A battle sorcerer has fewer daily spell slots than a standard sorcerer. Subtract one spell per day from each spell level on Table: The Sorcerer (to a minimum of zero spells per day). For example, a 1st-level battle sorcerer may cast four 0-level spells and two 1st-level spells per day (plus bonus spells, if any).
A battle sorcerer knows fewer spells per spell level than a standard sorcerer. Subtract one spell known from each spell level on Table: Sorcerer Spells Known (to a minimum of one spell per spell level). For example, a 4th-level battle sorcerer knows five 0-level spells, two 1st-level spells, and one 2nd-level spell. When she reaches 5th level, the battle sorcerer learns one additional 1st-level spell, but doesn't learn an additional 2nd-level spell (since two minus one is one).