter into math or scientific or engineering fields, and while it has very important lessons for fuzzies as well, much of this comes buried under things that many students won’t care about.

From both a techie and fuzzy standpoint, the most important thing I’ve learned throughout high school and now in retrospect is that mathematics is perhaps the most important step in furthering the capability to understand almost every other subject taught in school. This is very apparent when students first learn Algebra or Calculus, which first introduce the broad, overarching, important-to-everyone concepts, but a bit less so in all of the in-between classes that simply build on and abstract those ideas. For that reason it’s a good idea for any student to advance their math education as far as possible, particularly for the sake of reaching the Calculus plateau in senior year. The in-between classes, while still important from a pragmatic standpoint, don’t matter as much, and for that reason I wouldn’t get discouraged if they seemed boring or even if I was struggling a bit.

The biggest lesson that I’ve admittedly stumbled upon after the past two months of writing this (it’s been a busy on-and-off piece) is a general one, however, that really applies to all education, at every level. Education teaches a lot of things, but most all of it can be broken down into fundamental concepts and pragmatic applications. In every field of study there are fundamental concepts, and these are usually relevant to everyone, no matter what they’re studying or doing in their lives. Coincidentally, it’s these concepts that are most often the easiest part of a subject – there isn’t much work required, just critical thought in order to grasp the subject. In most fields, after these fundamental concepts come many pragmatic exercises and applications (although these in themselves may be prerequisites to understanding the next level of fundamental concept). For the most part, these aren’t relevant unless they’re a part of your study or working field, or cover an application that has broad and/or everyday significance. At the end of the day, it’s the pragmatic applications that make a career (partly why education gets more specialized and application-intensive once you start college), and the fundamental concepts that enrich a person and make them into better learners. Rather than grades or test scores, these are the most successful priorities one can possibly have throughout their high-school education.

Reflections on my high school education in the field of foreign language

In this series, I take a look back at my education as a high school student, and from a college perspective, how everything turned out. It may be a little late for this year’s seniors, but hopefully high school students at all levels can gleam some helpful advice about their class choices over their four years in high school.

The first discipline we’ll be covering is the realm of Foreign Language, a conveniently short first piece given my general lack of experience, and a subject that I and everyone else hated in middle school when they sprung it upon us as the inaugural Spanish class in 7^th grade. Why do we have to do this? This isn’t even useful for anything!, sentiments that are still somewhat echoed today.

I was a weakly bilingual student from the start. I grew up speaking the Cantonese dialect of Chinese, and although I could use it conversationally, I never comprehensively learned all the nuances of grammar or the entire extent of vocabulary, nor did I ever learn to read or write. I went on to take extremely basic Spanish in 7^th and 8^th grade in middle school, then took two years of Spanish at the high school level in my freshman and sophomore years where I did well on paper but really didn’t learn much. In the summer between my junior and senior years, I took a 5-week trip to Italy, and although I had little formal training (about a week), by the end of my stay I had learned enough Italian to carry out the daily functions of life. As an engineering student, I don’t have too much of a need for foreign language, and so far in my two semesters I haven’t taken any foreign language courses at the college level.

With that context in mind, what follows is a completely personal reflection on my high school education in the field of foreign language from the perspective of college.

Foreign language is a tough field to describe for me, not only because I honestly don’t have that much experience with it, but because unlike math or sciences or social sciences or even English, foreign language isn’t strictly regulated or standardized. There are no big state tests measuring school’s performance or statewide standard curricula, and so the methods used and materials taught in foreign language classes are often highly variable between schools and even teachers. My 2 years in high school Spanish was very much focused on basic literacy and the technical aspects of language than actual fluency. We never really spoke it conversationally in class (not like other classes where English isn’t used at all), and the course was dedicated to recognizing the grammar structure and memorizing vocabulary and conjugations. At the end of two years I could stumble through a text and get the gist of it, and could speak and listen with large latencies while I translated everything said and heard into English first, which I would say was typical for most students after two years (and most students I knew after three years as well, although I don’t have firsthand experience with third-year foreign language). Today, two years after that, I haven’t retained a single bit of Spanish.

In contrast, the 5 week trip and 10 day crash course I had in Italian was just the opposite – I spent a small amount of time getting the basics of conjugation and memorizing common survival vocabulary, but from then on there wasn’t any formal instruction – I learned Italian conversationally in class, or by actually using it in day-to-day activities. At the end of 5 weeks, I could carry on and understand conversations well (given the 5 weeks) and certainly better than I ever did with two years of Spanish, couldn’t read very well, and probably had grammar and syntax problems with everything I said, although the meaning was all there.

So what lessons did I learn? In my two years taking Spanish, after initially learning basic conjugation and grammar rules, I didn’t do much but continuously scrape together more vocabulary. This helped with reading, as I gradually understood more and more words, but I never approached the ability to carry a conversation, nor did I ever come close to fluency where I could interpret directly within Spanish itself, rather than translating everything into English first. Part of the problem was that this was all my high school foreign language classes ever aspired to – there was never any attempt to impose a Spanish-only environment that would force students to utilize the language, and I personally didn’t have any other environments or outlets through which I could practice and utilize Spanish on a regular basis. All skills eventually deteriorate without use, and not having an environment or being in a field of study that utilized foreign language, I had pretty much lost all that I had learned after I stopped with classes – the fact that I only ever learned conscious translational skills, like memorizing vocabulary, rather than secondhand-like conversational fluency skills only accelerated this.

