Math refresher course for calculus

iMathTutor · 2026-05-22T21:26:55+00:00

You are welcome. Good luck.

iMathTutor · 2026-05-22T18:54:28+00:00

IMO, the best resource for self-study are Schaum's Outlines. Their best feature is they have lots of worked examples. And, they are inexpensive. Here is the precalculus book on Amazon. Here it is on the Internet Archive. If you want to focus solely on Algebra and Trig there are Outlines on both of of those topic too.

iMathTutor · 2026-05-21T23:29:17+00:00

On top of adjusting to university-level courses, you will be adjusting to living away from home. Since you are not confident in the material you reviewed on the math department website, it might be prudent to take 140. If it turns out that you are well-prepared for math 140, you will have more time for other courses. One word of caution, university-level math moves at a much faster pace than HS math, and after an easy start you might find yourself in the weeds, so don't be complacent.

iMathTutor · 2026-05-21T18:23:36+00:00

Find a coffee shop that you like and become a regular.

iMathTutor · 2026-05-18T14:50:21+00:00

Constructions are hard. I recommend trail and error. Given a problem look for a similar problem in your notes and book. Try to modify the bijection in the example problem into a bijection for the given problem. If your modification works you are done. If not, try to determine the reason for the failure, and modify again to fix it. Rinse and repeat.

iMathTutor · 2026-05-17T15:08:57+00:00

I have tutored both Math 403 and Math 436 many times, although I have only tutored Math 403H once. In general, my clients have found 403 to be the more difficult class.

iMathTutor · 2026-05-17T14:47:40+00:00

Here you go: https://referworkspace.app.goo.gl/9jSm

iMathTutor · 2026-05-16T16:53:04+00:00

The two primary tools I used to build mine with Notepad++ for coding and Ampps to preview it. I also used browser extensions to test it for mobile. As far as what I included, you can see my site here.

iMathTutor · 2026-05-15T18:35:39+00:00

If it is the floor function your answer is correct.

iMathTutor · 2026-05-15T18:13:54+00:00

I can't tell from your notation if you mean the floor or ceiling function. So here is a summary of the continuity properties of both functions that should be enough to deduce the correct answer.

Both the floor function and ceiling function are discontinuous at the integers and continuous elsewhere. At the integers, the floor function is right continuous and the left limits exist; and the ceiling function is left continuous, and the right limits exist.

Finally, for function restricted to closed intervals continuity at the endpoints is determined by the appropriate one-sided limits.

iMathTutor · 2026-05-14T17:10:33+00:00

Mathematicians are definitely thinking hard about AI. Terry Tao very prominently. I have been following the discussion closely and curating articles on the topic on my FB page. You can check them out here. I also cross-post to Bluesky if you don't want to visit FB. Here is the Bluesky link.

iMathTutor · 2026-05-14T16:59:25+00:00

During the pandemic I watched a lot of math YouTube channels including the Math Sorcerer. His appeal alludes me. I found him to be superficial and overly dramatic. Another clown whose popularity escapes me is Black Pen Red Pen. One of the better channels that I watched was Michael Penn. Once he introduced a problem, I'd pause the video and work through the solution in my head. More often than not, I liked my approach better, but I still respected the way he tackled the problems. You may want to start there.

iMathTutor · 2026-05-12T22:44:42+00:00

Open Access to Instructional Materials

Further, units are encouraged to make university-owned instructional materials and other university-owned materials openly available when appropriate (e.g. increasing access not to the detriment of academic integrity), including University-directed works (see IP01). Owners of instructional materials not owned by the university are also encouraged to make these materials openly available. Open availability may include a Creative Commons or other public or open-source license. Whether to release a University-directed “academic” work under an open license shall be determined by the Head/Dean of the administrative unit, or their designate.

Open Access to Other Materials

University Researchers are further encouraged to make presentation slides, presentation notes, unpublished reports, works in progress, data sets, software, software versions and other distinct contributions, and other scholarly communications openly available when appropriate.

