Wikipedia:Reference desk/Archives/Mathematics/2014 November 10

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November 10

Math classes in the United States

I know there is variance from school to school, but assume we are talking about the *typical* math department in a US college or university. What would be the next related, but more advanced class you would take after Linear Algebra. I don't think most colleges have a Linear Algebra II the way the most of them have a Calculus II, but I could be wrong. Similarly, what is the next related, but more advanced class you would take after Discrete Math. If there is no "typical" math department, then it's ok to just give some examples from schools you are familiar with.--Captain Breakfast (talk) 00:11, 10 November 2014 (UTC)

Linear algebra is usually a prerequisite to abstract algebra. For example, here is Cal's course description page for math classes, with Math 113 (Introduction to Abstract Algebra) having a prerequisite of Math 54 (Linear Algebra and Differential Equations) or a course with equivalent linear algebra content. Note that 54 is a lower division (year 1 or 2) class, while those classes between 100 & 199 are upper division (year 3 & 4). But other classes, such as their Math 104 (Introduction to Analysis), Math 115 (Introduction to Number Theory), and Math 128A (Numerical Analysis) also have 54 as a prerequisite. As far as what the next related class is, that depends on your emphasis. From a pure mathematics point of view, linear algebra would be the most related follow up class, but from a computational point of view, numerical analysis might be. -- ToE 03:09, 10 November 2014 (UTC)

For engineering and the mathematical sciences, after linear algebra comes vector calculus and differential equations. Where I went to school, discrete mathematics courses were given by the CS department, as a prerequisite to algorithms courses. --Mark viking (talk) 03:29, 10 November 2014 (UTC)

The above choices are certainly possible, another might be a course in Numerical_analysis. Though there are plenty of nonlinear topics in numerical analysis, you can also spend a whole course on the linear bits. This is because, with high-powered numerical computation, most problems can be attacked through linearization (at least within a certain range... remember part of the value of linear methods is that many processes are well approximated by linear processes). Things like singular value decomposition, various types of spectral theorems, eigendecomposition, etc. can be taught at the intersection of advanced linear algebra and numeric methods. Depending on interests, these tools can then be applied to topics like signal processing, dimensionality reduction, and many others. SemanticMantis (talk) 14:58, 10 November 2014 (UTC)

Most universities offer more than just one linear algebra course. There is often one for engineers, one for pure math majors, and one for applied math majors. The first emphasizes matrices and matrix operations, and usually just manages to do eigenvalues. The second deals with things from the perspective of linear transformations and vector spaces, often as a prelude to abstract algebra (sometimes this course is part of a sequence that deals with other topics like Hilbert spaces). The third involves matrix computations and analysis, often using software like Matlab. There is often more than one course in such a sequence, or at least one offered at the graduate level. Sławomir Biały (talk) 15:23, 10 November 2014 (UTC)

Finding the Median of a complex dataset

Resolved

In my warehouse, I have 10,000 different products of differing weight, ranging from 0.01Kg to 30.00kg. The median weight of these products is around 2.82kg. Each week, I despatch in excess of 1,500,000 boxes of these products, in varying quantities. My dataset tells me how many boxes of each product I have despatched

e.g.

• Product 1 (1.75kg) 253 boxes
• Product 2 (1.02kg) 399 boxes
• Product 3 (9.78kg) 100 boxes etc.

How do I calculate the median weight of the 1,500,000 boxes I have despatched, without 'writing them out' as a long list? I have access to MS Excel and Minitab, if that helps. Thanks! — sparklism ^hey! 09:48, 10 November 2014 (UTC)

What you want to calculate is a weighted median. Unfortunately, I don't know of such functions in Excel or Minitab, but it is easy enough to do in R. --Mark viking (talk) 11:40, 10 November 2014 (UTC)

Right - the weighted median is exactly what I'm after, so thanks for that! Unfortunately, R (programming language) is beyond my capabilities at this point, but now I know what I'm after I shall see if it's do-able in Excel or Minitab. Thanks again! — sparklism ^hey! 12:16, 10 November 2014 (UTC)

...and after Googling, I found this, right? I'm going to try that anyway :) — sparklism ^hey! 12:25, 10 November 2014 (UTC)

The solution above seemed to work - hurrah! Thanks for your help Mark viking :) — sparklism ^hey! 14:26, 10 November 2014 (UTC)