How can I prove the linearity of $F_*$? What does $F_*$ eat?


  If $N$ is smooth manifolds and $F: M \to N$ is a smooth map, for each $p \in M$ we define a map $F_*: T_pM \to T_{F(p)}N$, called the push-forward associated with $F$, by
  $$(F_*X)(f) = X(f \circ F).$$



Question: cowsay not working?
Answer: Running sudo find / -name cowsay verified that cowsay is installed. Since prefacing the cowsay command with /usr/games worked, the problem is that the /usr/games directory is not in your path. To fix this add the following 

PATH=$PATH:/usr/games
export PATH


to the .bash_profile file in your home directory. 

How to do it:

Change to your home directory.

$ cd ~


Then type the following command to edit your bash profile.

$ sudo nano .bash_profile


Append the following lines to the end of the file.

PATH=$PATH:/data/myscripts
export PATH`


Save your changes and exit; then logout or reboot. Once you have done this you should be able to enter.

$ cowsay “$USER is my friend”