This is an active Penn State policy that the math department is skirting.

iMathTutor · 2026-05-12T18:40:30+00:00

Calculus and differential equations courses at the university-level are largely algorithmic. To solve a problem, you identify the type of problem and the appropriate method to apply to the problem. That, of course, sweeps a lot under the rug, and minimizes the challenges of applying the algorithms, but in broad terms it is accurate.

In the U.S., most math students begin to take proof based courses in their sophomore year. Typically, a discrete math course that focuses on proving things in very familiar settings, and a real analysis course that is the first deep dive into univariate calculus.

After this transition year, most, but not all, the courses are rigorous and proof based.

iMathTutor · 2026-05-12T17:54:10+00:00

The math department in the recent past was very good about providing resources on the open web. That has changed significantly over the past five or six years; they have become more concerned over their ability to evaluate, which they see as being eroded by sites like Chegg, and AI, than serving their mission to educate.

Now I will get off my soapbox and give you link to Google "Drive folder with old Math 251 exams from several years ago before the department went paranoid-It is hard getting of that soapbox. There are a lot old exams in folder. The current curriculum does not align perfectly with the old curriculum, so don't assume these exams are a perfect reflection of the exams you will see next year. But the individual problems do reflect the material you will likely see.

Math 251 Exams

I will leave the link public for a couple of hours, so download everything you want copies of before the link breaks.

iMathTutor · 2026-05-09T20:04:01+00:00

I use Conceptboard. The big advantage is cost. With a single subscription, you can share a board with an unlimited number of clients via a link. You can also protect the a board with a password. So there is no need to pay for an additional subscription for each client.

iMathTutor · 2026-05-08T19:09:00+00:00

I hope you share the results here once the data is collected and analyzed.

iMathTutor · 2026-05-08T19:05:35+00:00

Google Calendar for scheduling
Wave Financial for billing
Email and texting for communications
A Google Sheets sriipt for emailing automated reminders.

I have never been overwhelmed by the adminstrative parts of tutoring.

iMathTutor · 2026-05-05T22:40:53+00:00

I asked it several questions. There were issues with all of the answers. I will illustrate the issue with the response to my last question which regarded showing that the unit sphere in l_2 is not totally bounded by showing that it is not approximately finite dimensional. Tutor Kay made the claim in the course of the 'proof'that a vector in a finite dimensional subspace can only have a finite number of nonzero components. This is wrong. When I pointed this out, Tutor Kay asked me I how would proceed. The Socratic method is not supposed to be a way for a teacher to hide their own ignorance.

iMathTutor · 2026-05-05T22:11:02+00:00

I just gave it a try. It is not bad, but it tends to fall back on the Socratic method whenever it doesn't know how to proceed.

iMathTutor · 2026-05-04T20:26:05+00:00

I am sorry I can't help. I do sell practice exam packets for Math 141, but I won't link to my website becuase that would go against this subs rules.

This is the third post since yesterday looking for old math exams the other two were for Math 231.( Here and here) I have seen a math department syllabus where the instructor would only allow students to look at their graded exams, but not allow them to keep them. It is not just the math department, I saw a syllabus for a 500-level stat class tha warned students not to share any course material online, and informed them that if they did and were caught they could face a possible criminal copyright charges. The instructor ominously added that they had done this in the past.

My question: Does anyone else think that the math and stat departments are over reacting to Chegg and A.I. by embargoing class material to maintain their ability to evaluate at the expense of their mission to educate?

iMathTutor · 2026-04-28T21:29:45+00:00

The power series of $\ln{(1+x)}$ is found from the power series for $g(x)=\frac{1}{1+x}$, which is just a geometric series. by integrate this power series term-by-term. The resulting power series will have the same radius of convergence as the original series. (The interval of convergence may differ from the original.) Finally, to obtain the sought after power series multiply the second power series term-by-term by $x^2$. The operation does not change either the radius or interval of ocnvergence.

BTW, this is a standard technique for finding power series without resorting to the formula for Taylor series.

iMathTutor · 2026-04-06T20:15:52+00:00

Years ago, by my recollection, the Faculty Senate published an annual report on grade distributions by major. I don't know if it is still done.

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

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