After installing ubuntu to a 32 GB. flash drive from a live usb, i attempted to boot the flash drive on my mac using target disk mode, but the mac cannot find it. After this, i booted my mac from the live usb, and i looked at the partitions on the flash drive, and everything was the way i had set it up. i also looked at the flash drive using mac disk utility, and everything looked fine. I was wondering why my mac cannot see the flash drive in target disk mode?

system info:

Mac = macbook air 11" (2013 model)

OS X = 10.9 Mavericks

Ubuntu OS = 14.04.1 LTS

External Hard Drive = Sandisk Cruzer 32 GB

This may help
http://www.makeuseof.com/tag/how-to-...k-on-your-mac/

Unfortunately this is not the answer i was looking for. I wanted to know how to run ubuntu using a flash drive as the main hard drive instead of the built-in hard drive. I have no problems making a live usb. I wanted to install ubuntu on a flash drive, not just the live image. I ran the ubuntu installer so that it installed on a flash drive instead of the hard drive, but the flash drive with installed ubuntu isnt being found by target disk mode

Update:
I have reinstalled Ubuntu onto the flash drive with some success. Mac can now find the flash drive containing ubuntu, but all that shows up is a blinking cursor. Should i wait for it to boot up, or is it another failure on my part?

If you did an actual install to a flash drive, you would need to install the Grub bootloader to the master boot record of that drive, then set the flash drive to first boot priority or, configure whatever bootloader you use on the Mac to boot it

You need refit/refind to interrupt the boot process. Apple EFI is going to ignore the flash card without it remember Mac's can't read from nor write to ext4 without fuse. Just get refit/refind install it reboot and select the penguin

Is there any other way i can do this without using rEFInd?

Not that I know of, you need a boot interrupter