The "/Assault Mode" version has the same name as its counterpart, but with "/Assault Mode" at the end. They have 500 more ATK and DEF, two more Levels and a more powerful version of the Synchro Monster's effect (For example "Stardust Dragon/Assault Mode" can be Tributed whenever a Spell/Trap/Monster effect is activated whereas "Stardust Dragon" can only be Tributed to negate a Spell/Trap/Monster Effect that would destroy a card). When the "/Assault Mode" monster is destroyed the regular version may be Special Summoned from the Graveyard.
Creating a deck based around "Doomkaiser Dragon/Assault Mode" has been made more difficult with the limiting of "Plaguespreader Zombie" and "Mezuki" but it is still possible. With the addition of Pain Painter this is made a lot easier so go for broke. "Zombie Master" and "Plaguespreader Zombie" can Synchro Summon "Doomkaiser Dragon
The goal for you to accomplish today is to successfully create a /Assault mode deck revolving around the concept of Getting Doomkaiser Dragon/Assault mode on the field. You can do this in any way you please, but try to keep the basic cards needed there. The best deck that i find that represents a proper /Assault mode deck will get the SP for this lesson. Your reward is 350SP. Good Luck.