College admissions and Blair high school courses
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Anonymous
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I looked at the Blair Magnet Math courses: https://mbhs.edu/departments/magnet/courses_math.php
I can tell from the course description that these are especially basic variants of the college level equivalent. To compare: Blair- Linear Algebra is a field that deals with vectors, matrices, and spaces. You may think that these concepts sounds way too abstract, but in fact linear algebra may be one of the most applicable and foundational fields in mathematics. Besides being used to formalize a variety of fundamental ideas in mathematics, linear algebra is connected to a variety of computer applications, from computer graphics to network algorithms. In fact, the basic ideas used in modern search engines like Google are rooted in linear algebra. Complex Analysis- You may know that complex numbers arise when you play around too much with square roots and negative numbers. However, complex numbers aren't just curiosities resulting from bad mathematical behavior. The most advanced calculus class offered in the Magnet, Complex Analysis takes the concepts from the first two Analysis courses a step further by pushing them into the exotic realm of the complex plane. In this course you'll study some of the concepts that are being applied to the hottest problems in mathematics and physics today, such as the Riemann Hypothesis and string theory. College Level- Linear Algebra. Theory and applications of linearity, including vectors, matrices, systems of linear equations, dot and cross products, determinants, linear transformations in Euclidean space, linear independence, bases, eigenvalues, eigenvectors, and diagonalization. Complex Analysis. In this course we will apply familiar concepts such as line integrals and differentiability to complex-valued functions. We will investigate the Cauchy-Riemann equations, and study holomorphic and meromorphic functions via Taylor and Laurent series. Cauchy's theorem and integral formula along with the calculus of residues will be featured. We will also introduce conformal mappings and harmonic functions. They're nowhere near the same level in depth. Good as a stepping stone, but most of the students who take the course will have to take it in college again. |
Anonymous
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Whoops, there is a option to look at a formal course description from Blair. My apologies--
Lin Alg- Students learn the theory and practice of matrices and determinants and their use in solving linear equations. They study the structure and properties of linear transformations, vector spaces, and linear programming as they apply to such fields as biology, chemistry, differential equations, economics, psychology, and weather forecasting. Complex- Students are introduced to the theory of functions of complex variables, an essential part of the mathematical background of engineers, physicists, mathematicians, and other scientists. They review complex numbers and study complex functions and the calculus of complex functions, including derivatives and integrals. Other topics studied include series, residues, and conformal mappings. The linear algebra course seems too tangential and lacking in some of the content usually in a college level course. It's meant to be a proof based course, but the curriculum doesn't seem to emphasize it. The complex analysis course seems more promising, but it'd depend on the extent to which students are diving deep into content. The lack of specificity is concerning- are students merely scratching the surface? As mentioned previously, college courses tend to be a lot more challenging. |
Anonymous
Well, I was not a math major and those Blair offerings look nothing like what a math major would take. |
Anonymous
| Times have changed from when we all went to school. Many Blair kids use their internet access to online courses on upper level science and math topics which were not available back in the day. In addition, because of the peer group at Blair, kids on the math team, physics team, science bowl team, robotics team, etc, are learning many concepts that are not necessarily described in the blair curriculum that has been mentioned. In addition, each kid in the magnet completes a research project in their area of interest and a lot of outside study goes into developing interesting results and papers which are submitted to competitions like Intel and Siemens. I am sure that you are aware that Blair has been very successful in these competitions. These kids are very bright and very motivated and they are given the opportunity to enter college extremely prepared. And I stand by my recommendation regarding selecting a university with a strong graduate program. |
Anonymous
I think that’s a bs recommendation but whatever. Kids usually don’t stay at the same school for masters/phd work. |
Anonymous
| The entire discussion has been about undergraduate education and being able to take graduate courses during undergraduate studies. |
Anonymous
| I have toured over 10 colleges with my junior, and I have heard many, many directors of admissions speak about how the rigor of coursework counts more than anything. This past weekend, one at a top LAC specifically stated that if she was presented with two applications, one with a full IB diploma and a 3.4, and one with easier classes and a 4.0, she would pick the 3.4 every time. |
Anonymous
Pp here. I was going to continue on to say, take the harder classes, even if they are offered again in college. You want to show that you are up for a challenge and can hold your own in advanced coursework |
Anonymous
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The suggestion that one HAS to take math courses in graduate school to get into a competitive program is blatantly false.
