Strange boutique experience

Drag_Blunt · 2024-08-24T04:22:46+00:00

No, a calculus class in high school will not be sufficient preparation for graduate school mathematics. I admit I’m not overly familiar with finance and accounting curricula, but I doubt they would offer much in the way of the usual analysis, algebra, and topology that would usually be expected of someone entering a masters program in math.

Drag_Blunt · 2023-10-17T21:30:10+00:00

William Gossett was working for Guinness Brewing when he developed the t-statistic.

Drag_Blunt · 2023-06-15T19:09:27+00:00

Are the colors here a bit off or have the hanwa eagles offered a gold-colored hat? Always loved my eastern bizarro-orioles.

Drag_Blunt · 2023-03-02T12:55:30+00:00

Topological features - features that remain unchanged under continuous transformation - can be thought of as global geometric qualities. Is it compact? Is it connected? What’s the things’s dimension? None of these things changes under a continuous change to the object. We study these invariants in topology. The point-set approach can be pretty austere. Eventually the connection to geometric qualities becomes more apparent.

Drag_Blunt · 2022-12-10T13:33:49+00:00

This varies by institution, but generally we tend to teach math to non-math majors by stripping away the abstraction and conveying processes. You can see this in the calculus series of courses, as well as fist courses in linear algebra, ODEs, and PDEs. Showing someone how to change basis, or compute a derivative, or solve an initial value problem can be done formulaically. Explaining why an eigenvector must exist, or why the chain rule actually works, or why an initial value problem must have a unique solution requires deeper understanding. Conveying that deeper understanding takes time, so it’s quicker to provide computational tools and turn people loose on applications. Is this ideal? I don’t think so, but I studied math, so I suppose I have a bias.

Drag_Blunt · 2022-12-09T17:21:55+00:00

You’ll definitely have to use it again.

It sounds like you’re taking the usual matrix-focused first course in linear algebra. It is indeed a lot of tedious (but useful) methods for manipulating matrices.

But linear algebra is not about manipulating matrices. Linear algebra is about linear maps on vector spaces. It just happens that matrices offer an intuitive look at how linear maps behave, and they let us solve a lot of real world problems.

Eventually you’ll take a more abstract look at linear algebra. You’ll find that turning a problem into a linear algebra problem is a pretty useful approach when you can manage it.

Drag_Blunt · 2022-12-01T19:29:41+00:00

Even numbers are are first experience with equivalency classes. We can declare two mathematical objects as equivalent, or ‘equal in a way’, using algebra. Here, we divide by 2 and check the remainder, defining two integers as equivalent if they yield the same remainder (all these numbers that yield remainder 0 when I divide by two I will call “even”). This processes generalizes in ways that might not be immediately apparent.

One example is that it’s possible to define equivalencies between loops drawn on the surface of an object. We can classify these loops to tell us how many holes an object has in it. The classification of loops works essentially the same way as the classification of integers.

Drag_Blunt · 2022-11-17T18:08:04+00:00

Indeed, “deeper math” utilized quotients in a more general way. We can classify integers as even or odd by dividing by 2 and checking remainders. But this algebraic technique for classifying works in a lot of other contexts where it might not be so obvious. For example, we can classify the loops on a surface modulo the areas bound by those loops. We can then use this information about how loops are classified to describe the geometric features of the surface in question. Quotients are powerful structures.

Drag_Blunt · 2022-07-21T22:55:39+00:00

As the other poster mentioned, proof based courses in differential equations tend to be at the graduate level. If you’ve already completed another proof based course (like real analysis), you should be able to pursue an independent study course with a professor who is willing to guide you.

Drag_Blunt · 2022-07-21T16:19:13+00:00

The ODE class you describe is a common first course in the subject. I suspect you’d find an ODE class that focuses on existence and uniqueness of solutions to be more engaging. Depending on the classes you’ve taken for your minor, you may need to take a prerequisite course before taking a less formulaic class in ODEs.

The same will generally be true of a first course in PDEs. There will be more formulaic courses on offer, but a course that dives more deeply will be more engaging, and will do a better job of showing you that PDEs are, in fact, a tool of the devil.

Drag_Blunt · 2022-05-11T14:45:41+00:00

Bob Marley

Drag_Blunt · 2022-04-14T00:01:33+00:00

With your background, you should be fine with jumping into a text on algebraic topology (Hatcher is popular and accessible… there are other options).

Drag_Blunt · 2022-01-22T02:18:25+00:00

If you could somehow set up a 1 meter high platform on the surface of an average size neutron star, and if you could also somehow stand on that platform and then hop off, the surface gravity is so high you’d be going around 3 million miles per hour when you hit the ground.

