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Our take is Real Analysis before Complex Analysis. Real Numbers when couldn't accommodate square root of negative number - complex numbers were introduced. If you consider, complex number as an ordered pair - basically elements of $R^{2}$ - can that be better conceived without understanding the properties on R. Mathematics teaches us ways to generalize ...


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Assessment is the measure of progress and decides a student's capability or competence o get into the next level. General ability to solve problems is a broad term. But, as you said - "Should I assess their ability to use a particular method to solve a quadratic equation, or should I assess their ability to solve a quadratic equation in general?" ...


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Before listing 'resources', let me start with some official documents (e.g. to clarify the difference of sustainable math and math for sustainability, see xkcd:Sustainable :-). The official UN Site lists the 17 Goals for sustainability; especially Goal 4: Education. Still debating what this all means, I find the paper by Brundiers et. al. (2021, see below ...


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Since asking the question, I've come across Thomas J. Pfaff's website, Sustainability Math. Plenty of material there, including projects and links to further resources. Contains a blog that refers to current/recent events. I found Pfaff's website when perusing Mathematics of Planet Earth, specifically the list of curriculum materials. (Made this community ...


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As a fellow college algebra (et. al.) instructor, I think that knowing specific methods is a necessary thing to confirm. That's what I do on my tests. If you want and have time to add yet another general question (so as to assess both), then that's commendable. The point is that the specific methods will pop up in future courses in different contexts, and ...


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Possibly worth looking at is: Earth Algebra: College Algebra With Applications to Environmental Issues by Christopher Schaufele and Nancy Zumoff (1995 1st edition and 1998 2nd edition) See this review and this project/funding document. For what it's worth, in Spring 1993 I interviewed (on campus) for a tenure-track position at the university this was ...


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I suggest holding office hours, both one-on-one, and possibly in small groups, to help students with the assignments, or just to clarify the material presented in the lectures. Of course the prof may hold such office hours, but since you are giving tutorials, it seems natural, and might serve as a lower-stakes alternative for those afraid to visit the prof. ...


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While, yes, precise advise would depend considerably on context, I do think there are some features that should/could influence curriculum design/choices. Basic complex analysis (Cauchy's theorem and corollaries, power series and Laurent expansions, residues, ...) functions very well, answers questions, and can feel like a fulfillment or happy continuation ...


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In mathematics, at least, two concepts of function are used. We will distinguish them by using uppercase and lowercase letters: Function is a univalent relation f, i.e. (x, y), (x, y ') ∈ f -> y = y'. FUNCTION is a triple (f, D, K), which we usually write f: D -> K, which consists of sets D and K and a univalent relation f such that the set of its ...


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First, let's keep in mind who the students are who are taking these courses. They are either high school students or college students who are taking high-school math for remediation. A typical student in such a class is thinking of becoming a dentist or selling used cars. Your concerns will make no sense to such a student and will be of no educational ...


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The definition of function as a binary relation on two sets is related to the set theoretic foundations of mathematics. Under this foundations, we consider only sets as the primitive building blocks for all mathematics. You have mentioned functions, but other mathematical objects are defined (sometimes awkwardly) as some set. For example, tuples of numbers (...


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The question is probably too opinion-based to allow for a definite answer, but let me offer a few reasons why I think that we should rather not ignore domains and codomains when we teach functions to, say, highschool students (yes, this means I'm suggesting to do it differently from how it is now done in many places): (1) The OP is of course right that, from ...


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I appreciate your concern and have felt similar despair when teaching about functions and the awkward game of "finding their domains" in precalculus courses. But then I lift myself up by thinking about analytic continuation. A real variable construct like $\sqrt{x}$ somehow just knows, without human intervention, what its domain should be. In this ...


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