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\subsection{Synchronization of lecture and lab}  \label{sec:synchronicity}  In previous editions of AST 208, the lecture and lab operated more or less independently. The revisions to the lab (\S~\ref{sec:lab}), especially the use of ``real'' data and analysis tools, now demand a more rigorous treatment of statistics and a tighter integration of the course lectures with the lab activities. To do this, the lectures in the first half of the course now cover foundational topics---coordinates, topics in astronomy---coordinates,  sidereal time, parallax---and statistics. flux, parallax, and diffraction---and statistics (at the level of, e.g., \citet{Taylor1999An-Introduction}.  As motivation, we introduce these concepts in the context of detecting exoplanets; this ties the introductory material to the treatment of planetary science in the latter half of the course. The first two weeks of lecture now discusses angular coordinates, right ascension and declination, sidereal time, and parallax. In the first lab, students find objects on the sky using coordination  with the lectures, the first two labs use  \href{http://www.stellarium.org/}{Stellarium planetarium software}; in the second lab, software} and \href{http://www.pa.msu.edu/abrams/}{Abrams Planetarium} to help  the students determine which celestial objects are visible from the \href{http://www.pa.msu.edu/astro/observ/}{MSU Observatory} (and test their predictions, even on cold cloudy nights, become familiar  with the help of \href{http://www.pa.msu.edu/abrams/}{Abrams Planetarium}). angular coordinates.  The lectures then discuss the inverse-square law for flux, the magnitude scale, and the distance modulus. A discussion of lecture on  the wave nature of light, in particular diffraction, then follows. This dovetails with the lab, light is followed by a lab  in which students use the \href{http://ds9.si.edu/site/Home.html}{ds9 visualization software} to measure point-spread functions. Following these topics, While  the next three weeks of lectures are devoted to probability and statistics, with course notes drawn from \citet{Taylor1997An-Introduction} and \citet{Durrett1994The-Essentials-}. Starting with a derivation of probability rules from set-theoretical concepts, we discuss combinatorics and then build to a derivation of the binomial distribution in the context of the random walk. The small-probability limit as a Poisson distribution is introduced, and then we imagine measurement fluctuations as a random walk with a corresponding normal distribution. From there, we derive the uncertainty students work on statistics  in the mean, propagation of uncertainties, and the use of the $\chi^2$-statistic lecture  (see Figure~\ref{fig:sample-datasets}).  In parallel, Fig.~\ref{fig:sample-datasets}), in  thestudents work through a multi-part  labin which  they determine the age and distance of the Hyades star cluster, and with  associated uncertainties, using data from the Hipparcos satellite.This lab puts into practice the statistical concepts discussed in lecture.  The statistics unit culminates in a lab on signal-to-noise in astronomical observations, where students hone their intuition for how sensitivity depends on exposure time, telescope aperture, and atmospheric conditions.