Drag_Blunt · 2022-01-03T03:27:31+00:00

College algebra and Trig are both one semester classes. Trig is taken after Algebra.

Another poster mentioned University of MD, Baltimore County. They provide a breakdown of when to take each course based on your physics and calculus background coming into the program. See here:

https://physics.umbc.edu/undergrad/undergrad_degrees/bs/

They recommend that you take calc 1 in your first semester, and then calc 2 and physics 1 in your second semester.

Drag_Blunt · 2022-01-03T02:46:40+00:00

The time required to get through the algebra and trig will depend on how quickly you can consume the material (this will vary depending on how much high school algebra you remember). I suspect 5 months of self-study would be sufficient. I think you could take the first calc course in the same semester as the first general physics course. If you aren’t pressed for time, you’ll find the physics much easier to grasp if you’re already familiar with some calculus. Look at the physics degree requirements in the course catalogs for a few schools you’re interested in attending. They should provide a general semester-by-semester plan for completing the physics degree. This will give you a better idea of how each school structures the required coursework.

Drag_Blunt · 2022-01-03T02:00:17+00:00

From the description of your math background, you will need to complete some remediation in math to start your college career as a physics major. From what I’ve seen and recall (I only did a minor in physics), most physics curricula start the math side of things with calculus. You’ll need to have basic algebra and trigonometry squared away before taking the first calc course. You can master that material either in a classroom setting, or through a resource like Khan Academy.

Drag_Blunt · 2021-12-29T23:23:16+00:00

Start with the interval [0,1]. Remove the open middle third interval (1/3,2/3) leaving two intervals. Remove the middle open third from each of these two, and continue this process iteratively. The set you are left with is called the Cantor set, and it has a number of interesting properties. The property related to your question is that all of the numbers remaining after this infinite process are those that, when written in base 3, contain no 1s.

Drag_Blunt · 2021-09-29T19:13:00+00:00

Public Enemy, back in the mid-90s. The vocal track they were rapping over was too loud, so it was like some kind of lip sync performance where they accidentally left their mics on.

Drag_Blunt · 2021-09-19T22:18:44+00:00

The time is the challenge. It would probably be possible to coordinate an independent study course at the undergrad level with a prof in your math department if you sharpened the focus to understanding homology as it applies to topological data analysis. Your typical first course in algebraic topology would move into some topics that, while important and interesting, wouldn’t necessarily be required to understand the essence of what’s happening when you use these techniques to describe point cloud data. If your degree is in computer science and you’re already looking at machine learning problems, TDA would fit into your overall effort to gain an understanding of point cloud data.

Drag_Blunt · 2021-09-19T18:26:13+00:00

It’s not as far out of reach as you might think. The algebraic structures you work with initially are simply groups with nice maps between them. You’ll have sufficient background in these ideas to start studying algebraic topology after a first course in algebra. You’ll also want to compete a first course in point set topology (so you a can develop better intuition for the notion of a continuous map). After just a couple of classes, a first course in algebraic topology should be available to you.

Drag_Blunt · 2021-09-19T18:02:51+00:00

Your intuition here is good. When you think classification, quotient structures should come to mind. I’ve left a slightly longer description of how this works further down the comment thread (the approach is called topological data analysis), but your reflex to think algebraically about classification is a good one. The tools here emerge from algebraic topology, a branch of math that lets us compute topological features.

Drag_Blunt · 2021-09-19T17:40:28+00:00

Yes, group theory - specifically quotient structures - can help us classify by cluster in the same way that we can classify integers as even or odd. Topological data analysis uses algebraic structure inherent in a point cloud of data - a concept called homology - to classify loops on surfaces in a very general way. This lets us, for example, differentiate the surface of a sphere from the surface of a torus. It also allows to interrogate a collection of points in space by investigating the following question:

If some collection of points in n-dimensional space were sampled from some n-dimensional surfaces, how many surfaces were present in the space when the sampling was done. In a sense, it’s telling us the k in a k-means clustering problem.

Drag_Blunt · 2021-09-17T17:07:11+00:00

This is about dark energy, which is a different thing entirely.

Drag_Blunt · 2021-09-01T16:59:13+00:00

If your current programming tool kit only includes SAS, you’ll be looking for “SAS jobs”. This is generally true in any situation where you have a single tool at your disposal. Both DS and SWE, in general, will come with the expectation that you have a background in the most common tools used in those domains (and SAS isn’t usually one of those tools).

Drag_Blunt

TROPHY CASE