A C172 STUDENT PLT MAKES A PREMATURE TURN OFF RWY 29 AT SJC AND HAS AN NMAC WITH A DEP B757 OFF RWY 30 AT SJC; CA.

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SWITCHING FROM TWR TO APCH WITHOUT BEING TOLD TO DO SO. UNSURE OF DIRECTIONS TO FOLLOW. STUDENT PLT WITH LIMITED EXPERIENCE IN RADAR CTLED ENVIRONMENT WAS A CONTRIBUTING FACTOR. I AM THE FLT INSTRUCTOR WHO ENDORSED THE STUDENT PLT'S LOGBOOK AND PLT CERTIFICATE FOR A SOLO XCOUNTRY FLT FROM SJC TO STS. AS I UNDERSTAND; THE STUDENT PLT CONTACTED SJC CLRNC DELIVERY STATING THAT HE WAS INTENDING TO MAKE A VFR FLT TO STS. SJC CLRNC DELIVERY ISSUED A CLRNC TO FLY RWY HDG; MAINTAIN VFR AT OR BELOW 4000 FT; DEP FREQ; 121.30 AND A XPONDER CODE (UNKNOWN NUMBER). THE STUDENT'S READBACK DID NOT INCLUDE THE MAINTAIN RWY HDG PORTION OF THE CLRNC ISSUED. THE CTLR STATED THAT THE READBACK WAS CORRECT AND TO EXPECT A R TURN TO A HDG OF 020 DEGS (TOWARDS THE SUNOL INTXN). THE STUDENT PLT THEN CONTACTED SJC GND CTL FOR HIS TAXI CLRNC TO RWY 29 RUNUP AND THEN RWY 29. UPON HOLDING SHORT OF RWY 29; THE STUDENT PLT CONTACTED SJC TWR AND WAS CLRED FOR TKOF. AT ABOUT 300 FT AGL; THE STUDENT MADE AN UNAUTH FREQ CHANGE TO BAY DEP ON 121.30. THE BAY DEP CTLR; BELIEVING ALL TFC CONFLICTS HAD BEEN RESOLVED; INSTRUCTED THE STUDENT PLT TO RESUME HIS OWN NAV. UPON RECEIVING THIS INSTRUCTION; THE STUDENT PLT TURNED TO THE 020 DEG HDG HE WAS TOLD TO EXPECT FROM THE SJC CLRNC CTLR. UNFORTUNATELY; A B757 WAS CLRED FOR TKOF ON A PARALLEL RWY A FEW MINS AFTER THE STUDENT PLT DEPARTED. WHEN THE STUDENT PLT MADE HIS R TURN TO A 020 DEG HDG; HE PUT HIMSELF DIRECTLY INTO THE FLT PATH OF THE B757. THE B757 MADE A LOW LEVEL L TURN TO AVOID A MIDAIR COLLISION; MISSING THE STUDENT PLT'S ACFT BY 300 FT. THIS INCIDENT; I BELIEVE; WAS THE RESULT OF A STUDENT PLT NOT FULLY UNDERSTANDING THE DEP CLRNC INSTRUCTIONS GIVEN TO HIM; MAKING AN UNAUTH FREQ CHANGE TO DEP CTL AND NOT BEING AWARE OF THE POTENTIAL TFC CONFLICT TO WHICH HE WAS EXPOSING HIMSELF. A CONTRIBUTING FACTOR WAS THE STUDENT PLT'S HVY WORKLOAD DEMANDED BY A XCOUNTRY FLT AND LACK OF EXPERIENCE FLYING IN A CLASS C ENVIRONMENT.