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.”

Math 17 will exemplify these everlasting ideas and provide an overview of the “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:

P vs NP Problem	(unsolved, formulated in 1971)
Yang–Mills and Mass Gap	(unsolved, going back to the 1950s)
Riemann Hypothesis	(unsolved, formulated in 1859)
Poincaré Conjecture	(solved, formulated in 1904)
Birch and Swinnerton-Dyer Conjecture	(unsolved, formulated in 1965)
Hodge Conjecture	(unsolved, formulated in 1952)
Navier–Stokes Equation	(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:	peter.herbrich@dartmouth.edu

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