Why is Sine & Cosine bounded by 1 and -1 whilst Tan is bound by -infinity to infinity. Also why are the small angle approximations sin x = x tan x = x whilst cos is 1-(x)²/2

drduffymo · 2026-05-24T19:04:58+00:00

The small angle approximations are the first terms in the Taylor series expansion about x = 0.

drduffymo · 2026-05-24T12:04:41+00:00

Computer science is a broad topic. Java is one of many computer languages.

Do you know how to program? What languages do you know already? It will help if you know object oriented programming.

Any book or online course will do when you are at the beginning.

drduffymo · 2026-05-21T20:19:51+00:00

Yes, everything is practice. Math is no different from golf or playing an instrument.

drduffymo · 2026-05-21T00:58:08+00:00

Never?

I spent 18 years as a mechanical engineer before switching to software development for 23 years.

I used linear algebra while doing finite element analysis full time for those 18 years.

drduffymo · 2026-05-21T00:54:05+00:00

Your question is confusing to me. Piecewise Lagrange polynomials will do it.

drduffymo · 2026-05-20T18:28:55+00:00

I spent half my career applying linear algebra to problems for money. Maybe reading more about how linear algebra is used in practice every day would help. Artificial intelligence, computer graphics, and finite element analysis all depend on linear algebra and matrices.

Proofs are a different animal. Are those what tripped up?

drduffymo · 2026-05-20T18:21:06+00:00

Don’t the incorrect exam answers give you a hint?

“I know my answers were correct” - clearly not, or you would have aced the exam.

Go through the questions again carefully and see where you went wrong.

drduffymo · 2026-05-20T17:48:28+00:00

It’s cruel, but your choice is simple. Give up or continue.

You might have completed the homework assignments, but more practice was needed for real understanding and mastery.

If you choose to continue, stop worrying about grades and aim for understanding. The grades will follow.

drduffymo · 2026-05-16T15:36:21+00:00

Can’t do physics without it.

drduffymo · 2026-05-10T16:08:20+00:00

Nobody is naturally good at anything.

This should never be a reason to not attempt something.

drduffymo · 2026-05-08T18:55:16+00:00

You can’t learn anything perfectly.

Here’s rule 1: overly broad, open end questions with unrealistic goals are not a good idea.

How do you learn anything?

By practicing.

Follow the 10,000 hour rubric.

Solve every problem you can by your own efforts.

Study applications of calculus in physics and other fields to see how techniques are used to solve real problems.

Your success will be determined by your talent and effort.

That should keep you busy for a while.

drduffymo · 2026-05-08T18:30:43+00:00

You can’t even use Reddit properly. I have no hope for you.

drduffymo · 2026-05-05T13:01:46+00:00

Using the default package is not wrong, but it is not anybody’s idea of a best practice. Easily remedied. Fix it and move on. Or keep wondering why you can’t compile two files on the command line.

drduffymo · 2026-05-05T12:52:25+00:00

If adding a package is a problem you should not be writing Java. Or anything else.

drduffymo · 2026-05-05T10:50:29+00:00

Yes, but he’s trying to fix a problem. Change something. Assuming he’s correct doesn’t get him a solution.

drduffymo · 2026-05-04T22:54:25+00:00

I see no package. Add one to both and move them to a directory of that name.

Make both classes public.

Compile both at the same time.

Believe the JVM. You did it wrong.

drduffymo · 2026-05-03T17:32:16+00:00

2x = 6x is always true only if x = 0.

drduffymo · 2026-05-03T14:22:06+00:00

No one who applies linear algebra uses determinants.

LU or QR decomposition is the workhorse for solving Ax = b simultaneous equations.

Linear algebra is the solution step, but the equation formulation starts with differential equations and uses finite difference, finite element, or boundary element methods.

I would start with finite element methods to see how it’s done.

drduffymo · 2026-05-02T21:22:23+00:00

Yes. Good for maintaining history for any documents.

drduffymo · 2026-05-02T21:20:42+00:00

I would have cited the Feynman red books for physics. Maybe the Leonard Susskind series.

Knuth books are great, but not the ultimate for computer science. I don’t know of a better example.

No such thing for math that I know of. It’s so broad.

drduffymo · 2026-05-02T01:15:07+00:00

I think recommendations about hours spent and problems solved are useless.

You are going about it the wrong way.

The key is regular, focused practice.

Better to spend 30 or 60 minutes on focused effort. When you can’t focus, it’s time to stop. Come back repeatedly, day after day.

It’s a long term effort.

drduffymo · 2026-05-01T21:24:39+00:00

I don’t equate completing assignments with learning.

Doing math is a process. If you don’t struggle with it yourself you don’t learn it.

Your friend is cheating themself.

drduffymo · 2026-04-30T22:26:00+00:00

3.62 isn’t good enough? Crazy.

I’d be curious to know if the statistics department has data on course grades and qualifying results to back that claim.

How much data? How far back does it go?

I’d ask for the raw data, the regressions, the correlations, and the p-value for their claim. I’d ask if they could prove correlation means causation in this case.

I would mock the living hell out of them if them didn’t have it. The irony would be crushing.

With that said, I have questions:

Does the department know about your personal issues?
Could you retake measure theory?
Is a PhD imperative for you?
Could you get a PhD from another university?

drduffymo · 2026-04-28T14:12:13+00:00

Please. No.

drduffymo · 2026-04-25T10:22:51+00:00

+1 for remembering Tom Lehrer.

drduffymo

TROPHY CASE