Making Millions the Hard Way

Math 17 Winter Term 2016 - An Introduction to Mathematics Beyond Calculus

Virtually every mathematician has, at some point, been asked:

“What do mathematicians do?”

The famous 1940 essay A Mathematician’s Apology by British mathematician G.H. Hardy offers the following conceptual answer:

“A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.”

“queen of sciences”, as German mathematician C.F. Gauss (reportedly) called mathematics.

The course will explain the various branches of mathematics with the help of the seven Millennium Prize Problems of the Clay Mathematics Institute – each worth \$1,000,000:

 (unsolved, formulated in 1971) (unsolved, going back to the 1950s) (unsolved, formulated in 1859) (solved,     formulated in 1904) (unsolved, formulated in 1965) (unsolved, formulated in 1952) (unsolved, going back to the 1840s)

Math 17 is primarily aimed at first-year and sophomore students who have completed Math 8 (with ease), Math 11, Math 12, or Math 13. It is intended to prepare and inspire you to major in mathematics.

If you have any question, please get in contact with:

 Instructor: Peter Herbrich Office: Kemeny Hall 334 Email:

Weekly Schedule

 Monday Wednesday Friday 1 What is Mathematics? Logic Set Theory 2 Functions and Relations Theory of Computation P vs NP Problem 3 Groups Rings and Fields Polynomials 4 Linear Algebra Representation Theory Yang–Mills and Mass Gap 5 Algebraic Number Theory Analytic Number Theory Riemann Hypothesis 6 Topology Differential Geometry Poincaré Conjecture 7 Classification of Surfaces Algebraic Geometry Birch and Swinnerton-Dyer Conjecture 8 Complex Geometry Algebraic Topology Hodge Conjecture 9 Differential Equations Chaos Theory Navier–Stokes Equation