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The early part of the project was dominated by trying to understand the data that would be used.  The data used for distant galaxies was presented in \cite{Tomczak_2014}. This paper contains a table of mass vs number density (number of galaxies per unit volume) for $0.2 < z < 3$. 3$ which we use to construct the stellar mass function (SMF).  However, while we plotted this data and various subsets of it (only star forming or quiescent galaxies) we do not use the raw data. Instead, we use a paramaterised double Schechter function from \cite{Leja_2015}  which smooths the data and ensures the number density at each mass is monotonically increasing as $z \leftarrow 0$  We do not use the raw data  We made various graphs to better understand how the growth rate was affected by whether the galaxy was quiescent or star forming. We checked their use of Schechter and Double Schechter functions, before paramaterising the Schechter function to smooth the relationship and ensure that the number density at a specific mass increased monotonically as z approached 0 \cite{Leja_2015}. \rightarrow 0$.  With this done, graphs showing thechange in  mass over time between Z = 3 and Z = 0 were constructed $0.2 < z < 3$  for various start masses. masses were constructed.  A second distant The local group dwarf  galaxy dataset  wasalso introduced later in the project. This data,  taken from \cite{Whitaker_2014} was used to confirm that \cite{Weisz_2014}. This paper determines  the results were reasonable and backed up mass of a subset of the known dwarf galaxies between $0 < z < 2.6$ by calculating the star formation history (sfh). As with the distant galaxies, graphs showing the percentage of mass over time for various groups of the galaxies (grouped  by other galaxy shape or location) were plotted to better understand the  data.Again, a paramaterisation rather that raw data was used.  The local group dwarf A second distant galaxy  data set  was introduced later in the project. This data,  taken from \cite{Weisz_2014}. As with \cite{Whitaker_2014} was used to confirm that  the other data sets, comparison between  the first uses of this two main  data sets  were reasonable and conformed  to help my understanding. Graphs showing the percentage of mass over time of the galaxies were plotted. other data. Again, a paramaterisation rather than raw data was used.  \textbf{Analysis}  The major correction so far A number of corrections must be  applied tothis distant galaxy data concerns mergers. The local group data is based on galaxies that have not undergone mergers \textbf{is this true} and so to compare  these data sets, the effects of mergers must sets before they can  be removed from this data set. To do this, the method described in \cite{Gomez_2015} has been used. Supporting material consisting of graphs showing expected merger rates at various mass ratios and redshifts has also been prepared. compared.  The main analysis of the first correction is for mergers. The  local group data was is based on galaxies that have not undergone mergers \textbf{is this true?}, while some of the distant galaxies will have. We make the merger correction  todo with  the error bars reported by \cite{Weisz_2014}. These errors follow SMF using  the conventions specified method shown  in \cite{Dolphin_2012} for systematic uncertainties and \cite{Dolphin_2013} for random. However, these uncertainties are extremely conservative and so instead we use the same convention \cite{Gomez_2015}. Supporting material such  as in \cite{Weisz_2014} which conservatively a relative uncertainty plots  of 50\%. expected merger rates at various mass ratios and redshifts were also constructed to ensure that we were applying this correction correctly.  We also apply a correction for mass loss  to both the local group and \cite{Whitaker_2014} data to account for mass loss. Both of data. As  these methods measure both determine mass by integrating the star formation rate over time, the data shows  the total stellar  massof stars  formed in by a certain time, rather than  the galaxy and do not account for total  stellar death. mass present at that time.  Much of this death mass loss  is a result caused by the death  of high mass, short lifespan ($ < 100Myr$)  stars and so we approximate this loss can be approximated  as instantanious with instantaneous using  a multiplicative factor of 0.64. As the factor. The  \cite{Tomczak_2014} data observes the determines  mass of the galaxy rather than calculating it by from observed luminosity and not  star formation rates, and so  thisfactor  is not needed applied  there. Finally, a morphological correction is applied to the local group data. Approximately 50\% of the known galaxies in the local group appear in this data set. However, if we divide these galaxies into those attached to the milky way, those attached to M31 (Andromeda) and those in the field, we find that we do not sample from these groups evenly. This correction weights each galaxy to account for this sub sampling. sampling  The main analysis of the local group data was to do with the error bars reported by \cite{Weisz_2014}. These errors follow the conventions specified in \cite{Dolphin_2012} for systematic uncertainties and \cite{Dolphin_2013} for random. However, these uncertainties are extremely conservative and so instead we use the same convention as in \cite{Weisz_2014} which conservatively a relative uncertainty of 50\%.