For many incoming students at the Massachusetts Institute of Technology, the jump from high school calculus to upper-level theoretical mathematics feels like stepping off a firm dock into deep, murky water. In high school, math is often about calculation: find the derivative, solve for ( x ), compute the integral. But in college—especially at MIT—mathematics transforms into a discipline of logic, structure, and proof .
For MIT students, it’s a requirement. For anyone else reading this guide, it’s a blueprint. And 18.090 is the workshop where you learn the trade. Are you an MIT student currently enrolled in 18.090? Check the MIT Student Information System (SIS) for current offerings and the Math Department’s undergraduate office for office hours. For self-learners, Richard Hammack's "Book of Proof" is available for free at people.vcu.edu/~rhammack/BookOfProof/ — that is the closest you can get to the MIT experience without the tuition. 18.090 introduction to mathematical reasoning mit
But you will also experience the unique thrill of constructing an ironclad argument from nothing but logic. You will learn to read a theorem and see its skeleton. And when you move on to analysis, topology, or number theory, you will realize that 18.090 gave you the only tool that matters: the ability to reason. For many incoming students at the Massachusetts Institute
That bridge is officially called .
Why Hammack? It is exceptionally clear, conversational, and filled with graduated exercises. Chapters progress from simple truth tables to the mind-bending proof of the irrationality of ( \sqrt{2} ) to the fact that the real numbers are uncountable. Students repeatedly praise the book for its "hand-holding without being condescending." For MIT students, it’s a requirement