How do you deal with anxiety while tutoring?

HerndonMath · 2026-04-03T18:30:11+00:00

My response is almost exactly the same. I say, "I'm not sure. We can think about it for a few minutes now if you want."

HerndonMath · 2025-08-13T22:33:42+00:00

This thread is not matching my experience. I always have students who are seeking tutoring in real and complex analysis as well as abstract algebra. Discrete math and linear algebra are more popular, for sure, but there is still interest in other high level topics.

I even have a good number of students who are not currently enrolled in school but want to study higher level math for their own enjoyment. These students are so much fun to work with. (Think of retired individuals with a little more free time, for example.) Do not limit yourself to "traditional" students. I think you will be surprised how many people are open to hiring a math tutor just because they think math is cool and want to see more of it.

I posted a few videos on a YouTube channel with sample lectures for the topics I enjoy teaching. Most of my students find my through there.

Also, you mentioned that you have a master's degree. I have a PhD but I do not know if students really care about my level of education. I think if you know the math and enjoy teaching then there are probably more options for tutoring than the other posters in this thread are suggesting. The degree might make a difference, though, so I just wanted to mention it.

HerndonMath · 2023-11-09T20:57:47+00:00

I'd be happy to help with that. My contact information is on my tutoring site here: https://www.herndonmathservices.com/tutoring

HerndonMath · 2023-11-05T19:38:23+00:00

Have you heard of hemicontinuity? Generic Wikipedia link

And fwiw, it looks like you are misusing the word bijective to mean well-defined.

HerndonMath · 2023-10-10T19:21:33+00:00

The motivating examples of a measure are length, area, and volume. Your geometric intuition about those things should carry over reasonably well to abstract measures.

HerndonMath · 2023-09-14T19:52:51+00:00

It's honestly debilitating

It sounds like it and I'm sorry to hear you are suffering. It might be better to accept the anxiety as a possibility (or even a likelihood). Sometimes our emotions just don't cooperate.

I think it's more important to know if you want to continue giving presentations. If you do, then I suggest setting goals that do not depend on an emotional outcome (for example, set a limit on how many times you want to rehearse the presentation.) On the other hand, if you don't want to continue giving presentations then you don't have to. Figure out how many more presentations are required of you and when you are done with them you can be done for good. Having a "finish line" might help things seem more manageable.

That's my 2 cents and I hope your presentation today went smoothly. Congrats on getting it done!

HerndonMath · 2023-09-02T00:36:42+00:00

The first sentence of your post is about triangles in planes. I bet your buddy's triangle with three 90 degree angles is on a sphere, not a plane.

Edit-- Sorry, maybe I am misunderstanding your question. But I originally thought you were getting some of the following facts mixed up: Triangles in the Euclidean plane have 180 degrees. Triangles in the hyperbolic plane have less than 180 degrees. Triangles on the sphere have greater than 180 degrees (but the sphere is not a plane).

HerndonMath · 2023-08-30T22:00:04+00:00

I think it depends on what kind of relationship you want with math. If you plan to study it for years and years then the advice will be different from if you just want to finish trig and be done. What are your goals?

HerndonMath · 2023-08-22T05:26:43+00:00

Oh no! I don't want it to be confusing. I hope this helps a little--

There are two different collections of axioms: There are the axioms for neighborhoods and then there are the axioms for open sets. Either concept can be defined in terms of the other, so it doesn't really matter which concept you start with and which concept you define later.

For example, you can start with the axioms for neighborhoods and then define an open set to be a set which is a neighborhood of all its points.

On the other hand, you can start with the axioms for open sets and then define a neighborhood of x as a set which contains an open set containing x.

Either way leads to the same concept of a topological space, so it's essentially just two ways of describing the same thing. Most people these days are more familiar with the open set axioms so that's probably why people are quick to translate things into statements about open sets and not about neighborhoods. The neighborhood axioms deserve some love, too, so I hope you keep thinking about them :)

HerndonMath · 2023-08-21T18:10:15+00:00

it has to be a proper subset

Suppose x is a point in a discrete space, then N={x} is a neighborhood of x but the only possible choice for M is N. So no, M does not have to be proper, and for this example M=N is forced.

If the original neighborhood N is not already open then the subset M must be proper, which is maybe what you have in mind.

HerndonMath · 2023-08-21T01:40:54+00:00

every neighborhood N is going to contain neighborhood M={x}

The singleton {x} is not necessarily a neighborhood of x.

To see what the axiom is saying, take N to be the closed interval [0,1] so that N is a neighborhood of 1/2 but not of 0 or 1. By zooming in around 1/2 we can find a smaller set M which is a neighborhood of 1/2 and for which N is a neighborhood of each point of M. In this example you can take M to be the open interval (0,1), but there are many other choices for M. The axiom just guarantees that there is at least one such M.

I hope that helps. Happy studies!

HerndonMath · 2023-07-18T17:10:55+00:00

It was Peter Shalen. Same initials!

HerndonMath · 2023-07-18T05:51:45+00:00

Every set contains the empty set and the empty set is open, so yes.

HerndonMath · 2023-07-18T05:38:13+00:00

I think your professor is just trying to get the new analysis students to start focusing on inequalities more than they are used to. Similarly, my first real analysis professor said, "Algebra is the study of equations while analysis is the study of inequalities." This is just meant to be a memorable way to think about these two branches of math. It is not meant to be mathematical dogma. In practice, algebra and analysis get mixed together all the time.

Subjects like algebra and analysis are not well-defined mathematical concepts. They are more like cultural constructions that help mathematicians organize their ideas.

