New answers tagged learning
I have created some autocorrected online exercises in Mathematics that you could use as supplemental material. I have also started an online index to the fourth edition of James Stewart’s Calculus textbook, as a subset of “Mike’s Ready Reference”. My online index is much more detailed than that of the textbook itself.
Spivak as mentioned previously would be a good way to revise with some supplemental material on metric spaces. I find the ideal situation would be to retake the first semester and then take the second semester immediately after.
I would consider: Elementary Analysis: The Theory of Calculus (by Ross), and Spivak's Calculus I'm not really sure why Rudin's is still the standard text...anyway
You are given two sets $A$ and $B$, both provided with a binary operation $*\>$. This means that in $A$ as well as in $B$ for certain triples $x$, $y$, $z$ it is true that $z=x*y\>$; e.g., $13=5+8$, or $91=7\cdot 13$. A map $\phi:\>A\to B$ is a homomorphism if it preserves such "incidences": $$z=x*y\quad\Longrightarrow\quad \phi(z)=\phi(x)*\phi(y)\ ...
If you were really mainly interested in using math for other things, like physics or computer science, then I might suggest using an easier calculus book. However, you say you've decided to "learn mathematics properly," which means you need to wrestle with challenging problems like those in Spivak's book, sooner or later. The real question is whether the ...
In my experience, if you want to really understand mathematics, hard questions and problems are essential. My recommendation is that if explanations for any book are not clear to you, then get a secondary resource. But struggling is part of math, and solving a hard question will do more good than reading 10 different articles on a particular subject. Perhaps ...
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