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Calculus is designed as a gateway for all of our quantitative students, our future engineers and physicists in addition to our computer scientists, and so it's

Calculus is designed as a gateway for all of our quantitative students, our future engineers and physicists in addition to our computer scientists, and so it's already forced to wear many hats. Changing it isn't something we can do lightly, as it's integral in everything from standardized testing to college admissions (in the case of high school students); and nearly every quantitative track (in the case of college students). What good does splicing Big-Oh into the process do, when computer science enrollment is in steady decline, and understanding Big-Oh is pointless without first understanding the costs of polynomial algorithms? It would be nice if our calculus students knew Lebesgue integration too, but I would offer that the calculus sequence is not the right time. If the kids are in college, they can take Intro. to Comp. Sci., and if the kids are in high school, they probably shouldn't worry about Big-Oh at all. The biggest revision high school math needs is 1. A course which instills students with a basic statistical fluency, so they can read the newspaper and endure advertisements with a critical mind, and 2. A course for advanced students which teaches discrete math and basic non-geometrical proofs, for our increasingly discrete world.

LogicHoleFlaw 18y ago
In my experience, Calculus in the university is solely used as weeder material, designed to bludgeon students with the notion that mathematics is dull, tedious, and a necessary evil. Nothing did as much to destroy the joy I derived from math as did my college Calculus courses. The current pedagogy of Calculus is atrocious, and any method which helps impart the beauty of it without battering the souls of the students is worth pursuing. Feynman's great strength was his disregard for orthodoxy in the search for greater truth. Big-O notation is for more than just profiling the costs of computational algorithms. It is for reasoning about inexact quantities and seeing the greater patterns in the relationships between numbers and functions. Is using Big-O as a method of teaching Calculus better than the current process? Honestly, almost anything would be an improvement. Math and Calculus are both beautiful and practical. But the current way we teach them completely loses those notions in favor of rote memorization and techniques without context.
- amichail 18y ago
  Some places teach Calculus well. For example, check out the advanced Calculus courses at Waterloo.
  - LogicHoleFlaw 18y ago
    How well do the introductory courses fare?
    - amichail 18y ago
      I don't know what it's like now, but when I was there, the advanced courses were very intimidating. This is the real deal.
    - mrtron 18y ago
      The introductory courses are quite tough. They teach the material well, but when it comes to assignments and exams they ask questions that tend to force you to apply the things you learned with some sort of twist. I always thought I knew the material inside out and got crushed on exams compared to how I thought I did. edit: Actually, 137/138 (which you will take first and second term) have recently been nerfed since they eliminated OAC and stopped teaching much calculus in high school.
- brentr 18y ago
  I will agree with you on the point that mathematics is beautiful. I had always appreciated mathematics for its logic. A proof is either right (it proves) or it is wrong (it does not prove), however, it was not until I was introduced to double and triple integration that I realized the raw power and beauty of calculus. I start working towards my computer science and math degrees this summer, and my registered courses include discrete mathematics and probability. I can be confident in the fact that I will learn some easily learned ideas that are able to do very powerful things.
  - LogicHoleFlaw 18y ago
    Best of luck in your studies! Discrete mathematics was one of my favorite courses in school.
stcredzero 18y ago
I really wish that a lot of the non computer-science people I have to work with knew at least a smattering of what it means that something is O(n^2) versus O(n log(n)). In fact, I sometimes wish that programmers who I've had to work with understood!
- johnm 18y ago
  Indeed! I was "interviewing" with the head developer at a media startup who thought he knew his stuff and after handing him his hat on a number of things, he tried one last "zinger" question on O(). Turns out that neither he nor the head of engineering knew the difference between O(n^2) and O(n log n) but they were so confident that they did. Unbelievable.

LogicHoleFlaw 18y ago

In my experience, Calculus in the university is solely used as weeder material, designed to bludgeon students with the notion that mathematics is dull, tedious, and a necessary evil. Nothing did as much to destroy the joy I derived from math as did my college Calculus courses. The current pedagogy of Calculus is atrocious, and any method which helps impart the beauty of it without battering the souls of the students is worth pursuing. Feynman's great strength was his disregard for orthodoxy in the search for greater truth. Big-O notation is for more than just profiling the costs of computational algorithms. It is for reasoning about inexact quantities and seeing the greater patterns in the relationships between numbers and functions. Is using Big-O as a method of teaching Calculus better than the current process? Honestly, almost anything would be an improvement. Math and Calculus are both beautiful and practical. But the current way we teach them completely loses those notions in favor of rote memorization and techniques without context.

amichail 18y ago
Some places teach Calculus well. For example, check out the advanced Calculus courses at Waterloo.
- LogicHoleFlaw 18y ago
  How well do the introductory courses fare?
  - amichail 18y ago
    I don't know what it's like now, but when I was there, the advanced courses were very intimidating. This is the real deal.
  - mrtron 18y ago
    The introductory courses are quite tough. They teach the material well, but when it comes to assignments and exams they ask questions that tend to force you to apply the things you learned with some sort of twist. I always thought I knew the material inside out and got crushed on exams compared to how I thought I did. edit: Actually, 137/138 (which you will take first and second term) have recently been nerfed since they eliminated OAC and stopped teaching much calculus in high school.
brentr 18y ago
I will agree with you on the point that mathematics is beautiful. I had always appreciated mathematics for its logic. A proof is either right (it proves) or it is wrong (it does not prove), however, it was not until I was introduced to double and triple integration that I realized the raw power and beauty of calculus. I start working towards my computer science and math degrees this summer, and my registered courses include discrete mathematics and probability. I can be confident in the fact that I will learn some easily learned ideas that are able to do very powerful things.
- LogicHoleFlaw 18y ago
  Best of luck in your studies! Discrete mathematics was one of my favorite courses in school.

stcredzero 18y ago

I really wish that a lot of the non computer-science people I have to work with knew at least a smattering of what it means that something is O(n^2) versus O(n log(n)). In fact, I sometimes wish that programmers who I've had to work with understood!

johnm 18y ago
Indeed! I was "interviewing" with the head developer at a media startup who thought he knew his stuff and after handing him his hat on a number of things, he tried one last "zinger" question on O(). Turns out that neither he nor the head of engineering knew the difference between O(n^2) and O(n log n) but they were so confident that they did. Unbelievable.