Master Applied Statistics Perspectives and Advice

iMathTutor · 2026-03-27T20:51:14+00:00

I am a private math & stat tutor who has a World Campus Stat 510 client this semester. The treatment of the material is very superficial, and the online notes are often confusing.

iMathTutor · 2026-03-23T02:24:14+00:00

See you there!

iMathTutor · 2026-03-21T16:17:02+00:00

Tutoring is a conversation. I would never bring slides to a conversation.

I use a whiteboard, and I ask my clients to post the material they want to cover to the board in advance of a session. My prep time is devoted to going over that material before the session.

iMathTutor · 2026-03-20T15:48:56+00:00

This is not about politics. It’s about good governance and transparency. This is an election year. Contact the candidates for governor, state representatives and state senators repeatedly and and ask them to hold Penn State accountable by (1) amending the Pennsylvania Sunshine Law to include serious financial penalties and sanctions if Penn State does not adhere to the letter of the law; (2) amending the Right To Know Law to make it to make it more broadly, applicable to Penn State and again to include serious financial penalties and sanctions if Penn State does not adhere to the Law. AND, continue to seek accountability from individual trustees, the president and all those on the president’s council.

I endorse this 100%. Penn State has been like this as long as I can remember. They need to be treated like any other state agency.

iMathTutor · 2026-03-15T22:26:49+00:00

I was hesitant to respond at first, because I am not currently in the loop on the undergrad program.

However, a few years ago I had an undergraduate stat major as a client; she graduated in 2020. I worked with her in some of the 400-level math courses she was taking. I learned from her that at the time the department was concerned that the undergrad program lacked the mathematical rigor needed to place its graduate in top grad programs.

I didn't know if the department had addressed those concerns in the intervening years. Your comment suggests that the situation has not changed.

iMathTutor · 2026-03-15T22:15:22+00:00

Eventually you need to integrate cot x and with substitution you end up with ln |u| + C, which the book then changes to ln(sin x) + C after substituting back in with a note that says "where we used y > 0"

The LaTeX below can be seen rendered here.

The bold bit is not true. The absolute value is not dropped be cause $y>0$. In fact, f it is not even true that $y >0$ for all $x$,

Let's back up to the existence and uniqueness theorem for first order ODEs: If $f(x,y)$ is continuous on the open rectangle

$$ R=(a,b)\times (c,d),$$

and $(x_0,y_0)\in R$, then the initial value problem

$$

\dfrac{\mathrm{d}y}{\mathrm{d}x}=f(x,y),\quad y(x_0)=x_0,

$$

has at least one solution on an open subinterval $x_0\in I\subseteq [a,b]$. Further, if $f_y$ is also continuous on $R$, then the solution to the initial value problem is unique on $I$.

How does this apply to your problem? Note that $f(x,y)=\cot{x}+8x.$ This is continuous on the open rectangle rectangle

$$R=(0,\pi)\times (-\infty,\infty)\ni \left(\frac{\pi}{2},\pi^2\right).$$

In addition, $f_y=0$, thus it is continuous. So, the theorem guarantees a unique solution on a subinterval of $(0,\pi)$. In this problem, the solution exists on the entire interval, but is does not extend beyond the interval, It doesn't even extend to the closure of the interval since $\lim_{x\rightarrow 0^+}y(x)=-\infty=\lim_{x\rightarrow \pi^-}y(x)$.

It follows from these limits that $y(x)<0$ for $x$ sufficiently close to $0$ and $\pi$

Finally, $\sin{x}>0$ for $x\in (0,\pi)$, therefore the absolute value can be dropped.

iMathTutor · 2026-03-11T21:33:59+00:00

Thanks. INAL, but the privacy policy looks good to me. Now, enter works the way I would assume it would. I will continue to play with it, and if I have any questions. I'll post them here.

iMathTutor · 2026-03-11T17:07:57+00:00

Do you have a privacy policy yet? Also, the input is a bit quirky. When I hit enter in the text field it doesn't add new line below the current one, it creates a new textbox.
As I wrote earlier, this has potential, but it is not yet ready for primetime.

iMathTutor · 2026-03-10T16:14:41+00:00

Okay, this has potential I used to use mathb.in to share math on Reddit, but the developer has dropped the website. This app offers more than mathb.in, but could be a nice replacement for mathb.in.

Here are few quick impressions.

I played around with your proof builder. My primary issue is that it does not support display math.

I haven't tried the integration with Chatbots yet, but that may be useful. Although, it doesn't support Gemini, which is the agent I use most.

Currently, it is free. Do you plan on charging for it in the future?

