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Frank Li
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I would like to start learning my calculus course before in school. Are here any textbooks or science reading books that would help me with the situation?
Thanks I'll try thembacte2013 said:I strongly recommend George Simmon's "Calculus with Analytic Geometry". He writes very clear, sophisticated exposition for both high schools and beginning undergraduates. He also has excellent problems sets. I also recommend APEX Calculus, which is free to download and also has fascinating exposition.
smodak said:Simmons as suggested above is good. I have a lot of other favorites.
There is a small and fun to read book that makes the basics strong. https://www.amazon.com/dp/0883858126/?tag=pfamazon01-20
For Applications, you cannot beat https://www.amazon.com/dp/0992001005/?tag=pfamazon01-20
Great way to quickly learn calculus https://www.amazon.com/gp/product/0471827223/?tag=pfamazon01-20
Great book (Q&A style) https://www.amazon.com/gp/product/0486203700/?tag=pfamazon01-20
A really fun book to read https://www.amazon.com/gp/product/0691161909/?tag=pfamazon01-20
Really good Calculus books: https://www.amazon.com/gp/product/0691130884/?tag=pfamazon01-20 and https://www.amazon.com/gp/product/0312185480/?tag=pfamazon01-20
Oldies but goldies https://www.amazon.com/gp/product/B00GMPZBGA/?tag=pfamazon01-20, https://www.amazon.com/gp/product/0201048108/?tag=pfamazon01-20, https://www.amazon.com/gp/product/0030892686/?tag=pfamazon01-20 - These are much better (along with Simmons) than nay of the current calculus books.
A Tutoring Book https://www.amazon.com/gp/product/0879421835/?tag=pfamazon01-20
An Infinitesimal approach https://www.amazon.com/gp/product/0486484521/?tag=pfamazon01-20
The book that allegedly taught Feynman https://www.amazon.com/dp/1406756725/?tag=pfamazon01-20
For Problems https://www.amazon.com/gp/product/1592575129/?tag=pfamazon01-20
Lastly, there is the best of the best https://www.amazon.com/dp/0914098918/?tag=pfamazon01-20 (although in my opinion it serves the best as the second book rather than the first)
Hope you find something interesting in the above list. If I were you, I would opt for a non traditional textbook and have some fun reading through it. You will have to go through textbooks when they teach you at school anyways. You cannot really go wrong with any of the books I suggested or Simmons.
But it's really much more than calculus. It's also linear algebra, probability theory, ...Buffu said:No list is complete without Apostol's calculus.
:)alan2 said:but I can't think of a better way to make a new student hate math than to suggest to him that those books are representative of what they will likely do with calculus.
alan2 said:You really should stop recommending Spivak or Apostol for high school students who have no clue what calculus is. Those of us who understand it find them to be lovely books but I can't think of a better way to make a new student hate math than to suggest to him that those books are representative of what they will likely do with calculus.
Buffu said:No list is complete without Apostol's calculus.
.Quantum Aravinth said:M. Spivak
Really an awesome book
I am sorry. I recommended that book because other people were recommending all types of books except this one, so I thought I would complete the list.alan2 said:People above are recommending them. They really are inappropriate for a kid asking to learn calculus but every time the question comes up the same answers are given.
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Can you tell now more precisely what exactly was wrong with their way of teaching?vanhees71 said:When I was about in the 8th grade, I had big trouble with mathematics, and I couldn't make sense of my school book nor with the explanations of my teachers. ... they teach the subject without hiding it behind well-intended but flawed didactics!
I am assuming most of the high school textbook, were full of pictures,diagrams, non related math jargon, and only the calculation aspect. Maybe no explanation from the high school authors as to why we do such and such, and why its important, etc.Demystifier said:Can you tell now more precisely what exactly was wrong with their way of teaching?
They taught mathematics as a collection of recipies to solve the standard problems in the books but never explained why these recipies worked, let alone gave proofs (not even heuristic ones). What's even worse is that there was no systematics in teaching the subjects (a contradiction to what imho math is all about). The jumped from one topic (say naive geometry, where we had to construct things with help of a "geo triangle" and a compass; then totally unrelated some algebra like solving for quadratic equations) without any systematics. To me that's a big waste of time: Math should be taught as a way of thinking and a systematic tool to solve problems in everyday life rather than a collection of senseless recipies to solve certain types of textbook problems.Demystifier said:Can you tell now more precisely what exactly was wrong with their way of teaching?
vanhees71 said:They taught mathematics as a collection of recipies to solve the standard problems in the books but never explained why these recipies worked, let alone gave proofs (not even heuristic ones). What's even worse is that there was no systematics in teaching the subjects (a contradiction to what imho math is all about). The jumped from one topic (say naive geometry, where we had to construct things with help of a "geo triangle" and a compass; then totally unrelated some algebra like solving for quadratic equations) without any systematics. To me that's a big waste of time: Math should be taught as a way of thinking and a systematic tool to solve problems in everyday life rather than a collection of senseless recipies to solve certain types of textbook problems.