First of all, the highest upper-level courses at elite LACs are already modeled after first or second year graduate level courses. Looking at the Mudd listing of courses, I see at least 20 courses that would resemble graduate level courses at a major research U, like UCLA: https://www.math.ucla.edu/grad/courses The courses demarcated as "graduate level" for Mudd seem to be the seminars listed at the end, but the bulk- the upper 75% or so- is just advanced math courses. I'm part of the American Mathematical Association. One of the coveted distinctions is "Exemplary Program or Achievement in a Mathematics Department", given to one school each year for excellence in math. 3 LACs have won out of 12 recipients- Harvey Mudd (the first recipient), Bryn Mawr, and Williams. Mudd is one of maybe 12 schools or so which has placed in the top 10 of Putnam (top undergrad math competition) or had a Morgan prize winner (top undergrad research0based distinction in Math). Williams has produced a Fields Medalist (the Noble Prize in math), and of the past 5 recipients of the Morgan Prize, 2 of them participated in Williams's summer math research opportunity (SMALL- it's considered one of the top 3 summer math opportunities for undergrads) and cited it as an important force for them. They were from MIT and Harvard, but think about it- if Williams' professors (who lead the program in full and mentor their own math students during the school year) have the ability to give transformative experiences to what are virtually the BEST math students in the nation, you seriously think that your precious child who took a few intro-level math courses at Blair is too good for them? Here were the top 20 schools for producing Math PhDs on a size adjusted basis in order, based on the NSF: Mudd, Caltech (both far above the others), MIT, Carnegie Mellon, UChicago, Rice, Princeton, Swarthmore, Harvard, Reed, New Mexico Tech, Carleton, Williams, Bard, Haverford, Rose-Hulman, Pomona, RPI, Stanford, Amherst. That's 9 LACs. Math PhDs are so selective that common advice is to take as many advanced math courses as possible (while doing well) and to pursue research. The LACs in the top echelon know who they're competing against and what they need to do to prepare their students. Let's be clear- not all LACs are built the same. Few will have the range of courses that the Claremonts or Williams have. At some good but not exceptional LACs, an advanced student can definitely run out. Even some top tier LACs not known for math, like Middlebury, can be limited- Middlebury only offered 24 mid and upper level math courses in 4 years. The net result is that these schools do poorly in math PhD production- Middlebury is not in the top 100 for production of Math PhDs. The central premise- do your research. Have your child see where he or she is, how robust the curriculum is, and how often courses are offered. Look up success in sending students to academia. Don't assume that only schools with an associated graduate program can prepare students well. The only time I'd say a student would inherently pick a school with a graduate program in is for someone placing in International Math Olympiad or USAMO, which is just 500 high school students in the US per class year. In those circumstances, only 9 or so universities are recommended- MIT, UChicago, Princeton, Harvard, Stanford, Caltech, UCLA, UC Berkeley, Carnegie Mellon- and these students know this from the get-go. |
Anonymous
| I love how the previous poster never responded to the listing of Mudd upper level courses. Statement about not going to a LAC called out with some examples to the contrary, make up a false statement that it was at Mudd where said child was running out of courses, and then get a full response detailing the 70 (I counted) unique math courses offered in 2 years not including senior thesis, making that virtually impossible. It amuses me when people's preconceived notions are challenged with real evidence, yet they still remain adamant that they're correct. The Blair magnet courses are not that rigorous if students are finding them a "joke", and they seem to be superficial. It may sound impressive on paper, but I'd love to see the typical student in those courses at a Mudd or Williams equivalent and see if they still find it a joke. |
Anonymous
????? Who is finding the Blair magnet courses as "Joke"? |
Anonymous
Not true. My son is a junior at Blair, taking Multivariable Calculus. The teacher from his class has taught the class at a flagship university, and let us know at parent's night that this is the same class. I can confirm that, based on the homework I see him doing, and the fact that he is using the exact textbook (newer edition) that I used at my liberal arts program (one of the set that sends the highest proportions of students on to graduate school). From what I could see (paging through text and perusing homework), Linear Algebra also covers the same ground I covered as an undergraduate. |
Anonymous
Yep. |
Anonymous
| You Blair parents are so pathetic. You should be embarrassed. |
Anonymous
I also had a child who did the magnet program and went to one of the 20 schools mentioned. He had taken multivariable/diff EQs in 11th grade and Discrete/Linear in 12th grade. He brought the syllabus to the math department chair, and she encouraged him to take the advanced or specialized version of the courses instead of outright skipping them. His material was the equivalent of the foundation course offered across virtually any college in the country. He started with Honors Linear Algebra, which was much, much harder than the Blair equivalent. So hard that the whole class spent hours every night trying to tackle the problem sets. No textbook, just pure proofs applied by unique problems developed by the teacher- he did not struggle nearly as much in Blair with any course! Then he dove into Vector Calculus, a theory-based variant of Multivariable calculus that had some overlap, but not much. This is the textbook used- https://www.amazon.com/Vector-Calculus-Dover-Books-Mathematics/dp/0486466205 - as the reviews make clear, it's much more rigorous than a standard multivariable cal textbook. To note, even math majors with no experience in these courses jumped straight into Honors or Vector rather than taking normal Linear Algebra or multivariable (set aside for non-majors looking for a more applied course), so taking those Blair courses didn't position him as considerably stronger than his classmates. He was more interested in pure math so he didn't take differential equations, and the discrete math course he took was specialized for computer science (he was deciding between theory-based CS and math). If he could do it all over, he'd still have taken the courses at Blair. They are what cemented his love for math, and I do believe they made him stand out. But he'd be the first to tell you they were pretty standard courses, not especially akin to the rigor and depth of those at his college. Math has basically taken over his life at his school (the special feature is research- he's already been published in 2 papers with his professor and peers), and he loves it. But that's to be expected, isn't it? If you're paying the $$$ for a top private university, you want it to have much more depth than a magnet HS. Any school that's a top 20 feeder doesn't take just about any typical math student- the department and the courses would have to be set to a higher level to sufficiently prepare majors for competitive PhD programs. In any case, I think we're diving away from the core premise of this thread. Blair magnet students are lucky to be able to take the number of courses beyond Calc BC that they can. They're the smartest in a competitive school and have the stats rivaling those at any top college in the country. I just don't think the teachers do an especially great job matching the rigor with their ability- as you noted and as I observed, the courses are fairly similar to that offered at a state school or community college. |