During the first battle of Geonosis, Mace Windu joins the clones on the ground with Kit Fisto, Aayla Secura, and others. The other Republic gunship, with Anakin, Obi-Wan and Padme on board, follows Dooku's speeder to his secret hangar.
Why didn't Mace Windu go with Yoda to confront Tyranus? Surely it would have been wiser for Master Windu and Yoda to tackle Dooku at the same time. Dooku couldn't possibly their combined attack.