The session is a sampler across aspects of professional learning related to teaching, scholarly activity, service, and leadership development. The focus is on how to cultivate and use a portfolio document as a tool for planning, implementing, and reflecting on professional growth. We will start with an overview of the nature of “professional development” for those seeking faculty roles. Then, in small groups, we will look at some examples of teaching portfolios of college faculty. The third and final activity includes consideration of your own professional destination(s), how the documentation of your journey in a professional portfolio might look, and some initial planning about how to get there (wherever “there” is).
Meeting ID: 813 9009 4107 Passcode: 265706
On Being the Architect of Your Own Professional Future
Georg Cantor's "Continuum Hypothesis" (CH) postulates that every infinite set S of reals is either countable or equinumerous with the set of all reals. Using the axiom of choice this means that the "continuum" (the cardinality of the set of reals) is equal to aleph1, the smallest uncountable cardinal.
David Hilbert's first problem asked if CH is true; we know now that neither CH nor non-CH can be proved from the usual axioms of set theory (ZFC). Paul Cohen's method of forcing allows us to build universes (structures satisfying ZFC) where the continuum is arbitrarily large.
There are many relatives of the continuum, such as the answers to these questions: How many nulls sets (Lebesgue measure zero) do we need to cover the real line? How many points do we need to get a non-null set? How many sequences (or convergent series) do we need to eventually dominate all sequences (convergent series)? etc. All these cardinals are located in the closed interval between aleph1 and the continuum.
In my talk I will present some of these cardinals and hint at the methods used to construct universes where these cardinals have prescribed values, or satisfy strict inequalities.