# Tagged Questions

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### Need links for analysis lectures!! [closed]

I am taking a Real analysis course and have one of the worst teachers in the history of teaching, all he does is copy his notes on the board and nothing else. and if you ask a question that he doesn't ...
100 views

### How to know if I'm doing real analysis correctly?

I've just started a second year course in real analysis. This is my first proof-oriented course. Last year, our maths curriculum was introductory tertiary calculus and algebra. When I practised ...
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### Reference request to study Borel summation

Could someone recommend sources to learn about Borel summation procedure? Books, articles or reviews? I have a background in basic analysis.
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### Real and Rational Numbers

Intuitively, we often think of real numbers as existing in one-to-one correspondence with the points on a continuously drawn line, the real number line. One way of expressing the completeness of the ...
86 views

### Any finite set is a null-set

How can we prove that a finite set is a null-set? Maybe would it be easier to prove that the outer measure of a finite set is $0$? any ideas on how to tackle this problem? thanks,
248 views

### How to write well in analysis (calculus)?

This is kind of a subjective question, I know; often I find myself failing exams and homeworks because of the way i write down proofs. Either I don't know how to start, or somehow the main point of ...
694 views

### What are the main uses of Convex Functions?

Up till now I have just learned that the concept of convexity in functions of one variable is used to complete the graphs of functions, meaning to locate points of inflexion and see if the graph is ...
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### Pure mathematics for engineers

I have recently completed my first year of Eng. Physics taking the standard math courses: Calculus, Linear Algebra 1 and 2, Multivariable Calculus and Numerical Analysis. Recently though I have been ...
351 views

### Advanced undergraduate(?) Real Analysis book which is concise and lots of interesting problems

I have gone through the other book recommendations on Real Analysis, but I think my requirements and background is slightly different. I am a Physics undergrad teaching myself Pure math. My journey is ...
634 views

### Baby Rudin vs. Abbott

I am considering Stephen Abbott's Understanding Analysis and Walter Rudin's Principles of Mathematical Analysis. I am looking for a comparison between the two that addresses both of the following ...
108 views

### State-of-art of the Discrete Fourier Transform

I would like to know what is the state-of-art in the research of the discrete Fourier transform. I have listed some questions to help answering, please add your own to make the list more ...
152 views

### Is there an integral form of Newton's method?

Warning : This seems like a silly sort of question, not the kind I'd ask out loud. The contraction mapping theorem is a basic tool for proving existence of, and finding solutions to, equations. Given ...
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### Which topics of real-analysis should be studied if you have already done calculus

Which parts of real-analysis are worth studying if you have already taken several calculus courses? I know that real-analysis is more 'rigurous', but still I wonder whether it is worth to again go ...
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### What are the real-world applications of real analysis?

I've read the wikipedia article on mathematical analysis and this, but I can't exactly find an answer. Is real analysis just some pure math, or does it really have something to with physical ...
219 views

### Is there a symbol for the idea of the smallest value greater than zero?

I know that it isn't actually a number but I do think it's a concept in mathematics. So the question is, is there a symbol representing this concept? I thought maybe it was Phi but I couldn't find it ...
131 views

### Analogy between Integration and Summation

There are many analogies between definite integral and Summation: $$\int_a^b \leftrightarrow \sum_a^b$$, This makes me wonder if there is analogous concept of indefinite integral, derivative and ...
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### Similar textbook to Konigsberger's Analysis 2?

I am currently taking an introductory course to real analysis and my professor has decided to leave Rudin's "Principles of Mathematical Analysis" when teaching us the concepts of Lebesgue integration. ...
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### Is the $ϵ,δ$ definition of a limit not well-defined?

I just watched this youtube video: http://www.youtube.com/watch?v=K4eAyn-oK4M He lays out his objections against the $ϵ,δ$ definition around 14 min. Here is the discription of the video: In ...
378 views

### How to deal with Homeomorphisms?

I have one doubt that may be too general, I don't know, so sorry if this is not a good place to ask it. I've also seem many other people with the same problem that I have, so I think that if this ...
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### What kinds of sets are reasonable to place on the continuum?

Warning: I don't know anything about set theory so I wouldn't really know how to spot an existing answer if it were around. Suppose I want to model some economic good or product. I would like to ...
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### Real analysis textbok that develops the subject in a self-motivated, coherent fashion?

Well, it seems as though I just failed my analysis prelim for the second time... I have one more try in about $5$ months. I'm failing to build up a framework for how to think about analysis problems. ...
312 views

### Learning Aid for Basic Theorems of Topological Vector Spaces in Functional Analysis

I am self-teaching myself the basics of functional analysis (e.g. topological vector spaces), and frankly I am starting to get a migraine sorting out/organizing in my head all of the ...
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### What should I know about Sobolev space?

I have done some Sobolev spaces with some embedding theorems, trace theorems etc. Sorry that my question is really vague. If my professor asks me what is great about Sobolev space, what should I ...
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### What on earth is the difference between Calculus and Analysis [duplicate]

I noticed that there isn't a word for Calculus in my native language, Dutch. So I just went to the English wikipedia entry on Calculus, and tried searching for the Dutch article, and as I suspected, ...
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### Book Recommendations and Proofs for a First Course in Real Analysis

I am taking real analysis in university. I find that it is difficult to prove some certain questions. What I want to ask is: How do we come out with a proof? Do we use some intuitive idea first and ...
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### Volterra's Function - Context and History

This is a rather soft question, but I am preparing a short presentation on Volterra's function for an analysis course. Specifically, I'm wondering why was the Volterra's function a big deal during ...
### can it be said that $a<a$ where a is a real?
can it be said that $a<a$ where a is a real number? i think so but i wanna clarify.i had a fight over this with a junior who thinks otherwise. what does "or" mean in the law of trichotomy.I may be ...
### what's special about $\frac{1}{x}$ among other powers? [duplicate]
Possible Duplicate: What is so special about $\alpha=-1$ in the integral of $x^\alpha$? We all know the rule to find primitives (=antiderivatives) of powers of $x$:  \int x^\alpha dx = ...