All posts by Chad

Solutions by Chad to Finite-Dimensional Vector Spaces by Paul R. Halmos

I am starting to write out some of my solutions to the exercises in the book Finite-Dimensional Vector Spaces by Paul R. Halmos. They can be found here:

Or in PDF form: Solutions.html

It would be a lot of work to type all of my solutions so I only wish to do it if there is interest. Please let me know at


The year is 3400 and human civilization has spread to its second home and first colony. Peace and prosperity have generally prevailed though there has been some conflict between the two factions leading colony construction and terraformation. The colony structure where we live and work consists of a gigantic network of underground corridors which are navigated via spaceship-like vehicles. Rifts between the factions left areas of the colony low on resources and led to much hardship. Most colony sectors were prepared for this and hoarded resources to make it through rifts. All colony sectors, however, were not prepared for the alien armada that would sever the transport of the vital Earth-based resources needed by the colony. Why did they not land on Earth or the Colony immediately? We could only guess that they did not have the landing craft needed for an invasion.

Without needed resources, sectors of the colony could not be maintained. The citizens in these sectors had to be evacuated to less resource-intensive sectors. This process took two years and all the while, the aliens seemed to do nothing.

In the third year after the alien arrival, though, sensors in the vacated sectors started to register movement and atmospheric changes. Maybe they were just waiting for us to invite them in.

ColonyBorn is a 3D spaceship flight game for android phones that is in development. Fly through corridors and fight against the invasion. There will be single player and multiplayer. While in development, an early release version will be updated and available for download here. Thank you for coming by and we look forward to bringing you an action packed gaming adventure.

Tutorial Video

Below is a tutorial video (no audio).  There are several control options in ColonyBorn and this only shows one setting. You can change the control options in the settings menu.  The settings for this video are:

Steering: Type-B

Movement: Joystick at Touch

More information about the game

The controls make use of your phone’s ability to sense rotation. There are strafe controls on-screen too so you have full six degrees of freedom.  There are currently three single-player levels. In the first level you must find and destroy a boss enemy ship. The second level has several warp tunnels that form puzzles you must navigate. The third level has large rotating rooms that you have to navigate to retrieve power cells.

Here is another video: