The Millennium Prize Problems –
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:
ÒWhat
do mathematicians do?Ó
The famous 1940 essay A MathematicianÕs Apology by British mathematician G.H. Hardy offers the following
conceptual answer:
ÒA 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.Ó
Math 17 will exemplify these everlasting ideas and provide an
overview of the Òqueen of sciencesÓ, 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 firstyear 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 
PoincarŽ
Conjecture 
7 
Classification of Surfaces 
Algebraic Geometry 
Birch and SwinnertonDyer
Conjecture 
8 
Complex Geometry 
Algebraic Topology 
Hodge Conjecture 
9 
Differential Equations 
Chaos Theory 
Navier–Stokes
Equation 