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The definition of locally Lipschitz - Mathematics Stack Exchange
$||x-{x}_{0}||<{\delta }_{0}\phantom{\rule{thickmathspace}{0ex}} \phantom{\rule{thickmathspace}{0ex}}||f(x)-f({x}_{0})||\le M||x-{x}_{0}||.$ Here's a scan of the first edition of the text, where the only change from the second (latest) edition referred to above is that the last sentence now reads "This is called the local Lipschitz property" (emphasis mine). Two questions: Is the correct ...
What books are prerequisites for Spivak's Calculus?
Discrete math/structures are more relevant and applicable to the courses you'll be taking at first. For discrete math, I think Susanna Epps' discrete math book is good and has a lot of computer science application sections. Grimaldi's discrete math book is also excellent as well.
How to prove the chain rule? - Mathematics Stack Exchange
I have just learned about the chain rule but my book doesn't mention the proof. I tried to write a proof myself but can't write it. So can someone please tell me about the proof for the chain rule in
What is the best book for studying discrete mathematics?
Discrete Math knowledge is needed to become adept in proving the correctness and deriving the complexity of algorithms and data structures. You will be taught those in Algo/DS books, but you can only get the mathematical proficiency by practicing just discrete math. Knuth book is very good for that.
geometric topology - How to visualize the real projective plane ...
Keep in mind, that linked picture of a Klein bottle does not depict an embedding of the Klein bottle, in other words the Klein bottle is not homeomorphic to the subset being depicted. That depiction is what topologists call an immersion. The projective plane also has an immersion, the "Boy's surface" linked in the answer of @AloizioMacedo. The only problem is, the Boy's surface immersion of ...
reference request - Good abstract algebra books for self study ...
Please keep in mind that I am not a math major, and that I would like books which are suited for self study (thus a lot of examples and intuition). Thanks in advance!
Prove that the set of all algebraic numbers is countable
This is a better proof than the one suggested by the hint (which is, I believe, the proof in, say, Rudin). There are obviously infinitely many algebraic numbers (consider Q Q $\mathbb{Q}$!), but there are at most countably many of them since there are only countably many coefficients, each of these contributing finitely many roots.
Math formula with $\\mathcal N$ symbol. What is it?
Calligraphic math symbols are more of a font thing that a unicode thing I think. [1]: You might want to experiment with putting all the different alphabet letters in calligraphic font as well to see what they look like.
How to prove a sequence of a function converges uniformly?
For $n \\in \\mathbb{N}$, define the formula, $$f_n(x)= \\frac{x}{2n^2x^2+8},\\quad x \\in [0,1].$$ Prove that the sequence $f_n$ converges uniformly on $[0,1]$, as ...
Quadratic equations: Why does factoring by grouping work?
We are learning factoring by grouping - The teacher explained the process but didn't explain the logic behind it. You need to multiply the coefficient on the x-squared term by the constant to get a
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