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 success 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).
Mantra for Goddess Saraswati
An invocation to Goddess Saraswati is as follows – she who holds the (musical instrument) veena in her hands and opens the channels of learning for her disciples. Saraswati is also revered as the Goddess of music and creative (particularly, the spoken) arts.
yaa kundendu tushhaar haara dhavalaa yaa shubhravastraavR^itaa .
yA vINaavarada.nDa ma.nDitakaraa yaa shvetapadmaasanaa .
Saraswati Gayatri Mantra
The Saraswati Gayatri is a mantra written specifically to invoke Goddess Saraswati in the 24-metre tradition of the Gayatri Mantra.
Virinji Pathniyai cha Dheemahe
Thanno Vani Prachodayath.
Om, Let me meditate on the goddess of speech,
Oh, wife of Lord Brahma, give me higher intellect,
And let Goddess Vani illuminate my mind.
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
tanno devi prachodayaat.