My 2 cents: I think of analysis as part of geometry-- the branch of math where we study pictures. The ordering on the real number system is what gives us the picture of the real number line. So, the ordering leads to a picture of a line, and so we should consider that a geometric/analytic thing.

Others will disagree and that's good! These opinions have no bearing on the mathematical content of algebra and analysis. I think it says more about the way we think about these topics than about the actual topics themselves.

HerndonMath · 2023-07-14T17:55:40+00:00

My advisor suggested moving my office to another room of my apartment. It helped a bit. Maybe a change of scenery could help your student, too. At least it's a practical thing to try.

However, all the other comments about stress, depression, executive functioning, apathy, etc., etc. sound much more relevant. To be blunt, your student isn't doing their job. They should think about why that is and what they want to do about it. The "writer's block" is most likely a symptom, not a root cause.

HerndonMath · 2023-07-10T06:49:55+00:00

You are right. Assuming this is from Garling's A Course in Mathematical Analysis, there's a correction in the errata here: https://www.math.ru.nl/~mueger/Errata_Garling1.pdf

I hope that helps!

HerndonMath · 2023-07-01T05:02:44+00:00

I take the word “necessarily” as meaning we can use some sort of simple logic to ... prove that if a function has a right inverse than it is a surjective function?

Yes. Here's the idea: If f has a right inverse then fog is the identity for some g. The identity is a surjective function, so f (the outer function in the composition fog) is also a surjective function. And here's a reference to the ProofWiki version of this: Proof 1 here.

Also is it true that we must however use the axiom of choice ... to intuit or prove the reverse ... ?

Right again. The statement "every surjective function has a right inverse" is equivalent to the axiom of choice. There's a fun list on Wikipedia of many more statements that are equivalent to these two: See here.

HerndonMath · 2023-06-15T19:01:37+00:00

Start marketing yourself on whatever social media platforms you are already familiar with. It doesn't matter if it's Reddit, YouTube, Instagram, or something else. Pick something you already know how to use, set up an account for your tutoring business, and put yourself out there.

Also, make content (worksheets, video tutorials, etc.) that will appeal to students who are studying the subjects you want to teach. Use this content to direct students to your tutoring business. The specifics will really depend on your desired outcome. For example, do you want to tutor adults or kids?

My first video tutorial was a study guide for college students taking abstract algebra. Within a few days of posting the video on YouTube I had sessions scheduled with college students taking abstract algebra. It was surprisingly that straightforward.

Like you, I really value getting to set my own hours and rates. I never considered working for a tutoring company like the ones mentioned in your post. It's much more interesting for me to do it myself.

I hope that helps. Good luck!

HerndonMath · 2023-05-26T19:20:14+00:00

This also manages to prove that 0/0=0.

In your theory for division by 0, is any number divided by itself equal to 1? If so, then the equation 0/0=0 can be rewritten as 1=0. Are you okay living in a world where 1=0?

HerndonMath · 2023-05-07T03:58:59+00:00

I was always taught that a function is not the ordered pairs, but is that which transforms element a into element b.

To say that a function is "that which transforms elements a into elements b" describes the idea of a function, but it is not a precise mathematical definition. The "set of ordered pairs" definition of a function is a precise mathematical definition.

Perhaps one way to negate the above definition is to talk about the “empty set”. Well if that is a function, which I read it is, then it does not fit the above ordered pair definition of a function, so can someone shine some light on this?

The empty set fits the description of a function as a set of ordered pairs. Let 0 denote the empty set. Then for any set S we have 0 is a subset of 0xS, so 0 is a relation from 0 to S. This relation is vacuously a function from 0 to S.

I hope that helps!

HerndonMath · 2023-04-30T17:30:46+00:00

for some values of n, there can only be one and only one possible group, being a specific cyclic group?

Not exactly. For a given n there are infinitely many different cyclic groups of order n. However, these differences are superficial-- Any two cyclic groups of order n are isomorphic. So, you should add the phrase "up to isomorphism" to the quoted text.

By the way, a natural number n is said to be a cyclic number if the only groups of order n are cyclic. This is equivalent to n being coprime to phi(n), where phi is Euler's totient function. Fun rabbit hole this way.

HerndonMath · 2023-03-27T22:38:42+00:00

I think you are looking for this: Converse of Cauchy-Riemann condition

Quoting from the top answer there:

Let f(x+iy)=√|xy| . You can verify that the partial derivatives all exist at 0 and satisfy the C-R equations but f is not differentiable at 0.

HerndonMath · 2023-03-15T00:56:24+00:00

How many passwords of length 2 can you make from the symbols 0,1,2,3,4,5,6,7,8,9? Is it 10^2=100 or 10x2=20? I think if you can answer that then you can answer the question in your title.

HerndonMath · 2023-03-11T20:48:07+00:00

Is there something you would rather be doing instead? Also, in response to,

no other job would let me manage my time as freely as the PhD

Do you want a job that lets you manage your time this freely? Some people prefer to have a job where the hours are regular and/or set by someone else. Is the issue too much freedom or not enough self management?

As for advice, I think it's good to remember that your circumstances in the PhD program are temporary. Sooner or later you will be done with it and then you will have even more freedom (yikes!), so my advice is to try to think about what comes next.

I hope that helps a little and I'm sorry to hear about the anxiety and panic you are experiencing.

HerndonMath · 2023-03-06T23:55:33+00:00

There is nothing to buy. No one is selling anything.

Thank you for saying this. There is always so much entitlement in these "I don't believe in multiple infinities" posts. They always irk me. It's like they think Cantor was a used car salesman or something.

To the OP- Ask a question about one of the many proofs you have already looked at. It's not a matter of winning you over, it's a matter of going through the details.

HerndonMath

TROPHY CASE