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I am planning to develop a course which I tentatively call as 'Quantitative Reasoning'. The goal of the course is to equip a typical undergraduate student with sound quantitative reasoning skills so that they can critically evaluate statistical and related quantitative claims they may encounter as part of their personal/professional lives.

The course will not have require any previous math or statistics background. The goal is to focus on the high level conceptual details rather than the details of density functions, t-tests, ordinary least squares etc. Thus, the hope is that the course will be useful and will appeal to a wide spectrum of students (think of majors such as: english, arts, sciences, social sciences, math etc). A similar question on stats.SE List of topics for a 'quantitative reasoning' course may give you a sense of what I intend to cover in the course.

The primary focus of this course will be on statistics. However, I am wondering what if any math skills/topics would be important for the average undergraduate student to know/understand.

In light of the above, my three questions are:

  1. What math topics should you think I should include/exclude from such a course?

  2. Are there any textbooks that may be useful given the above goal?

  3. Are you aware of any other course that attempts to accomplish the above? Links to syllabus would be very helpful.

If it matters, the target student for the above course is an undergraduate student in the US possibly at the freshman or sophomore level.

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Let's see, aside from a general overview of probability and statistics? I would say the concepts of exponential decay and growth, chaos -- but only in terms of "sensitive dependence on initial conditions", possibly a little bit of utility theory. How to read a graph, and conversely, how a graph can distort the information that it is presenting. –  Craig Sep 8 '11 at 14:23
    
No such course will appeal to such a wide spectrum of students: mathematical backgrounds vary too much. If we’re being honest, no such course will actually appeal to very many students at all: it will be taken either because it’s a specific requirement or because it’s perceived as the easy way to satisfy a distribution requirement. Will this course compete with existing ‘liberal arts math/statistics' courses, or with existing discipline-oriented basic statistics courses in, e.g., psychology? –  Brian M. Scott Sep 8 '11 at 18:33
    
On the statistical matters: you might want to get some inspiration from this... –  J. M. Oct 8 '11 at 15:57
    
There was a similar discussion at MO which you might want to look at: mathoverflow.net/questions/28695 –  Noah Snyder Dec 18 '12 at 12:37

2 Answers 2

Many "Liberal Arts" Universities include quantitative reasoning, or something isomorphic, as part of the undergraduate distribution requirements. So a good idea would be to check their course announcements for ideas.

For example, Princeton University actually has a distribution requirement named precisely Quantative Reasoning. If you go to the search page, click the checkboxes for "Courses" and "QR", leaving the text field blank, and click search, you will see a list of all courses considered by the registrars at the university to fit your label.

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How easy going do you want the course to be? There's an easy going course titled "Understanding Uncertainty and Statistical Thinking" from the NUS which is used for their breath requirement. The "textbook" used was "Everyday Probability and Statistics: Health, Elections, Gambling and War" by Woolfson and there were examples drawn from "Understanding Uncertainty" by Lindley. It was taught by David Nott and Chen Peiyi back in 2009, and I thought it was interesting for a university freshman. They seem like nice people, and might share some ideas with you.

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