## Real Analysis Tutors

### Quality without compromise

Most of the real analysis tutors on these pages hold advanced degrees in their fields, many with Ph.D.'s or the equivalent. All real analysis applicants must supply academic transcripts for each degree they hold, and are tested and screened carefully by our staff. We’ve also implemented ratings and reviews in order to increase our level of transparency and show you the actual performance of each real analysis tutor. It’s real, it’s believable – no shenanigans!

### How do I find a real analysis tutor?

Usually there is no need to select a real analysis tutor because our system will either take your request through a hierarchy of tutors, or make it visible to all of the tutors for that subject area. Of course you’re more than welcome to browse our highly qualified real analysis tutors and select one that you personally prefer!

### Experts at your disposal

Our tutors have profiles with quite a bit of information in them. You’ll be able to find the subjects that they cover, when they started working with us, the number of their completed sessions, and overall ratings! You can also find real analysis tutors’ qualifications and solutions in the Homework Library.

Using our tutor profiles you can submit a request for homework help or a live session directly to a particular real analysis tutor.

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Of course! You can submit a request through that tutor’s profile or just type that tutor’s username in the appropriate box when submitting your request.

### Need help with Real Analysis?

You can send us an email ([email protected]), get in touch with us over our chat or call us at (845) 429-5025.

## Real Analysis Help

Real Analysis is a category of calculus which studies real numbers, convergence of sequences and series, the continuity and discontinuity of functions, and the real number line unbounded from negative infinity to positive infinity. Important topics include power series, Riemann sums, limits of functions, complex numbers, and measure theory.

We provide comprehensive Real Analysis tutoring for students including the following Real Analysis topics:

- Absolute Convergence
- Archimedean Property
- Bolzano-Weierstrass Theorem
- Cantor Set
- Cauchy Sequences
- Closed Sets
- Cluster Points
- Completeness Property
- Complex Numbers
- Conditional Convergence
- Continuity of Functions
- Convergence of Sequences
- Convergence of Series
- de Morgan’s Law
- Dirichlet Function
- Discontinuity of Functions
- Euler Number
- Field Properties
- Fourier Series Theory
- Heine-Borel Theorem
- Fubini’s Theorem
- Hypergeometric Series
- Infinite Series
- Integration Theory
- Lebesgue’s Theorem
- Limit of Functions
- Measure Theory
- Merten’s Theorem
- Monotone Sequences
- Ordered Fields
- Order Properties
- Periodic Functions
- Power Series
- Real Number System
- Recursive Sequences
- Riemann Integral
- Riemann Sums
- Series of Products
- Subsequences
- Taylor’s Theorem
- Uniform Convergence

## How should one tutor a student in undergraduate real analysis?

I am an undergraduate. Other undergraduates sometimes ask me to tutor them in an introductory real analysis course that covers the equivalent of the first half-dozen chapters of Rudin's *Principles of Mathematical Analysis* (baby Rudin). We meet once a week for about an hour to discuss concepts and their problem sets.

In the beginning of the semester, I seem to spend about half the time on concepts (mainly repeating definitions and giving examples) and the other half giving hints on the homework problems. Later in the semester (and in the second semester continuation), I spend most of the time giving them considerable help with the homework. I don't have any trouble explaining concepts. However, I have a lot of difficultly with providing the appropriate amount of help with problem sets. The biggest problem I see with my students is a lack of problem solving ability. Part of it is a result of a poor grasp on the material and part of it is laziness. They don't seem to be able to think about a problem constructively for more than 5 or 10 minutes before giving up. Further, many of the problems are relatively easy once you see the essential idea or 'trick'. So either I show them the 'trick' or they just get the answer from another student. I usually end up giving too much assistance.

I have suggested they try easier exercises to build up their problem solving skills. Abbott's *Understanding Analysis* is a good source of these. However, they are unwilling to do much extra work on their own. Of course, this is ultimately their problem, but as a busy undergraduate myself, I am sympathetic.

Another common concern is preparing for exams. A 1-hour exam is a much different format than an untimed problem set and much less forgiving. My standard advice is to first to memorize all of the definitions, be able to give examples and non-examples (where relevant), and memorize the statements of all of the important theorems. After they have done this, I suggest solving easy exercises from their textbook and trying to prove simple propositions in their book without looking at the book's proof (e.g. a finite intersection of open sets in $\mathbb R^n$ is open).

How should I address these issues? Are there any other techniques I could use to make my tutoring more effective? I am particularly interested in ideas that are specific to real analysis.

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## Analysis tutor real

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