In 1936, Shannon began his graduate studies in electrical engineering at MIT, where he worked on Vannevar Bush's differential analyzer, an early analog computer. While studying the complicated "ad hoc" circuits of this analyzer, Shannon designed switching circuits based on Boole's concepts. In 1937, he wrote his master's degree thesis, "A Symbolic Analysis of Relay and Switching Circuits". A paper from this thesis was published in 1938. In this work, Shannon proved that his switching circuits could be used to simplify the arrangement of the electromechanical relays that were used then in telephone call routing switches. Next, he expanded this concept, proving that these circuits could solve all problems that Boolean algebra could solve. In the last chapter, he presented diagrams of several circuits, including a 4-bit full adder.