, what do think ? should someone taught everything from differentiation to vector calculus before starting anything else ?"What's even worse is that there was no systematics in teaching the subjects (a contradiction to what imho math is all about). The jumped from one topic (say naive geometry, where we had to construct things with help of a "geo triangle" and a compass; then totally unrelated some algebra like solving for quadratic equations) without any systematics."
You must be a mathematician.Buffu said:Though I think physics education is the one that is really messed up. They teach concepts of differential equations and vector calculus with shtty hand waving without any proofs, just gives an impression that physics have no formalism in it and people who study physics just do ad-hoc proofs to get desired result.
+1Demystifier said:You must be a mathematician.
Just recall how calculus has been introduced by its inventors, Newton and Leibnitz. There is a good reason why hand-waving appeared before the proper proofs.
I do not believe OP in a much different situation than my daughter is.would like to start learning my calculus course before in school. Are here any textbooks or science reading books that would help me with the situation?
I don't think that you should start with calculus in high school. It's not so much the content than the way it's taught I criticize. Math should be taught as a coherent way of thinking about logical "universes", not as a collection of unrelated recipies to solve (often unrealistic and boring) problems in bad textbooks.Buffu said:I deeply agree with everything you said except , what do think ? should someone taught everything from differentiation to vector calculus before starting anything else ?
Though I think physics education is the one that is really messed up. They teach concepts of differential equations and vector calculus with shtty hand waving without any proofs, just gives an impression that physics have no formalism in it and people who study physics just do ad-hoc proofs to get desired result.
How do you learn all that physics without calculus? Perhaps our definition of 'calculus' is different :)vanhees71 said:I don't think that you should start with calculus in high school. It's not so much the content than the way it's taught I criticize. Math should be taught as a coherent way of thinking about logical "universes", not as a collection of unrelated recipies to solve (often unrealistic and boring) problems in bad textbooks.
Physics is different. I think, my physics education in high school was way better than the mathematics, but maybe that's an exception, because I had an exceptionally good teacher. She worked as a postdoc on atomic physics before becoming a high-school teacher, and she taught the curriculum in a very coherent way, doing a lot of demonstration experiments and, even more important, letting us do experiments as much as possible. We learned a lot on classical physics (mechanics and electrodynamics) and even a good overview on "modern physics" (relativity and quantum theory, even up to simple applications of the Schrödinger equation, atomic and nuclear physics and a glimpse on HEP physics).
vanhees71 said:She worked as a postdoc on atomic physics before becoming a high-school teacher
smodak said:How do you learn all that physics without calculus? Perhaps our definition of 'calculus' is different :)
Because she did not know 'real' calculus LOL. Sorry could not resistBuffu said:Why did she become a high school teacher ?
In my opinion the best way to learn calculus is by doing mechanics and vice versa. Starting with calculus and mechanics together in high school (as I did some 30 years ago) worked well for me.Buffu said:Who needs calculus to do physics in high school ?
smodak said:In my opinion the best way to learn calculus is by doing mechanics and vice versa. Starting with calculus and mechanics together in high school (as I did some 30 years ago) worked well for me.
OP, I apologize. We took this discussion far away from your original question. I will try not to respond off-topic anymore.
Buffu said:What calculus did you do in mechanics ? because most calculus I did was proof of laws of kinematics.
Taking Maths was not compulsory. You can take Biology instead of Maths and still take Physics.
Sigh. I didn't say, I don't want any calculus at high school but I don't want to begin with calculus. You need algebra and geometry first. I define high school as in Germany to start with the 5th grade. Calculus is introduced in 10th (or 11th) grade depending on whether you have 12 (or 13) years until the final exam (Abitur).smodak said:How do you learn all that physics without calculus? Perhaps our definition of 'calculus' is different :)
I think she wanted to have more time for her family than she could have when pursuing a career as a physics researcher. I and I think anybody needs calculus to do physics in high school (in the higher grades of course). Without calculus most of physics stays qualitative and a lot if then missing from the true "flavor of physics", and in my opinion high-school students should get a realistic flavor of all subjects to be able to choose what to do for the rest of their lives.Buffu said:Why did she become a high school teacher ?
Who needs calculus to do physics in high school ?
Very well said. Completely Agree.vela said:So getting back to the original point of this thread, the same considerations apply to learning calculus. Does the student want to learn the basic ideas of calculus, how to apply them, and how to do the calculations? Or should he or she immerse themselves into proving every last detail to get a true feeling for what real mathematicians do? For someone starting out, I'd lean toward the former. Ideally students should understand the reasoning used to reach various results, but I don't think it's particularly useful to spend a lot of time at this level trying to write proofs for everything.