Goddess Saraswati is universally recognized in Hinduism as the Goddess of learning and knowledge. Students in any and all fields of learning pray to Saraswati for sucess in completion of their studies. Saraswati is the companion of Lord Brahma (the creator). She represents speech (Vach), the mechanism or divine energy with which Brahma created the universe. The importance of Goddess Saraswati (saras = fluid, wati = easily, i.e. easily flowing energy) is her ability to bring into manifestation the concept of Creation thought by Brahma in his thoughts. The words (or Vach) spoken by Brahma to create the universe is indeed Sarswati!
The Goddess Gayatri is synonymous with Goddess Saraswati in the sense that Gayatri is another form of Saraswati. Hence, the Gayatri Mantra is indeed the best invocation for Goddess Saraswati. Legend has it that Saraswati appeared as Gayatri in order to assist Brahma in the completion of an important yagna being conducted in homage to the Sun God (Surya Devataa).

Saraswati Beej Mantra

This is an extract of the Beej (or Seed) Mantra invoking Goddess Saraswati. Beej Mantra(s) are based on mono-syllables. The Beej Mantra for Saraswati is based on the two words "Bhreem" and "Shreem". The mantra is simple - "AUM Shreem Bhreem Saraswat-yea Namaha". (ॐ श्रीम भ्रीम सरस्वतये नमः)

Saraswati Gayatri Mantra

Another version of the Saraswati Gayatri which may of relevance to those seeking blessings for success in the areas of education, fine arts (like theatre, painting etc.) is
ॐ वाकदैव्यै च विद्महे कामराजाय धीमहि। तन्नो देवी प्रचोदयात्‌।
AUM Vaakdeviyai cha Vidhmahe
kaamraajaaya dheemahi
tanno devi prachodayaat.