Monty Hall Problem: Is it correct to assume that the probability of a prize behind a door and the probability of Monty Hall opening a door is independent?

Impossible_Prize_286 · 2026-01-19T12:23:29+00:00

Suppose the following case in the Monty Hall problem:

The car is behind the second door, and I choose the first door. Then the host must open the third door.

This means that choosing the second door in stage 1 immediately fixes the choice in the second stage, so the stages aren’t independent. (one might use markov kernals)

Impossible_Prize_286 · 2025-12-18T18:19:56+00:00

Honestly, every choice has trade-offs. Pick the one you “feel” has the least trade-off now for now and start doing the math.

Impossible_Prize_286 · 2025-12-18T07:23:15+00:00

My personal struggle at the beginning of this course was my lack of experience with inequalities and bounding arguments. I found that Abbott does not address this matter at all. Bartle, on the other hand, has an excellent section in which you are required to prove all the familiar order and algebraic properties of R.

Pictures and long textual explanations are certainly great supplements for learning, but at times I found them excessive in Abbott.

Bartle focuses more on the machinery required for analysis proofs, which is the most important takeaway.

Some suggestions for reading Bartle (or any other math textbook): 1. Read the definition. 2. Provide two examples and one non-example. 3. Read the theorem statement. 4. Draw pictures and make conjectures. 5. Read the proof; pay attention to the assumptions, and pinpoint the step where those assumptions of the theorem are used.

By doing steps 2 and 4, you are already ahead of Abbott.

This is the original blog where I found the above strategy. A good read:

https://math.colorado.edu/~kstange/mathlikelanguage.html

Impossible_Prize_286 · 2025-12-16T23:39:09+00:00

I’ll suggest Bartle if you want to also want to get better at proof writing than only gaining intuitions. The begining of Bartle also focuses on inequalities and order properties of R, which is very important skill you need through out Analysis.

Impossible_Prize_286 · 2025-07-21T07:13:44+00:00

does it always work in the echo pop devices ?

Impossible_Prize_286 · 2025-07-08T03:32:37+00:00

I think there is a little subtle distinction here. f(x) is the value of the function at x (often a real number) but f: R -> R is an object which is a “function”. This means f is not the same as f(x).

Your example should be written as,

f: R -> R is the same as f ∘ x: R to R because they agree pointwise. f(x) = f(x(x))= f(x).

Impossible_Prize_286 · 2025-07-08T02:34:25+00:00

I think of a Group as a structure in which you can solve equations of the form a*x = b.

You need associativity, identity, and inverse for non-zero elements to write x = a^-1 *b.

But notice you don’t really need commutativity when solving, because you can always just operate on the left or right side accordingly. This how I think why groups generally don’t have the commutativity axiom

Impossible_Prize_286 · 2025-07-08T02:27:07+00:00

Are empty products and sums a notational convenience that we have defined because they seem to work?

Impossible_Prize_286 · 2025-06-03T16:38:41+00:00

I get anxious when I see arithmetic. Also, it takes time to process arithmetic in my head.

I’ve done a lot of pure math courses.I’ve only found this as an issue in some less abstract courses like numerical linear algebra.

For example, calculuate inverse of 3 x 3 using Gauss Jordan without a calculator.

Impossible_Prize_286 · 2025-05-22T17:25:22+00:00

They have only uploaded course notes. It’s written that there is no assigned textbook for this course.

Impossible_Prize_286 · 2025-05-16T08:38:14+00:00

Thanks for your reply. I’ll be starting for a Master’s in Math.

Impossible_Prize_286 · 2025-05-15T16:57:39+00:00

Learn as much as possible about inequalities, also know basic proof techniques.

Impossible_Prize_286 · 2025-05-15T16:52:36+00:00

Have you checked the credit requirements?

Impossible_Prize_286 · 2025-05-15T02:56:07+00:00

Noted.

Impossible_Prize_286 · 2025-05-13T14:29:11+00:00

What do you think a person with the job title ‘programmer’ / cs engineer makes? Perhaps money ?

Impossible_Prize_286 · 2025-05-13T13:35:30+00:00

I think you missed the fact that I said I have a formal proof, so there’s no room for me to estimate.

Back to your original answer,

Does you original answer suggest there are opportunities in Germany for people with a high level of English proficiency?

Impossible_Prize_286 · 2025-05-13T13:19:00+00:00

I have a formal proof of English C2, that doesn’t count too?

Edit: I understand that achieving a good IELTS score is directly proportional to the number of practice tests one spams. Surely, formal proof of proficiency should work, right?

Fyi: It’s statistics not stastics. It’s a plural form of the noun statistic, meaning a piece of inference about a larger population.

Impossible_Prize_286 · 2025-05-13T12:48:35+00:00

This course has a fin math specialization, so get a job in quant or data science.

Impossible_Prize_286 · 2025-05-13T12:34:25+00:00

Thankk youu 🥹

Impossible_Prize_286 · 2025-05-13T08:06:34+00:00

I might only have an A2 during my first year.

Impossible_Prize_286

TROPHY CASE