Questions tagged [mathematical-analysis]
For questions applying to analysis courses: Real and complex analysis. Typically a higher and more proof-based level than calculus.
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A visualization for the quotient rule
Context: first year didactics of mathematics course for middle school teacher students (in Norway).
I have a reasonable visualization for the product rule of derivatives: Consider a rectangle with ...
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How to assess students in real analysis?
Terence Tao says the following in the preface to his book Analysis I:
With regard to examinations for a course based on this text, I would recommend either an open-book, open-notes examination with ...
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Real-World Problems for Teaching Extrema and Derivative Tests in STEM Education
For educational purposes, I am seeking example problems in the realm of natural sciences, engineering, and business that satisfy the following criteria:
Consider a one-dimensional real function $f$ (...
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Motivating a definition of "gap" in a line just barely more advanced than the one used in the typical first-year calculus course
Imagine a course barely getting into some topics more theoretical than what is done in the typical very staid first-year calculus course, and the kind of students for whom such a course is appropriate....
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Flashcards and Study Methods for Undergraduate and Masters Degrees
I need advice on methods and techniques for studying mathematics that are commonly used at undergraduate and masters level in mathematics.
What are some strategies that you find useful in coping with ...
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How can we motivate that Newton's method is useful?
If you teach Newton's method for finding roots of real functions on the high school (or freshmen) level, I think some students may reason like a variant of the following:
Why do I need learn such a &...
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Why do most Analysis textbooks overlook, and fail to teach delta-epsilon proofs, using the K-ε principle?
When writing $\delta$-$\varepsilon$ proofs, it's common that the ''natural'' choice of $\delta$ leads to the final inequality in the form, say, $|\ldots| < \varepsilon+\varepsilon+\varepsilon$ ...
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Do undergraduates struggle with δ-ε definitions because they lack a habit of careful use of their native language?
I transcribed this excerpt starting at the 22-minute mark, of Okinawa Institute of Science and Technology’s May 19 2020 podcast with Professor Tadashi Tokieda:
For example, this is a bit too ...
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What is important to keep in mind in grading proof-based courses?
I am an undergraduate grader at my institution where I have been entrusted with grading a section of an undergraduate analysis course; it's usual for this role to be offered exclusively to graduate ...
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Should one study Laplace Transformation before Fourier Transforms?
(Im sorry if the question is out of the scope of the forum)
Hi, Im currently a Physics student. I have studied most of the Calculus. Now, according to the book Im using, there is chapter on "...
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If I take Modern Analysis next year, will I be prepared to teach multivariable/vector calculus?
I’m currently getting my Master’s in Math at Portland State University so that I can teach community college mathematics. I’m specifically hoping to teach calculus, statistics, and linear algebra, so ...
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Suggestion for IB program Analysis and Approaches SL book?
What is the most suitable book for the IB program Analysis and Approaches SL for a student with significant weaknesses?
I had suggested the book from HAESE Mathematics yet he finds it particularly ...
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What is the text for "the other second-term course in analysis at MIT?"
My question comes from first few paragraphs of preface of "Analysis on Manifolds" by James R. Munkres, as excerpted below:
A year-long course in real analysis is an essential part of the
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What are your experiences with Buck’s Advanced Calculus?
I stumbled across the book when searching for rigorous alternatives to Rudin with some solutions. It’s an “old school” (1965) calculus text but, I think, covers similar material to Rudin in a more ...
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Should an undergraduate math program contain a course on Lebesgue integration?
Is it standard for a math undergraduate program to have a course on Lebesgue integration?
Does Riemann integral suffice for undergraduates?
The reason of my question is I read a paper by Bartle titled ...
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