| > Can you give some specific examples of the math and physics that you think are beyond the capabilities of a bright high school graduate (that seems like a reasonable minimum bar to expect for someone picking up a book targeted at freshmen at MIT)? I'm going to stop you there. If you think that jumping into approximating square roots via newton's method is not a "high level of competence in math and physics" then you have lived in a completely different world than I did. And the issue isn't knowledge (that's shared in plenty of detail in the book), but the maturity of mathematical reasoning. The level of calculus taught to me in high school (and college) was at the same level as Algebra and Trigonometry. It was taught as a tool for engineers to use, not as a framework for building your own tools (proof-based calculus). The only people around me that reached that level of mathematical maturity were Maths, Physics, and Computer Science majors. And often it wouldn't "sink in" until around junior year for them. > The \sqrt(x) = the y such that y >= 0 and y^2 = x. This is an extremely dense mathematical sentence that requires a high level of mathematic maturity to understand that the author isn't just throwing that out randomly. It wasn't until I took a formal proofs/introduction to analysis course that it sunk in that a mathematical definition isn't just a sentence describing a new piece of vocabulary but is instead a highly technical engineering spec for a mathematical tool. And until I made that transition I couldn't follow the flow of the logic, implications of the ideas/problems presented, or see the bigger picture of how these things fit together. They were technically accessible to me (I could read and understand the words and problems), but they completely lacked coherence to me. |