Lectures in Projective Geometry (Dover Books on Mathematics)

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But say you were a great teacher, and knew that clear teaching was worse than imperfect teaching. Could you actually make your lectures less clear on purpose? Personally I thought the Feynman lectures were ok but with room for improvement. Vol 1 was good. Vol 2 was good though overly repetitive, iirc it's 90 percent Maxwell's equations. Vol 3 was unintuitive to me. Which suggests there are better ways to learn than Feynman 3.

My understanding is that you can't learn without going through mistakes first. If you find it intuitive, you find it correct and the brain doesn't change your neural structure; because why would it? People want intuitive explanations because it seems the easiest.

It is, that's the problem. Learning is supposed to be painful. You have to get your hands dirty. It's easier to feel that you know something than to actually know it. Learning requires a lots of false starts, traps, etc.

After doing the hard learning, you can lecture your intuitive mental model you have. But it's difficult to install that mental model into a beginner's mind. Often the intuitions are illusory mnemonics for the deeper understanding, which if you never learned in the first place would just point to nothing. You have to do the hard learning to arrive at the "intuitive" mental model. While i see where you are coming from; i feel that you are putting the cart before the horse. While Intuition by itself is not enough, it should absolutely be the first thing you should focus on before doing the hard work through rigor and formalisms.

The former can be "grasped" while the latter needs "practice and applications". This is how Science itself developed a good example is Faraday vs. Maxwell's approaches. You need both, each amplifying the other's effects at various stages. Campbell, Life, p. In a later letter, Faraday elaborated: I hang on to your words because they are to me weighty There is one thing I would be glad to ask you.

When a mathematician engaged in investigating physical actions and results has arrived at his conclusions, may they not be expressed in common language as fully, clearly, and definitely as in mathematical formulae? If so, would it not be a great boon to such as I to express them so? I have always found that you could convey to me a perfectly clear idea of your conclusions Life, p. Hard work is going through a lot of intuitive models that turn out to be false.

If seen this way, the comment you respond to, makes sense. Well said! All students need to keep this in mind. At Caltech home of Feynman in the s, his books were not used as the main texts in physics classes, but as supplements. For mathematics, I would recommend: 1.

Lectures on Analytic and Projective Geometry: Dirk J. Struik: compwilsoftfa.tk

An Elementary Approach to Ideas and Methods" by Courant and Robbins -- a general book on mathematics in the spirit of Feynman lectures. Tristan Needham, "Visual Complex Analysis", beautiful introduction to complex analysis. Cornelius Lanczos, "The Variational Principles of Mechanics" -- this is a physics book, but one of the classics in the subject, and as Gerald Sussman once remarked, you glean new insights each time you read it.

Cornelius Lanczos, "Linear Differential Operators" -- an excellent treatment of differential operators, Green's functions, and other things that one encounters in infinite-dimensional vector spaces. This book has some very intuitive explanations, e. For chemistry, I would recommend "General Chemistry" by Linus Pauling, even though it's a bit outdated. From From the description: "This course of 25 lectures, filmed at Cornell University in Spring , is intended for newcomers to nonlinear dynamics and chaos.

It closely follows Prof. Analytical methods, concrete examples, and geometric intuition are stressed. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors. A unique feature of the course is its emphasis on applications.

These include airplane wing vibrations, biological rhythms, insect outbreaks, chemical oscillators, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory. The theoretical work is enlivened by frequent use of computer graphics, simulations, and videotaped demonstrations of nonlinear phenomena.

The essential prerequisite is single-variable calculus, including curve sketching, Taylor series, and separable differential equations. In a few places, multivariable calculus partial derivatives, Jacobian matrix, divergence theorem and linear algebra eigenvalues and eigenvectors are used.

Fourier analysis is not assumed, and is developed where needed. Introductory physics is used throughout. Other scientific prerequisites would depend on the applications considered, but in all cases, a first course should be adequate preparation. Just a note, "Visual Complex Analysis" is a terrible book to learn complex analysis.

Proofs are very iffy, akin to sketches of proofs. With that said, it is a excellent supplement to another std. Is it just the normal difference between e.

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I can think of a lot of fields where a decent grasp of complex analysis concepts would be very helpful even without being able to do rigorous proofs. In terms of depth and breadth, the Princeton companions get close to Feynman. It's easy to gain physical intuition because you can often explain one physical phenomenon in terms of another physical phenomenon that you have much more real life experience with.

But with mathematics, "intuitive" analogies are all in terms of other mathematical objects! You can't build intuition if you don't even know what they trying to abstract over. In that regards, The Princeton Companion to Mathematics is fantastic because it maps out how the different fields of mathematics are interrelated. I think everyone in this topic is missing the point of what makes the Feynman Lectures unique. I'd use 3 words to describe Feynman's style: clarity, accessibility, and fascination. This description made me think of the "Mathologer" channel on YouTube.

ArtWomb 17 days ago. Good list!

Lectures in Projective Geometry (Dover Books on Mathematics)

A standard textbook for incoming students across disciplines and very accessible. We used that book for a course and I found it among my less favourite ones. UncleSlacky 17 days ago. I much preferred Stroud's "Engineering Mathematics" which was a course book for engineers at my university I studied physics. ArtWomb 16 days ago. Boas is maybe not as inspiring as Feynman. But when you see a copy on someone's bookshelf. It tends to be just as dog-eared and spine-cracked as Surely You're Joking Another resource I just thought of.

Introduction to Projective Geometry - WildTrig: Intro to Rational Trigonometry - N J Wildberger

While not a textbook per se. I purchased [2], having enjoyed Nick Higham's other book a treatise on matrix computations , and knowing how well-received [1] was. But, [2] turned out to be kind of a dud. It was not really fun to browse, and I wasn't sure who it was directed to. The articles that I sampled read like they were intended for academic applied math folks, rather than introductions for interested outsiders.

It's a huge book, so YMMV, and has been very well-reviewed by high-profile and well-qualified academics like Steven Strogatz but I spent a couple evenings with the book and could not recommend. In any event, it's not like Feynmann's lectures! It's an encyclopedia. TLDR: "it was good for someone, but it was not the book I wanted". Spivak's Calculus.

It's "just" calculus It's a wonderful book, written in a very engaging style, and it shows you how mathematicians think and how they play. It shows you why we have proofs, why things go wrong, and all that had to happen before we came up with a definition of derivatives and integrals that we're happy with and of course, all of the things we can do with our newfound definitions.

Lectures in Projective Geometry (Dover Books on Mathematics) Lectures in Projective Geometry (Dover Books on Mathematics)
Lectures in Projective Geometry (Dover Books on Mathematics) Lectures in Projective Geometry (Dover Books on Mathematics)
Lectures in Projective Geometry (Dover Books on Mathematics) Lectures in Projective Geometry (Dover Books on Mathematics)
Lectures in Projective Geometry (Dover Books on Mathematics) Lectures in Projective Geometry (Dover Books on Mathematics)
Lectures in Projective Geometry (Dover Books on Mathematics) Lectures in Projective Geometry (Dover Books on Mathematics)

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