On the other hand, taking a foreign language at all laid a very good groundwork for picking up languages in general, and especially similar languages. Though by the summer of my junior year I had forgotten most of the Spanish I had learned, concepts like conjugation or basic grammar in Italian, another Romantic language, came very easily, and remnants of the vast stores of vocabulary I had memorized came in handy with many of the similar Italian words. All the extra vocabulary I picked up in my second year probably didn’t help, but the first year introduced the perspective of language from a technical sense; without foreign language you’d never think about the English language in terms of something like conjugation, for example – it does happen, but we conjugate all of our verbs instinctively, by habit (we have so much exposure to our own language that we just memorize and know things) or experience (this suffix “sounds right” for this verb form), and the conscious, technical skill of English conjugation was lost way back in the 2^nd grade. This is needed because learning any foreign language needs a technical understanding of the language system as a foundation, since no one studying a language has the time to get the fourteen childhood years of fully-immersed language experience we use as the foundation for our native languages.

For myself, I didn’t gain very much at all after my first year with a foreign language – without an environment that was truly dedicated to teaching fluency in a language (in my opinion a foreign language-only environment is needed to teach this), continually harping on the grammatical and vocabulary aspects of a language couldn’t take me very far in any usable foreign language skills. (I’m certainly not a universal case, however, and keep in mind that as a math & sciences type of student, I never had much intent to learn a foreign language in the first place).

For myself at least, my 5 weeks in Italy validated my belief that the only way to truly learn a foreign language was to fully immerse myself in a completely non-English environment. Out of the necessities of daily life I had to utilize Italian, and through repetition more than anything learned the words and grammar and conjugations, much like the way we all learn to speak in our native languages. In this way, Italian came to me much more second nature than Spanish ever did even after two years of study. On the other hand, my proficiency in Italian never progressed beyond a basic level of comprehension and conversation, due to only having five weeks but more importantly not having any technical understanding of the language as a foundation to organize everything I learned. Through everyday experience, I absorbed a ton of language, but all I could ever really do was replicate.

(I’m formulating my thoughts as I type this out) … so perhaps the only way to ever really learn a language is to have both a technical understanding for a foundation, and the experience of real-world immersion into the language, preferably the former first in order to make sense of everything absorbed in the latter. For anyone serious about learning a language, it doesn’t make sense to half-ass it and only do one: by only studying the language and memorizing vocabulary you’re never able to develop any usable, practical language skills, but on the other hand by simply placing yourself in that environment and learning through experience without ever attempting to organize and make sense of the language, you’re never able to move beyond the point of simply replicating what you’ve already experienced. It’s nearly impossible to approach fluency through solely pursuing one method, and without actual fluency, memorizing all the vocabulary or knowing all the survival terms by instinct alone aren’t really of any practical use.

[Awkward segue]

As this post is intended for the college blog, what are my perspectives about high school from college education? What mattered? What would I do over again? As an engineering major, my field of study and probable eventual line of work doesn’t cross the need for foreign language much, if at all (mathematics is our native Esperanto, har har!), and for the College of Engineering here at Berkeley at least, foreign language isn’t a requirement at all. Was all my foreign language education for naught? For an engineering major, probably, although don’t discount the instances in actual, non-academic or -professional life where the foundation of foreign language may be useful. For many other majors however, foreign language is often one of many breadth requirements, and even though you won’t get credit for classes you take in high school, from my experience, just having taken courses in any foreign language at all will help in picking up any other language.

Perhaps the biggest students most students will come to this blog about however, is how many years of foreign language to take, and perhaps more specifically, should I take 3 years or 2 years?

For my college applications (most notably the UC system), most college admissions required two (2) years of foreign language, and three (3) as “recommended”. As an eventual engineering student, my actual need for foreign language in my field of study was essentially none, although if I were to do it over again I’d probably take one year as, personally, the subject was a good exposure to have. I stopped taking foreign language after two years, not really because I wasn’t interested but simply because I wasn’t learning anything useful, and couldn’t see how I could have, from my school’s particular class environments – I didn’t see a need in continuing to waste time while not gaining any appreciable language skills, and ideally this should really be the criterion on which you decide whether or not to take another year of foreign language, or any class for that matter.

At this point, I come into disagreement with a lot of people, which will probably be apparent if I ever find other writers to offer their perspectives (and so I simply inform you of this contrasting viewpoint in the meantime). For myself, I was doing well enough in other aspects and wasn’t applying to a major related to foreign language, and so my decision to take just two years rather than the “recommended” three probably didn’t matter that much, and I would tend to say that students doing engineering or science (i.e. not anywhere near fuzzy majors) would do just fine taking the minimum two years, advice which probably has the consensus of others also.

For fuzzy majors on the other hand, the issue is a bit trickier – I don’t know of any students who took “only” two years and got rejected, although the information I have is rather limited, and I can’t begin to speculate on the reason why admissions boards reject or accept individual applications. From a logical standpoint, I would think that a third-year is a non-issue: nothing most students take in high school (the exception being the rare AP foreign language class) will be considered college-level, and thus almost every student who would need to take foreign language at the college level would end up retaking everything again starting at the most basic and fundamental level, regardless of having a second or third year of study. The college requirements, in addition, are minimum requirements – like “minimum test scores” that are generally extremely low, they aren’t in anyway a guideline for “what you need to get in”, but are rather requirements – (speculation) admissions boards simply check to make sure students have at least met these requirements, and then go on to other decidedly more important and telling factors of your college application. And in this case, unless your intended major actually has something to do with foreign language, an entire year of class is much better spent on a course actually relevant to your field of study.