On a given day the home-schooled teen recently named a finalist in the 2013 Intel Science Talent Search might study French and chemistry at home, attend a math class or two at Stanford University, then head over to Palo Alto High School for after-school math team activities.
She may also spend time singing or playing violin with fellow devotees of Indian classical music.
Vasudevan attended public schools until the age of 14, when her unusual schedule of advanced math classes became too difficult to reconcile with a regular high school day.
"Instead of being in one place, for me school is a lot of different places," she said in an interview with the Weekly.
"I meet a lot of people, so I don't really feel I've missed out on the social aspect of anything."
Paly math teacher Suz Antink called Vasudevan an "enthusiastic" and "innovative" member of the school's Advanced Problem Solving team.
"She loves to discuss how to solve the problems as much as she enjoys finding the solution," Antink said.
"Discussions with Sahana are animated and lively. She smiles easily and appreciates the insights of others. She's great on team contests, too."
Born in Mountain View, Vasudevan went to preschool in Bangalore, India. She began kindergarten at a public school in Buffalo, N.Y., Country Parkway Elementary School.
When her parents both software engineers returned to the Bay Area, she transferred to Vargas Elementary School in Sunnyvale in third grade. Her mathematics was so advanced that she already was taking classes at Stanford by the time she graduated from Joaquin Miller Middle School in San Jose.
At that point the family moved to Palo Alto partly to be closer to Stanford and Vasudevan completed her freshman year at Paly.
"Paly was awesome," she said. "It was really nice. I wish I could have continued there, but the reason I'm home-schooled is that I wanted to take multiple math courses at Stanford in the same quarter."
Vasudevan and her parents chose the name "Gnyanam Academy" "gnyanam" is Sanskrit for knowledge for their home school.
"My parents are more my supervisors than my teachers," she said. "They make sure I do what I'm supposed to be doing, and I usually teach myself stuff.
"My parents occasionally administer tests and stuff like that, and at the end of the year I take AP exams."
Though she hasn't yet been to France, Vasudevan has studied French since middle school. At home, the family speaks Tamil.
She's currently taking Functional Analysis and Mathematical Methods of Classical Mechanics in the Stanford Math Department.
"It's hard to quantify the amount of time I spend on math, but I do spend a lot of time doing math and on music," she said.
"Since I was young I was interested in math, and I don't ever remember not liking it."
Vasudevan also began learning vocal music and violin before the age of 5 and travels to India twice a year to study and perform and to visit relatives. Early in her musical study she began focusing on Carnatic music, a genre from southern India.
"When I go to India I focus on music," she said. "Just like math, I've been interested in music since I was really young."
Vasudevan said she embarked on the Intel contest after making progress on a problem given to her by Stanford math professor Persi Diaconis.
Her project, "Minimizing the Number of Carries in the Set of Coset Representatives of a Normal Subgroup," was chosen to be one of 40 finalists in a contest that initially drew 1,700 entries.
Next month, she and the other finalists will present their projects to judges in Washington, D.C., for a crack at the top prize of $100,000.
"I'm kind of nervous and kind of excited," she said. "It will be really nice meeting the 39 other finalists."