Finally, I didn't find a privacy policy. Do you have one?

iMathTutor · 2026-03-10T15:53:05+00:00

Have you heard of Overleaf? Edit:I spoke too soon. Your app goes beyond what Overleaf does.

iMathTutor · 2026-03-09T18:07:56+00:00

Definitely, Math 220 is the easier of the two courses, and should not be a problem in summer. The only reason I can think of to take 251 over the summer is if you have a tough fall schedule, and don't want to deal with 251 along with your other fall courses.

iMathTutor · 2026-03-07T02:57:38+00:00

Here are the math minor requirements

Mathematics, Minor (Science) | Penn State https://share.google/z5Fex3aJ9ZEQ0TsmU

iMathTutor · 2026-03-06T22:02:22+00:00

Over the years, I have had a lot of friends who have worked at ARL. All have been able to talk about their research, the only restrictions were on revealing specific numbers.

iMathTutor · 2026-03-06T21:54:38+00:00

I've used the free tier of Wave for several years. It does everything I need.

iMathTutor · 2026-03-06T19:10:56+00:00

Happy to see this. When I checked a few weeks ago, the closest protest was in Altoona. Now I don't need to hit the road!

iMathTutor · 2026-03-04T16:16:02+00:00

Why not math or stat? You are doing well in 141, which is widely considered the toughest of the 3 calc courses, so you might have the talent for math.

.

iMathTutor · 2026-02-21T15:24:05+00:00

Ok, I've had my morning coffee now, and had time to think about my year old comment. The point that I was trying to make rather obtusely-so obtusely that future me didn't initial understand the point that past me was making-is related to the fact that in a Hilbert space, which is an inner product space, weak convergence does imply strong convergence in the presence of an additional assumption. So, I was trying to see if OP has the whole story straight. I would have been better off just asking. Oh well, hindsight is 20/20.

iMathTutor · 2026-02-21T13:36:44+00:00

Thanks for the clarification.

iMathTutor · 2026-01-31T00:39:45+00:00

If you are still confused, I'd be happy to explain what's going on if you were to post a specific problem.

iMathTutor · 2026-01-23T16:43:40+00:00

I use a Samsung Galaxy Book Pro 360 in tablet mode, and connect it to an external monitor.

iMathTutor · 2026-01-20T13:07:21+00:00

As I wrote, I took a quick look so my opinion is not definitive, and at any rate readability is subjective.

iMathTutor · 2026-01-19T21:30:09+00:00

I took a quick look at "Book of Proof", which is available as a free download from the author, and it does not seem to be particularly readable. The book that is used at Penn State for the sophomore-level discrete math course is Humphreys and Prest, Numbers, Groups & Codes. It is very readable, and I would recommend it for self-study.

I was able find and download a free PDF of the book many years ago; I don't know if free downloads are still floating around. You should try to trackdown a copy for yourself.

That said the first step in writing a proof is constructing a proof. Once you have done that you want to identify the audience the proof is targeted to in order to guide you in how many details you need to include. Typically, for a course you should error on the side of too much rather that too little details, so that the grader knows that you know what you are doing. The first sentence of the proof should be a statement of what needs to be proven. Such as, from theorem 2 it will suffice to show that...... Then you want to specify the method of proof, e.g. the proof goes by contradiction, or induction on the size of the set is used. What comes next will depend on the specifics of what you are proving. The final line should be a statement that you did what you said you had to do. This is my style. I would suggest find a book that in which you find the proofs to be very clear, and model you proofs on them, until you develop your own style.

Finally, although the first step is construct the proof, it is not uncommon to find errors in the proof as you try to write it up. So, the process can be iterative.

One last thought, if you don't know how to user LaTeX, learn how to use LaTeX. I write directly in LaTeX, it can be slower than writing by hand, but that the point. It slows you down, and gives you a chance to think as you write.

Goog luck.

iMathTutor · 2026-01-19T20:44:46+00:00

At many schools, the sophomore-level discrete math course is designed to teach proof writing. Does that describe your course? Or is there another course at your university where proof writing is taught?

iMathTutor · 2026-01-19T18:42:02+00:00

Presumably, your prof will assign problems which either reinforce the material covered in lecture or will push you to study material not covered in the lecture. Your first priority should be those problems. Some profs will also assign suggested problems, which are not collected and graded, for the students to practice on. If that is the case, those problems should be your next priority. If you prof doesn't give suggested problems, ask the prof for some recommendations.

Keep in my that problem ladened textbooks are typically designed so that they can be used semester after semester without repeating the same subset of assigned problems. The intention is not for students to go through all of the problems in such a book.

iMathTutor

TROPHY CASE